1 00:00:01,100 --> 00:00:03,440 The following content is provided under a Creative 2 00:00:03,440 --> 00:00:04,860 Commons license. 3 00:00:04,860 --> 00:00:07,070 Your support will help MIT OpenCourseWare 4 00:00:07,070 --> 00:00:11,160 continue to offer high-quality educational resources for free. 5 00:00:11,160 --> 00:00:13,700 To make a donation or to view additional materials 6 00:00:13,700 --> 00:00:17,660 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,660 --> 00:00:19,022 at ocw.mit.edu. 8 00:00:22,060 --> 00:00:24,896 GABRIEL SANCHEZ-MARTINEZ: So today, we'll 9 00:00:24,896 --> 00:00:26,020 talk about cost estimation. 10 00:00:26,020 --> 00:00:30,930 It's the first of the modeling lectures. 11 00:00:30,930 --> 00:00:33,460 We'll talk very briefly about the role-- 12 00:00:33,460 --> 00:00:36,180 the different roles that cost models 13 00:00:36,180 --> 00:00:39,090 have in transit agencies. 14 00:00:39,090 --> 00:00:41,800 And then we'll discuss three types of-- 15 00:00:41,800 --> 00:00:43,990 three categories of cost models. 16 00:00:43,990 --> 00:00:45,350 So all right, let's get into it. 17 00:00:45,350 --> 00:00:48,840 So what are the roles? 18 00:00:48,840 --> 00:00:50,760 How could cost models be used? 19 00:00:50,760 --> 00:00:55,680 And to start, a cost model is a model, a mathematical model 20 00:00:55,680 --> 00:00:58,680 that takes some variables and predicts 21 00:00:58,680 --> 00:00:59,865 some costs for the agency. 22 00:00:59,865 --> 00:01:01,190 It could be operational cost. 23 00:01:01,190 --> 00:01:02,700 It could be fixed cost. 24 00:01:02,700 --> 00:01:04,379 So how could these be used? 25 00:01:04,379 --> 00:01:07,590 The first row is predicting the cost change associated 26 00:01:07,590 --> 00:01:08,970 with a service change. 27 00:01:08,970 --> 00:01:13,170 So this is a very traditional typical example. 28 00:01:13,170 --> 00:01:15,400 So you might extend the route as we 29 00:01:15,400 --> 00:01:19,110 are thinking about in this assignment, Route 1770A, 30 00:01:19,110 --> 00:01:20,100 extending it. 31 00:01:20,100 --> 00:01:24,180 And you might wonder, how much will that cost to operate? 32 00:01:24,180 --> 00:01:26,670 So you could use a cost model in that situation. 33 00:01:26,670 --> 00:01:28,890 Or maybe there's a wider increase in service. 34 00:01:28,890 --> 00:01:32,640 Maybe service is being expanded from ending 35 00:01:32,640 --> 00:01:34,980 at 2 AM to running 24 hours. 36 00:01:34,980 --> 00:01:36,930 How much would that cost? 37 00:01:36,930 --> 00:01:39,840 So these are the kinds of questions, service changes 38 00:01:39,840 --> 00:01:42,450 that you might want to have an idea of how much 39 00:01:42,450 --> 00:01:45,150 will it cost me. 40 00:01:45,150 --> 00:01:50,530 So they are often concerned with marginal or incremental costs, 41 00:01:50,530 --> 00:01:52,450 especially in this application. 42 00:01:52,450 --> 00:02:00,220 So if you expand service to cover all night, for example, 43 00:02:00,220 --> 00:02:03,000 you may not need that-- that change may not 44 00:02:03,000 --> 00:02:06,060 trigger the need for a new bus maintenance 45 00:02:06,060 --> 00:02:09,660 facility, or some large capital expenditure. 46 00:02:09,660 --> 00:02:12,510 So we're talking here about per-- incremental cost. 47 00:02:12,510 --> 00:02:14,760 As I add buses, or as I add bus hours, 48 00:02:14,760 --> 00:02:19,490 or as I add driver hours, how much extra do I pay? 49 00:02:19,490 --> 00:02:22,270 You have different results over different time periods. 50 00:02:22,270 --> 00:02:23,590 This is important. 51 00:02:23,590 --> 00:02:27,060 It doesn't cost the same to run service off-peak or at night 52 00:02:27,060 --> 00:02:28,725 as it does on-peak. 53 00:02:28,725 --> 00:02:31,640 I will talk more about that later in this lecture. 54 00:02:31,640 --> 00:02:34,030 But having that in mind, and having a cost model that 55 00:02:34,030 --> 00:02:36,240 is sensitive to time periods might 56 00:02:36,240 --> 00:02:40,880 be very important to get accurate estimates. 57 00:02:40,880 --> 00:02:43,080 OK, so these models can also be used 58 00:02:43,080 --> 00:02:45,720 for routine performance monitoring and service policy 59 00:02:45,720 --> 00:02:46,350 triggers. 60 00:02:46,350 --> 00:02:49,350 You might remember from the short-term planning 61 00:02:49,350 --> 00:02:53,850 lectures that there are some processes where every bus 62 00:02:53,850 --> 00:02:54,960 route might be reviewed. 63 00:02:54,960 --> 00:02:58,530 And you might decide that you need to add service 64 00:02:58,530 --> 00:03:00,000 based on its performance. 65 00:03:00,000 --> 00:03:03,570 Or you might decide that a bus route 66 00:03:03,570 --> 00:03:08,710 isn't meeting the requirements to be financially sustainable. 67 00:03:08,710 --> 00:03:11,130 So if you are considering removing, dropping 68 00:03:11,130 --> 00:03:14,670 service [INAUDIBLE],, how much will you save by doing that? 69 00:03:14,670 --> 00:03:17,770 All of those are applications of bus mode. 70 00:03:17,770 --> 00:03:19,590 OK, the second point here is that you 71 00:03:19,590 --> 00:03:21,480 can predict the cost change associated 72 00:03:21,480 --> 00:03:24,090 with the change in a production process. 73 00:03:24,090 --> 00:03:26,260 Now, we're not talking so much about service, 74 00:03:26,260 --> 00:03:28,260 but we're thinking of, what happens 75 00:03:28,260 --> 00:03:33,210 if I'm in a labor agreement that does not allow part timers, 76 00:03:33,210 --> 00:03:37,200 and now has negotiated the ability to hire part timers? 77 00:03:37,200 --> 00:03:40,900 What will that do to cost, sort of cost structure? 78 00:03:40,900 --> 00:03:43,290 What about if I want to contract out maintenance work? 79 00:03:43,290 --> 00:03:45,180 I'm doing that right now in-house. 80 00:03:45,180 --> 00:03:48,980 And now maybe for a portion or for all of it, 81 00:03:48,980 --> 00:03:52,800 we are looking at public-private partnerships 82 00:03:52,800 --> 00:03:55,320 to contract out maintenance work. 83 00:03:55,320 --> 00:03:57,630 Or contracting out suburban bus routes-- for instance, 84 00:03:57,630 --> 00:03:59,400 I have low ridership. 85 00:03:59,400 --> 00:04:01,170 And they're kind of on the outskirts. 86 00:04:01,170 --> 00:04:03,180 You don't want to drop service, but maybe you 87 00:04:03,180 --> 00:04:05,610 don't need big 40-foot buses and you can run them 88 00:04:05,610 --> 00:04:07,590 with smaller buses. 89 00:04:07,590 --> 00:04:09,270 Could you contract those out? 90 00:04:09,270 --> 00:04:11,070 What will that do to cost? 91 00:04:11,070 --> 00:04:13,565 New fare technology, the MBTA-- 92 00:04:13,565 --> 00:04:15,690 I don't know who was here a long time ago. 93 00:04:15,690 --> 00:04:16,875 We had tokens here. 94 00:04:16,875 --> 00:04:18,570 And we moved to the CharlieCard. 95 00:04:18,570 --> 00:04:21,930 And now the MBTA is thinking about the next generation 96 00:04:21,930 --> 00:04:26,340 of fare collection for Boston. 97 00:04:26,340 --> 00:04:28,680 AUDIENCE: When was the CharlieCard invented? 98 00:04:28,680 --> 00:04:29,535 GABRIEL SANCHEZ-MARTINEZ: I don't remember the year. 99 00:04:29,535 --> 00:04:29,700 AUDIENCE: 2005. 100 00:04:29,700 --> 00:04:30,600 GABRIEL SANCHEZ-MARTINEZ: But it was-- 101 00:04:30,600 --> 00:04:31,766 yeah, it was the mid-2000s-- 102 00:04:31,766 --> 00:04:33,000 AUDIENCE: 2005. 103 00:04:33,000 --> 00:04:35,630 GABRIEL SANCHEZ-MARTINEZ: --because I remember in 2004 104 00:04:35,630 --> 00:04:37,864 there being tokens still. 105 00:04:37,864 --> 00:04:39,780 AUDIENCE: I think the last station with tokens 106 00:04:39,780 --> 00:04:42,844 was Government Center in 2006. 107 00:04:42,844 --> 00:04:44,760 GABRIEL SANCHEZ-MARTINEZ: So anytime something 108 00:04:44,760 --> 00:04:47,790 like this happens, there is a change 109 00:04:47,790 --> 00:04:49,890 in costs, administration costs. 110 00:04:49,890 --> 00:04:54,300 And the recovery of the fare recovery ratio might change. 111 00:04:54,300 --> 00:04:56,435 So can we model that? 112 00:04:56,435 --> 00:04:59,130 And can we use cost models to predict those changes 113 00:04:59,130 --> 00:05:02,110 in cost or in revenue? 114 00:05:02,110 --> 00:05:06,420 OK, then another sort of third and very important application, 115 00:05:06,420 --> 00:05:10,530 not so much in Boston right now, but certainly 116 00:05:10,530 --> 00:05:13,800 in other jurisdictions, is the allocation 117 00:05:13,800 --> 00:05:16,540 of subsidy required by jurisdiction. 118 00:05:16,540 --> 00:05:20,152 So if you look at, for example, the WMATA in Washington, DC, 119 00:05:20,152 --> 00:05:21,402 there are different districts. 120 00:05:21,402 --> 00:05:23,590 And they all have to pay for service. 121 00:05:23,590 --> 00:05:30,460 So there are many examples of this over the states and also 122 00:05:30,460 --> 00:05:36,250 internationally, where different jurisdictions are essentially 123 00:05:36,250 --> 00:05:40,840 partnering to subsidize public transportation service. 124 00:05:40,840 --> 00:05:46,580 And we know what the total cost of operation is. 125 00:05:46,580 --> 00:05:50,180 So how much is fair that each restriction pay? 126 00:05:50,180 --> 00:05:52,804 According to size, according to how many people-- 127 00:05:52,804 --> 00:05:54,470 often, it's according to how many people 128 00:05:54,470 --> 00:05:58,720 ride from those jurisdictions. 129 00:05:58,720 --> 00:06:03,020 So you might have a data collection to figure out 130 00:06:03,020 --> 00:06:06,780 how many people are taking buses from each of the jurisdictions. 131 00:06:06,780 --> 00:06:09,770 And then you need to allocate a cost allocation model 132 00:06:09,770 --> 00:06:12,920 to take all of the costs, including the things that 133 00:06:12,920 --> 00:06:18,020 are sort of more obvious, like the bus hours that operate 134 00:06:18,020 --> 00:06:20,750 in those jurisdictions, but also things that are not directly 135 00:06:20,750 --> 00:06:23,480 connected to the jurisdictions, such as administration 136 00:06:23,480 --> 00:06:26,180 costs, and facility maintenance, and those things. 137 00:06:26,180 --> 00:06:28,920 So all of that needs to be allocated to each jurisdiction 138 00:06:28,920 --> 00:06:33,230 so that the cost can be evenly or fairly split. 139 00:06:33,230 --> 00:06:36,620 And doing that right is critical, often, 140 00:06:36,620 --> 00:06:39,770 even for the decision to participate or not 141 00:06:39,770 --> 00:06:42,800 in this program. 142 00:06:42,800 --> 00:06:43,670 Question? 143 00:06:43,670 --> 00:06:45,370 AUDIENCE: For jurisdictions, you mentioned Washington. 144 00:06:45,370 --> 00:06:47,330 Would that be like Virginia and Washington DC? 145 00:06:47,330 --> 00:06:47,870 GABRIEL SANCHEZ-MARTINEZ: Yeah. 146 00:06:47,870 --> 00:06:49,760 AUDIENCE: Or in New York, it would be New York-- 147 00:06:49,760 --> 00:06:51,230 Port Authority of New York and New Jersey? 148 00:06:51,230 --> 00:06:51,428 GABRIEL SANCHEZ-MARTINEZ: Yeah. 149 00:06:51,428 --> 00:06:53,870 AUDIENCE: Or would you also mean, like, counties? 150 00:06:53,870 --> 00:06:55,911 GABRIEL SANCHEZ-MARTINEZ: There are many examples 151 00:06:55,911 --> 00:07:00,470 and different structures of how different jurisdictions come 152 00:07:00,470 --> 00:07:02,070 together to provide service. 153 00:07:02,070 --> 00:07:05,800 So in some cases, you have many different operators, 154 00:07:05,800 --> 00:07:08,630 and more commonly in the West of the US, 155 00:07:08,630 --> 00:07:13,490 many different operators all providing service somehow. 156 00:07:13,490 --> 00:07:16,490 In other cases, you have one major operator funded 157 00:07:16,490 --> 00:07:20,720 by different jurisdictions. 158 00:07:20,720 --> 00:07:23,280 All right, so you might remember, 159 00:07:23,280 --> 00:07:26,120 we've only talked about modal capacities and costs 160 00:07:26,120 --> 00:07:31,070 that, especially in the US, in North America, 161 00:07:31,070 --> 00:07:35,300 costs are divided into capital expenditures and operations 162 00:07:35,300 --> 00:07:36,350 expenditures. 163 00:07:36,350 --> 00:07:39,120 So capital costs have to do with the purchase of vehicles, 164 00:07:39,120 --> 00:07:45,600 or the [INAUDIBLE] of vehicles, heavy maintenance, 165 00:07:45,600 --> 00:07:48,950 the fixed facility construction, so construction 166 00:07:48,950 --> 00:07:54,010 or major repairs of trucks, garage, stations, 167 00:07:54,010 --> 00:07:56,600 bus stops, things like that, and then 168 00:07:56,600 --> 00:08:00,470 other long-term physical assets, so administration buildings, 169 00:08:00,470 --> 00:08:02,310 and things like that. 170 00:08:02,310 --> 00:08:04,020 And then there's operating costs. 171 00:08:04,020 --> 00:08:05,310 So those have to do with-- 172 00:08:05,310 --> 00:08:07,160 they're more proportional to how much 173 00:08:07,160 --> 00:08:11,630 service you output, so labor wages and benefits, materials 174 00:08:11,630 --> 00:08:12,570 and supplies. 175 00:08:12,570 --> 00:08:17,440 Materials includes fuel, and tires, and electricity 176 00:08:17,440 --> 00:08:20,480 to run the-- power the metro. 177 00:08:20,480 --> 00:08:23,780 Then there's agency administration and other kinds 178 00:08:23,780 --> 00:08:25,370 of expenses of this nature. 179 00:08:25,370 --> 00:08:29,910 So it's important to keep those two in mind, 180 00:08:29,910 --> 00:08:36,150 because the cost models that we specify 181 00:08:36,150 --> 00:08:38,220 should take this into consideration 182 00:08:38,220 --> 00:08:43,500 and be able to allocate the capital and operating 183 00:08:43,500 --> 00:08:45,590 expenses separately. 184 00:08:45,590 --> 00:08:48,350 All right, so there are three types of cost models 185 00:08:48,350 --> 00:08:49,750 that we're going to discuss. 186 00:08:49,750 --> 00:08:52,230 The first is a fully allocated causal factor model. 187 00:08:52,230 --> 00:08:54,770 It's the simplest of ones that we'll discuss. 188 00:08:54,770 --> 00:08:56,450 One of the problems with that model 189 00:08:56,450 --> 00:09:01,100 is that it allocates all of the costs to some categories. 190 00:09:01,100 --> 00:09:04,450 And it's not sensitive to time periods. 191 00:09:04,450 --> 00:09:08,730 As I said earlier, some costs vary a lot by time period. 192 00:09:08,730 --> 00:09:12,620 So the second model essentially is a variation or an extension 193 00:09:12,620 --> 00:09:16,940 of the first one, where we do take some specific costs that 194 00:09:16,940 --> 00:09:20,240 are very sensitive to time and capture that, 195 00:09:20,240 --> 00:09:22,160 those differences, over time. 196 00:09:22,160 --> 00:09:24,980 And then we'll talk about incremental fixed/variable cost 197 00:09:24,980 --> 00:09:25,480 models. 198 00:09:25,480 --> 00:09:29,440 We're going to give examples of all of these using MBTA bus 199 00:09:29,440 --> 00:09:31,350 from the '90s as an example. 200 00:09:31,350 --> 00:09:33,770 Let's start with the first one, the fully allocated 201 00:09:33,770 --> 00:09:34,650 causal factor model. 202 00:09:34,650 --> 00:09:36,860 So here's what you do. 203 00:09:36,860 --> 00:09:38,870 You select some causal factors. 204 00:09:38,870 --> 00:09:43,430 So these are not necessarily-- maybe causal factor is one 205 00:09:43,430 --> 00:09:47,280 of the best term, but that's what this model is-- 206 00:09:47,280 --> 00:09:48,290 class is called. 207 00:09:48,290 --> 00:09:50,750 I would say, these are explanatory variables more 208 00:09:50,750 --> 00:09:51,600 than causal factors. 209 00:09:51,600 --> 00:09:54,930 They don't have to cause the cost directly, 210 00:09:54,930 --> 00:09:59,000 but they are used as explanatory variables in a model of cost. 211 00:09:59,000 --> 00:10:03,240 So then you assign each expense type to each of the factors. 212 00:10:03,240 --> 00:10:06,410 So for example, operator wages and benefits, 213 00:10:06,410 --> 00:10:07,310 where would that go? 214 00:10:07,310 --> 00:10:12,260 If you were thinking of three kinds of explanatory variables, 215 00:10:12,260 --> 00:10:15,234 vehicle hours being one, vehicle miles being the second, 216 00:10:15,234 --> 00:10:16,650 and peak vehicles being the third, 217 00:10:16,650 --> 00:10:19,610 and you're going to assign every cost you incur 218 00:10:19,610 --> 00:10:24,050 to one of those three, then operator wages and benefits 219 00:10:24,050 --> 00:10:27,800 are more appropriately assigned to vehicle hours, 220 00:10:27,800 --> 00:10:30,950 because the pay drivers by the hour, 221 00:10:30,950 --> 00:10:35,380 so this is the one that it relates to most closely. 222 00:10:35,380 --> 00:10:38,780 Fuel-- so fuel may be a combination of vehicle hours 223 00:10:38,780 --> 00:10:39,560 and vehicle miles. 224 00:10:39,560 --> 00:10:43,250 Or if you have to assign them to one, then vehicle miles-- 225 00:10:43,250 --> 00:10:46,940 you think of the fuel mileage of vehicles. 226 00:10:46,940 --> 00:10:50,930 So that's the one that most closely 227 00:10:50,930 --> 00:10:55,700 relates vehicle miles to fuel. 228 00:10:55,700 --> 00:10:59,092 And then administration-- well, administration, you 229 00:10:59,092 --> 00:11:00,800 might want to assign it to peak vehicles, 230 00:11:00,800 --> 00:11:03,376 because peak vehicles is a proxy for how big is this agency. 231 00:11:03,376 --> 00:11:05,750 And the bigger that agency, the bigger the administration 232 00:11:05,750 --> 00:11:06,380 costs. 233 00:11:06,380 --> 00:11:09,980 So it's one way of assigning these things. 234 00:11:09,980 --> 00:11:13,232 So this is an example. 235 00:11:13,232 --> 00:11:14,690 After you do all those assignments, 236 00:11:14,690 --> 00:11:18,720 you calculate the average costs for each of the factors. 237 00:11:18,720 --> 00:11:23,192 So you have, for example, the cost 238 00:11:23,192 --> 00:11:25,400 assigned to vehicle hours divided by the total number 239 00:11:25,400 --> 00:11:26,480 of vehicle hours. 240 00:11:26,480 --> 00:11:28,460 And you have those unit costs. 241 00:11:28,460 --> 00:11:30,530 And then the cost model is simply 242 00:11:30,530 --> 00:11:32,350 each of those unit costs divided-- 243 00:11:32,350 --> 00:11:35,000 or multiplied by the three explanatory variables 244 00:11:35,000 --> 00:11:36,290 that you included. 245 00:11:36,290 --> 00:11:39,260 So you multiply your unit vehicle hour cost 246 00:11:39,260 --> 00:11:42,350 by the number of vehicle hours, your unit vehicle miles 247 00:11:42,350 --> 00:11:45,020 cost by vehicle miles, and your unit peak 248 00:11:45,020 --> 00:11:47,070 vehicles cost by peak vehicles. 249 00:11:47,070 --> 00:11:50,040 And that is the total cost of the agency. 250 00:11:50,040 --> 00:11:50,540 Questions? 251 00:11:50,540 --> 00:11:52,290 AUDIENCE: This assumes that you're somehow 252 00:11:52,290 --> 00:11:54,710 able to split the data into those categories, 253 00:11:54,710 --> 00:11:57,440 to say the costs assigned to vehicle hours are x. 254 00:11:57,440 --> 00:11:59,870 GABRIEL SANCHEZ-MARTINEZ: Yes, so that's one 255 00:11:59,870 --> 00:12:03,080 of the characteristics and perhaps weaknesses of this kind 256 00:12:03,080 --> 00:12:05,540 of model, that it requires the judgment of the person 257 00:12:05,540 --> 00:12:06,590 to assign-- 258 00:12:06,590 --> 00:12:08,747 to first, to generate these classes 259 00:12:08,747 --> 00:12:10,580 and these explanatory variables, and second, 260 00:12:10,580 --> 00:12:14,690 to assign them to each cost of this class or each 261 00:12:14,690 --> 00:12:20,090 account in a ledger to each of these explanatory variables. 262 00:12:20,090 --> 00:12:25,680 So But these models are used in the industry. 263 00:12:25,680 --> 00:12:30,151 So if you plug in the number of vehicle hours, 264 00:12:30,151 --> 00:12:31,650 and vehicle miles, and peak vehicles 265 00:12:31,650 --> 00:12:33,700 that you used to estimate this model, 266 00:12:33,700 --> 00:12:37,860 then you're just going to get the total cost 267 00:12:37,860 --> 00:12:39,460 of operations or of-- 268 00:12:39,460 --> 00:12:45,330 or total combined cost on the same period 269 00:12:45,330 --> 00:12:47,400 that this data came from. 270 00:12:47,400 --> 00:12:51,630 But more interestingly, if you are considering 271 00:12:51,630 --> 00:12:55,080 expanding service, and that will increase vehicle hours, vehicle 272 00:12:55,080 --> 00:12:57,390 miles, and peak vehicles, then this model 273 00:12:57,390 --> 00:13:00,960 will work in some ways to forecast 274 00:13:00,960 --> 00:13:05,250 what the total cost will be after you grow your agency. 275 00:13:05,250 --> 00:13:08,032 So this is one application of this simple model. 276 00:13:08,032 --> 00:13:10,490 AUDIENCE: Is there a time unit that you're supposed to use, 277 00:13:10,490 --> 00:13:12,240 like a full year to capture [INAUDIBLE]?? 278 00:13:12,240 --> 00:13:14,031 GABRIEL SANCHEZ-MARTINEZ: This is up to you 279 00:13:14,031 --> 00:13:15,756 as well, another judgment call. 280 00:13:15,756 --> 00:13:17,640 It shouldn't be one day, but-- 281 00:13:17,640 --> 00:13:21,340 because you want to see all the kinds of expenses. 282 00:13:21,340 --> 00:13:25,670 So I think a year makes sense, a fiscal year, 283 00:13:25,670 --> 00:13:30,870 because you will have to put out a statement for [INAUDIBLE].. 284 00:13:30,870 --> 00:13:34,040 You do accounting on that fiscal year basis. 285 00:13:34,040 --> 00:13:41,190 OK, so here's an example from 1996 of a bus on the MBTA. 286 00:13:41,190 --> 00:13:44,130 So we have those three variables that we 287 00:13:44,130 --> 00:13:45,780 talked about-- vehicle hours, vehicle 288 00:13:45,780 --> 00:13:47,820 miles, and peak vehicles. 289 00:13:47,820 --> 00:13:51,650 We divide each of those into variable or fixed. 290 00:13:51,650 --> 00:13:54,870 So some of the expenses are considered variable, 291 00:13:54,870 --> 00:13:59,070 because they sort of scale up more linearly as you increase 292 00:13:59,070 --> 00:14:00,420 the number of vehicle hours. 293 00:14:00,420 --> 00:14:03,240 And others are more fixed expenses. 294 00:14:03,240 --> 00:14:08,100 You wouldn't expect to get extra fixed costs 295 00:14:08,100 --> 00:14:10,020 by adding a few buses, right? 296 00:14:10,020 --> 00:14:13,410 So one example of that is, if you 297 00:14:13,410 --> 00:14:17,370 get 10 more buses for a new bus route, 298 00:14:17,370 --> 00:14:19,440 you don't need a new maintenance facility. 299 00:14:19,440 --> 00:14:21,030 So your maintenance facility might 300 00:14:21,030 --> 00:14:22,980 be considered a fixed expense. 301 00:14:22,980 --> 00:14:24,840 And you might want a variable cost model 302 00:14:24,840 --> 00:14:28,200 to predict the changes of that small change 303 00:14:28,200 --> 00:14:29,740 or that marginal change. 304 00:14:29,740 --> 00:14:33,520 So that's why we divide things into fixed and variable. 305 00:14:33,520 --> 00:14:39,120 The total cost to be allocated is $173.6 million. 306 00:14:39,120 --> 00:14:43,720 And we divide it over these six categories, so the three 307 00:14:43,720 --> 00:14:49,630 variables and their fixed and variable variance. 308 00:14:49,630 --> 00:14:54,160 Here we have the percentages of each and the unit costs. 309 00:14:57,220 --> 00:15:01,370 So now, what are possible cost models following this approach? 310 00:15:01,370 --> 00:15:05,140 A first and simple one, a very traditional model, 311 00:15:05,140 --> 00:15:06,490 is the first one listed here. 312 00:15:06,490 --> 00:15:13,120 So 39.82, which is the total unit cost of revenue vehicle 313 00:15:13,120 --> 00:15:16,660 hours-- it's the sum of 37.13 and 2.69-- 314 00:15:16,660 --> 00:15:19,780 times the number of revenue vehicle hours, and then 2.41, 315 00:15:19,780 --> 00:15:25,410 which is the sum of 2.270 and 0.14 times revenue vehicle 316 00:15:25,410 --> 00:15:27,750 miles times some factor. 317 00:15:27,750 --> 00:15:31,440 And that factor, essentially here, we have-- 318 00:15:33,984 --> 00:15:35,400 we're not capturing the difference 319 00:15:35,400 --> 00:15:37,320 between fixed and variable costs. 320 00:15:37,320 --> 00:15:41,707 So that's why we add them up here, 39.82 and 2.41. 321 00:15:41,707 --> 00:15:43,290 The other characteristic of this model 322 00:15:43,290 --> 00:15:45,660 is that it does not have peak vehicles 323 00:15:45,660 --> 00:15:47,430 as an explanatory variable. 324 00:15:47,430 --> 00:15:51,090 So we address that with this adjustment factor. 325 00:15:51,090 --> 00:15:57,660 If you take the total cost, which is 173.6, 326 00:15:57,660 --> 00:16:05,550 and you divide it by the sum of the unit costs for revenue 327 00:16:05,550 --> 00:16:09,310 vehicle hours and revenue vehicle miles, you get 1.26. 328 00:16:09,310 --> 00:16:11,550 And that's the adjustment factor. 329 00:16:11,550 --> 00:16:16,112 So any questions-- 330 00:16:16,112 --> 00:16:16,820 AUDIENCE: Sorry-- 331 00:16:16,820 --> 00:16:18,778 GABRIEL SANCHEZ-MARTINEZ: --with that approach? 332 00:16:18,778 --> 00:16:21,470 AUDIENCE: You said the 1.26 is calculated by doing what? 333 00:16:21,470 --> 00:16:23,761 GABRIEL SANCHEZ-MARTINEZ: Let me write it down for you. 334 00:16:25,680 --> 00:16:40,042 So you have a total of 173.6. 335 00:16:40,042 --> 00:16:41,130 And that's a total. 336 00:16:44,610 --> 00:16:49,830 And you divide it by the total of the total number of unit 337 00:16:49,830 --> 00:16:53,110 costs that you are capturing with explanatory variables, 338 00:16:53,110 --> 00:17:05,195 which is 29 plus 5.7 plus 50-- 339 00:17:05,195 --> 00:17:06,140 AUDIENCE: Plus 3. 340 00:17:06,140 --> 00:17:07,598 GABRIEL SANCHEZ-MARTINEZ: --plus 3. 341 00:17:07,598 --> 00:17:08,800 AUDIENCE: [INAUDIBLE] 342 00:17:08,800 --> 00:17:09,660 AUDIENCE: And last [INAUDIBLE]-- 343 00:17:09,660 --> 00:17:10,860 GABRIEL SANCHEZ-MARTINEZ: --equals 1.261. 344 00:17:10,860 --> 00:17:12,079 AUDIENCE: [INAUDIBLE] 345 00:17:17,624 --> 00:17:19,040 GABRIEL SANCHEZ-MARTINEZ: So we're 346 00:17:19,040 --> 00:17:21,740 dividing the total by the amount that we did capture. 347 00:17:21,740 --> 00:17:25,550 And then that factors out of the model. 348 00:17:25,550 --> 00:17:28,520 So this is a very simple model of a full annual cost 349 00:17:28,520 --> 00:17:30,830 for the agency. 350 00:17:30,830 --> 00:17:32,730 Here we're looking at the fiscal year. 351 00:17:32,730 --> 00:17:35,750 And it's sensitive to two variables. 352 00:17:35,750 --> 00:17:38,090 It's not sensitive to time period. 353 00:17:38,090 --> 00:17:41,990 And it's mixing fixed and variable costs. 354 00:17:41,990 --> 00:17:46,054 So this model may not be the best one for some applications. 355 00:17:46,054 --> 00:17:47,720 AUDIENCE: But just, what's the intuition 356 00:17:47,720 --> 00:17:50,420 behind using vehicle hours and vehicle miles? 357 00:17:50,420 --> 00:17:52,545 GABRIEL SANCHEZ-MARTINEZ: It's something that you-- 358 00:17:52,545 --> 00:17:54,230 that agencies always measure and report, 359 00:17:54,230 --> 00:17:58,490 so it's something that there's already a data collection 360 00:17:58,490 --> 00:18:00,740 effort for it. 361 00:18:00,740 --> 00:18:03,830 If you think about especially the traditional applications 362 00:18:03,830 --> 00:18:07,270 without automatic data collection, 363 00:18:07,270 --> 00:18:10,220 there is an effort to measure anything 364 00:18:10,220 --> 00:18:15,720 you deliver to collect how much output you produce. 365 00:18:15,720 --> 00:18:18,090 And so we already have that. 366 00:18:18,090 --> 00:18:21,920 It's something that then you can use as an explanatory variable. 367 00:18:21,920 --> 00:18:23,330 And it relates to service. 368 00:18:23,330 --> 00:18:25,650 So it's your service output. 369 00:18:28,920 --> 00:18:30,330 These are variables that are also 370 00:18:30,330 --> 00:18:33,960 going to be found in any service funding proposal 371 00:18:33,960 --> 00:18:36,150 in some way or another. 372 00:18:36,150 --> 00:18:39,574 If you extend routes, then that increases both of these. 373 00:18:39,574 --> 00:18:41,490 AUDIENCE: I guess my other question was, like, 374 00:18:41,490 --> 00:18:45,870 what's the intuition behind vehicle hours being relatively 375 00:18:45,870 --> 00:18:47,400 more expensive than vehicle miles? 376 00:18:47,400 --> 00:18:48,983 GABRIEL SANCHEZ-MARTINEZ: That depends 377 00:18:48,983 --> 00:18:52,672 on how you assign each of these cost categories to it. 378 00:18:52,672 --> 00:18:55,005 AUDIENCE: It's not that, like, operating a bus implies-- 379 00:18:55,005 --> 00:18:57,213 GABRIEL SANCHEZ-MARTINEZ: Well, I mean, in this case, 380 00:18:57,213 --> 00:18:57,780 wages are-- 381 00:18:57,780 --> 00:19:01,520 wages and benefits are a principle or one of the key-- 382 00:19:01,520 --> 00:19:02,981 AUDIENCE: Got it, OK. 383 00:19:02,981 --> 00:19:04,980 GABRIEL SANCHEZ-MARTINEZ: --one of the key costs 384 00:19:04,980 --> 00:19:05,800 for the agency. 385 00:19:05,800 --> 00:19:09,030 And that's being reflected entirely in vehicle hours. 386 00:19:09,030 --> 00:19:12,510 And potentially fuel is a second one. 387 00:19:12,510 --> 00:19:15,660 And that is at least partially covered 388 00:19:15,660 --> 00:19:17,890 by running vehicle hours. 389 00:19:17,890 --> 00:19:18,480 It could be. 390 00:19:18,480 --> 00:19:20,310 I'm not sure in this model if it is. 391 00:19:20,310 --> 00:19:22,830 I suspect that everything was assigned to vehicle miles, 392 00:19:22,830 --> 00:19:25,910 but it could be. 393 00:19:25,910 --> 00:19:30,410 So yeah, vehicle hours is a proxy for more things. 394 00:19:30,410 --> 00:19:34,040 More costs are being assigned to that variable. 395 00:19:34,040 --> 00:19:34,710 Eli? 396 00:19:34,710 --> 00:19:36,210 AUDIENCE: Can you give some examples 397 00:19:36,210 --> 00:19:39,099 of variable and fixed costs? 398 00:19:39,099 --> 00:19:40,640 GABRIEL SANCHEZ-MARTINEZ: Yeah, we'll 399 00:19:40,640 --> 00:19:43,060 actually see more of those later in the lecture. 400 00:19:48,410 --> 00:19:54,190 Fuel is variable, because as you drive more 401 00:19:54,190 --> 00:19:59,860 and you consume more-- and if you all of a sudden 402 00:19:59,860 --> 00:20:01,600 operate less service, then you'll 403 00:20:01,600 --> 00:20:03,910 see that drop immediately. 404 00:20:03,910 --> 00:20:08,950 A fixed cost could be the administration costs 405 00:20:08,950 --> 00:20:15,400 for, let's say, your service planner team. 406 00:20:15,400 --> 00:20:17,140 So you've hired people. 407 00:20:17,140 --> 00:20:19,240 And if you drop service a little bit, 408 00:20:19,240 --> 00:20:22,540 you're not necessarily going to fire people. 409 00:20:22,540 --> 00:20:25,600 Or if you expand service, you're not necessarily 410 00:20:25,600 --> 00:20:28,250 going to hire a bunch of people. 411 00:20:28,250 --> 00:20:30,040 Or you may not need new offices for them. 412 00:20:30,040 --> 00:20:33,222 So all of those things are more fixed. 413 00:20:33,222 --> 00:20:33,930 AUDIENCE: Thanks. 414 00:20:37,080 --> 00:20:39,330 GABRIEL SANCHEZ-MARTINEZ: OK, second model, so here we 415 00:20:39,330 --> 00:20:42,030 have the same first part of the model, 416 00:20:42,030 --> 00:20:44,190 but now, instead of using the adjustment factor, 417 00:20:44,190 --> 00:20:49,120 we directly take the unit cost of peak vehicles and add it in. 418 00:20:49,120 --> 00:20:53,340 So now we have a model that is sensitive to peak vehicles 419 00:20:53,340 --> 00:20:53,945 as well. 420 00:20:53,945 --> 00:20:55,320 And we don't need the adjustment, 421 00:20:55,320 --> 00:20:58,140 because all of the things that have been assigned 422 00:20:58,140 --> 00:21:02,685 to peak vehicles are being directly related 423 00:21:02,685 --> 00:21:03,810 to peak vehicles. 424 00:21:03,810 --> 00:21:05,670 So it's a simple variation. 425 00:21:05,670 --> 00:21:08,950 And here, we have a variable annual cost model. 426 00:21:08,950 --> 00:21:14,560 So these first two have all of the costs, fixed and variable. 427 00:21:14,560 --> 00:21:16,020 But for some applications, you're 428 00:21:16,020 --> 00:21:17,790 only interested in variable annual cost. 429 00:21:17,790 --> 00:21:20,330 And I've given the example of minor expansion 430 00:21:20,330 --> 00:21:25,020 in service, where you add a little bit of service 431 00:21:25,020 --> 00:21:26,550 or remove a little bit of service. 432 00:21:26,550 --> 00:21:29,820 And you wouldn't expect to incur fixed costs as a result. 433 00:21:29,820 --> 00:21:33,960 So here, we then only consider the unit costs 434 00:21:33,960 --> 00:21:36,960 of the variable portion of revenue vehicle hours, which 435 00:21:36,960 --> 00:21:42,120 is 37.13, and 2.57 for revenue vehicle miles. 436 00:21:45,380 --> 00:21:49,410 Any questions on these simple models? 437 00:21:49,410 --> 00:21:54,600 OK, as I mentioned before, one of the key weaknesses 438 00:21:54,600 --> 00:21:57,910 of these models is that they're not sensitive to time periods. 439 00:21:57,910 --> 00:22:02,150 So it's much more expensive to operate sort of on the peak 440 00:22:02,150 --> 00:22:03,035 than it is off-peak. 441 00:22:03,035 --> 00:22:07,040 So if you were to use, say, variable annual cost model 442 00:22:07,040 --> 00:22:12,080 for bus routes 70 and 78 and now you 443 00:22:12,080 --> 00:22:14,330 want to expand it to go to Kendall, 444 00:22:14,330 --> 00:22:18,590 or Lechmere, or somewhere else, and you have a greater number 445 00:22:18,590 --> 00:22:22,820 of revenue vehicle hours than your revenue vehicle miles, 446 00:22:22,820 --> 00:22:24,500 if you-- maybe if you expand service 447 00:22:24,500 --> 00:22:28,230 proportionally throughout the peak and off-peak, you're fine. 448 00:22:28,230 --> 00:22:31,550 But if you only expand service in the peak or do it 449 00:22:31,550 --> 00:22:34,160 disproportionately peak/off-peak, 450 00:22:34,160 --> 00:22:37,830 then this model will not capture those differences very well. 451 00:22:37,830 --> 00:22:42,129 And for that, we need temporal variational, 452 00:22:42,129 --> 00:22:42,920 which is our next-- 453 00:22:42,920 --> 00:22:45,500 AUDIENCE: Just a second, but why wouldn't you capture it? 454 00:22:45,500 --> 00:22:46,830 Because suppose I had service. 455 00:22:46,830 --> 00:22:48,260 Suppose I had a bus in the peak. 456 00:22:48,260 --> 00:22:51,620 So now peak vehicles, that gets impacted. 457 00:22:51,620 --> 00:22:55,370 But suppose I take fuel and I say, OK, there is fuel. 458 00:22:55,370 --> 00:22:59,310 Fuel affects revenue miles, but also it affects revenue hours. 459 00:22:59,310 --> 00:23:03,260 And I put fuel in twice, both in the hours and the miles. 460 00:23:03,260 --> 00:23:06,080 Now I can also take into account the fact 461 00:23:06,080 --> 00:23:09,660 that the bus is sitting in traffic and burning fuel 462 00:23:09,660 --> 00:23:10,670 and also-- 463 00:23:10,670 --> 00:23:12,620 but I'm taking that into account. 464 00:23:12,620 --> 00:23:15,370 So why is this model necessarily [INAUDIBLE].. 465 00:23:15,890 --> 00:23:17,640 GABRIEL SANCHEZ-MARTINEZ: So the questions 466 00:23:17,640 --> 00:23:19,870 why does this model not adequately capture 467 00:23:19,870 --> 00:23:22,230 peak versus off-peak costs? 468 00:23:22,230 --> 00:23:25,130 So it goes back to this calculating average costs 469 00:23:25,130 --> 00:23:26,210 by factor. 470 00:23:26,210 --> 00:23:27,399 So these are averages. 471 00:23:27,399 --> 00:23:29,690 You're taking averages of all the vehicles at all times 472 00:23:29,690 --> 00:23:32,840 of day and dividing by-- 473 00:23:32,840 --> 00:23:35,360 explaining them with an explanatory variable 474 00:23:35,360 --> 00:23:38,690 that is not necessarily was directly causing it. 475 00:23:38,690 --> 00:23:44,000 And so especially driver costs are going to vary a lot by sort 476 00:23:44,000 --> 00:23:45,290 of peak/off-peak. 477 00:23:45,290 --> 00:23:46,740 And we're taking an average. 478 00:23:46,740 --> 00:23:49,980 So if you increase service proportionately, you're fine. 479 00:23:49,980 --> 00:23:52,850 But the unit cost is not reflecting the difference 480 00:23:52,850 --> 00:23:54,200 between peak and off-peak. 481 00:23:54,200 --> 00:23:56,090 So it's the unit cost itself more than 482 00:23:56,090 --> 00:24:00,334 the independent variable that you put in, 483 00:24:00,334 --> 00:24:01,500 which is what you're saying. 484 00:24:01,500 --> 00:24:05,270 You're saying, I can measure the independent variable precisely, 485 00:24:05,270 --> 00:24:06,440 so I can plug it in here. 486 00:24:06,440 --> 00:24:08,875 Well, but your factor is average. 487 00:24:08,875 --> 00:24:10,740 AUDIENCE: I see. 488 00:24:10,740 --> 00:24:13,190 GABRIEL SANCHEZ-MARTINEZ: So the approach 489 00:24:13,190 --> 00:24:16,670 of this model, which is an extension of the first one, 490 00:24:16,670 --> 00:24:20,780 is to do everything that we did except for driver costs, 491 00:24:20,780 --> 00:24:23,990 because these costs are very sensitive to time of day. 492 00:24:23,990 --> 00:24:30,450 And for those costs, per crew costs, we take the day. 493 00:24:30,450 --> 00:24:32,820 We divide it into 30-minute periods. 494 00:24:32,820 --> 00:24:34,290 And then we look at all runs. 495 00:24:34,290 --> 00:24:38,780 Now, a run is what a driver does in a day. 496 00:24:38,780 --> 00:24:40,720 That's their shift. 497 00:24:40,720 --> 00:24:43,130 That's a sequence of trips that are being 498 00:24:43,130 --> 00:24:44,950 operated by a single driver. 499 00:24:44,950 --> 00:24:48,650 And we look at all runs and all periods. 500 00:24:48,650 --> 00:24:53,350 And for each period, any run that is at least this-- 501 00:24:53,350 --> 00:24:55,310 has at least 15 minutes in that period 502 00:24:55,310 --> 00:24:57,800 gets included in that period. 503 00:24:57,800 --> 00:25:02,360 And then we compute the average paid per vehicle hour 504 00:25:02,360 --> 00:25:05,420 by dividing the daily pay by the number of vehicle hours 505 00:25:05,420 --> 00:25:07,500 over all runs in that period. 506 00:25:07,500 --> 00:25:11,420 So each of these runs is going to have a different cost. 507 00:25:11,420 --> 00:25:14,450 Some runs are going to operate more in the peak. 508 00:25:14,450 --> 00:25:16,670 And they're going to have more overtime, for example, 509 00:25:16,670 --> 00:25:18,430 or more spread penalties. 510 00:25:18,430 --> 00:25:19,950 And we'll talk about those now. 511 00:25:19,950 --> 00:25:23,900 And so those runs will be more expensive. 512 00:25:23,900 --> 00:25:27,590 Other runs that are straight are going to be less expensive. 513 00:25:27,590 --> 00:25:30,680 And you can calculate an average for each 30- 514 00:25:30,680 --> 00:25:33,000 or 50-minute period. 515 00:25:33,000 --> 00:25:35,990 So now we have an average again, but it's 516 00:25:35,990 --> 00:25:39,200 by time of day for a small bucket of time. 517 00:25:39,200 --> 00:25:43,940 And then for each of those, we find the minimum, the average, 518 00:25:43,940 --> 00:25:44,750 and the maximum. 519 00:25:44,750 --> 00:25:46,760 So we're not only going to look at averages. 520 00:25:46,760 --> 00:25:49,820 We're going to also look at the distribution of costs 521 00:25:49,820 --> 00:25:52,140 along each period. 522 00:25:52,140 --> 00:25:56,555 And this is just an equation for average. 523 00:25:56,555 --> 00:26:02,660 So what we have here is the sum over all 524 00:26:02,660 --> 00:26:06,850 runs in a specific period. 525 00:26:06,850 --> 00:26:10,790 This is the wage, the total paid for that run, divided 526 00:26:10,790 --> 00:26:12,560 by the number of hours for that run. 527 00:26:12,560 --> 00:26:15,780 So we compute the average. 528 00:26:15,780 --> 00:26:20,600 OK, if we look at the driver requirements for the MBTA back 529 00:26:20,600 --> 00:26:26,610 in 1983, the early 1980s, this is what we get. 530 00:26:26,610 --> 00:26:30,410 So many more drivers are required 531 00:26:30,410 --> 00:26:34,490 in the AM peak and the PM peak than are required off-peak, 532 00:26:34,490 --> 00:26:39,110 or early in the morning, or late in the afternoon and evening. 533 00:26:39,110 --> 00:26:41,209 Why is that? 534 00:26:41,209 --> 00:26:43,000 We've talked a little bit about it already. 535 00:26:43,000 --> 00:26:44,291 AUDIENCE: There's more service. 536 00:26:44,291 --> 00:26:47,064 GABRIEL SANCHEZ-MARTINEZ: So you provide more service. 537 00:26:47,064 --> 00:26:48,730 Why do you need to provide more service? 538 00:26:48,730 --> 00:26:49,510 AUDIENCE: Because that's when the-- 539 00:26:49,510 --> 00:26:49,650 AUDIENCE: More demand. 540 00:26:49,650 --> 00:26:51,290 AUDIENCE: --commuters are moving. 541 00:26:51,290 --> 00:26:51,940 GABRIEL SANCHEZ-MARTINEZ: Because there's 542 00:26:51,940 --> 00:26:53,050 more demand for it, right? 543 00:26:53,050 --> 00:26:54,850 So if provided the same level of service, 544 00:26:54,850 --> 00:26:56,349 then your buses would be too crowded 545 00:26:56,349 --> 00:26:58,120 and you would not deliver enough capacity. 546 00:26:58,120 --> 00:26:59,430 What else? 547 00:26:59,430 --> 00:27:01,055 AUDIENCE: They're also in traffic more. 548 00:27:01,055 --> 00:27:01,895 So buses are out-- 549 00:27:01,895 --> 00:27:03,520 GABRIEL SANCHEZ-MARTINEZ: So every trip 550 00:27:03,520 --> 00:27:07,170 that you run takes longer, and stuck in traffic. 551 00:27:07,170 --> 00:27:09,790 And the dwell times are longer. 552 00:27:09,790 --> 00:27:11,890 OK, so if you need more, if you need 553 00:27:11,890 --> 00:27:15,480 to provide more frequent service and each run that you do, 554 00:27:15,480 --> 00:27:18,790 each trip that you run is slower, 555 00:27:18,790 --> 00:27:22,120 than that means that you have a greater cycle 556 00:27:22,120 --> 00:27:25,780 time and a greater frequency, and therefore, 557 00:27:25,780 --> 00:27:29,777 a greater vehicle requirement from your first assignment. 558 00:27:29,777 --> 00:27:32,110 And of course you need drivers the drive those vehicles, 559 00:27:32,110 --> 00:27:34,690 so your driver requirement also goes up. 560 00:27:34,690 --> 00:27:37,150 Great, so what's wrong with the time? 561 00:27:37,150 --> 00:27:41,200 What's inconvenient about the timing of the peaks? 562 00:27:41,200 --> 00:27:42,700 AUDIENCE: They're eight hours apart. 563 00:27:42,700 --> 00:27:43,890 GABRIEL SANCHEZ-MARTINEZ: They are eight hours apart. 564 00:27:43,890 --> 00:27:45,595 And how long are shifts typically? 565 00:27:45,595 --> 00:27:45,890 AUDIENCE: Eight hours. 566 00:27:45,890 --> 00:27:47,681 GABRIEL SANCHEZ-MARTINEZ: Eight hours long, 567 00:27:47,681 --> 00:27:50,620 so if we hire someone to start their shift at 6:00 AM, 568 00:27:50,620 --> 00:27:52,270 they can't cover the PM peaks. 569 00:27:52,270 --> 00:27:53,790 They only cover the AM peak. 570 00:27:53,790 --> 00:27:56,260 OK, so what do we do? 571 00:27:56,260 --> 00:27:59,140 One option is to hire part timers. 572 00:27:59,140 --> 00:28:04,390 So use full-time employees for the base. 573 00:28:04,390 --> 00:28:07,880 And then hire part timers for the peaks. 574 00:28:07,880 --> 00:28:11,800 That's the least expensive and most efficient option. 575 00:28:11,800 --> 00:28:16,360 But unions don't like it, because if you 576 00:28:16,360 --> 00:28:19,930 have a high percentage of part-time drivers, then 577 00:28:19,930 --> 00:28:24,160 it's not to the benefit of their union employees. 578 00:28:24,160 --> 00:28:26,320 If you don't allow part timers or you 579 00:28:26,320 --> 00:28:29,050 cap the allowance on part timers, 580 00:28:29,050 --> 00:28:33,130 then the agency is required to hire full-time employees 581 00:28:33,130 --> 00:28:36,790 to cover the AM and the PM peak. 582 00:28:36,790 --> 00:28:39,720 And if you only do that, then that's 583 00:28:39,720 --> 00:28:42,220 terribly inefficient, because you're hiring for eight hours. 584 00:28:42,220 --> 00:28:44,020 Then you can only operate two or three. 585 00:28:44,020 --> 00:28:46,540 That's all that you need that driver for. 586 00:28:46,540 --> 00:28:49,660 But there is some arrangement. 587 00:28:49,660 --> 00:28:53,170 You can actually have shifts that 588 00:28:53,170 --> 00:28:54,890 have a break in the middle of the day. 589 00:28:54,890 --> 00:28:57,100 And these are called spread shifts. 590 00:28:57,100 --> 00:29:01,840 So some of these shifts operate for two or three 591 00:29:01,840 --> 00:29:04,930 hours in the morning, have a long break during the day, 592 00:29:04,930 --> 00:29:08,050 and operate for two or three hours in the afternoon. 593 00:29:08,050 --> 00:29:13,250 And often, these shifts are paid a spread penalty. 594 00:29:13,250 --> 00:29:17,620 So in this example, what we have in white here 595 00:29:17,620 --> 00:29:22,700 are shifts that last between 10 hours and 11 hours. 596 00:29:22,700 --> 00:29:25,840 So the spread is the difference between the check-out time 597 00:29:25,840 --> 00:29:27,910 and the check-in time. 598 00:29:27,910 --> 00:29:36,360 And shifts in white here have a spread between 10 and 11 hours. 599 00:29:36,360 --> 00:29:42,720 Those drivers are paid a 50% premium for any hours 600 00:29:42,720 --> 00:29:45,900 above 8 hours. 601 00:29:45,900 --> 00:29:48,750 And then there are these other shifts that 602 00:29:48,750 --> 00:29:51,580 are between 11 and 13 hours. 603 00:29:51,580 --> 00:29:55,770 So 11, 12 in dark gray, and 12 and 13 604 00:29:55,770 --> 00:29:59,790 shaded diagonally, these shifts are paid 100%. 605 00:29:59,790 --> 00:30:04,790 So they're paid double for any hours in excess of the-- 606 00:30:04,790 --> 00:30:08,130 I guess in excess of 11, in this case. 607 00:30:08,130 --> 00:30:10,740 So that's going to drive costs up, 608 00:30:10,740 --> 00:30:14,520 because if you look at the total pay for that shift 609 00:30:14,520 --> 00:30:21,380 over the day, then the unit pay per hour for each 610 00:30:21,380 --> 00:30:24,140 of those drivers is higher. 611 00:30:24,140 --> 00:30:26,917 And if you look at any time slice of the day, 612 00:30:26,917 --> 00:30:29,000 peaks are going to have many more of those drivers 613 00:30:29,000 --> 00:30:30,400 than off-peak. 614 00:30:30,400 --> 00:30:33,710 So the average across the drivers on any bucket of time 615 00:30:33,710 --> 00:30:36,965 that is 30 minutes wide is going to be higher. 616 00:30:36,965 --> 00:30:39,050 AUDIENCE: Sorry, could you explain maybe for like, 617 00:30:39,050 --> 00:30:42,650 let's say I'm a driver that runs the shifts with 12 hours 618 00:30:42,650 --> 00:30:45,122 less than spread, 13 hours, the bottom one. 619 00:30:45,122 --> 00:30:46,830 GABRIEL SANCHEZ-MARTINEZ: This one, yeah. 620 00:30:46,830 --> 00:30:49,190 AUDIENCE: [INAUDIBLE] they're driving, the peak ones-- 621 00:30:49,190 --> 00:30:51,740 like, when would I work and what hours do I get paid for? 622 00:30:51,740 --> 00:30:52,490 GABRIEL SANCHEZ-MARTINEZ: Excellent segue 623 00:30:52,490 --> 00:30:53,281 for the next slide. 624 00:30:56,030 --> 00:31:01,670 So here we have essentially the runs by a driver. 625 00:31:01,670 --> 00:31:04,145 And you can see the-- if you draw a line here, 626 00:31:04,145 --> 00:31:07,910 this is 8:00 AM, so AM peak. 627 00:31:07,910 --> 00:31:11,970 And then this is 5:00 PM right around here. 628 00:31:11,970 --> 00:31:18,230 So you see that, if you draw a line between 8:00 and 5:00 PM, 629 00:31:18,230 --> 00:31:22,310 these are the shifts that start during the AM peak. 630 00:31:22,310 --> 00:31:25,200 And those shifts have the biggest spreads. 631 00:31:25,200 --> 00:31:30,440 So any one of these rows is an example of one run. 632 00:31:30,440 --> 00:31:32,550 And if you could be one of these drivers-- 633 00:31:32,550 --> 00:31:37,760 so if you have this day, you check in at 6:30. 634 00:31:37,760 --> 00:31:39,710 You have a pretty long break during the day. 635 00:31:39,710 --> 00:31:43,850 And you check out at 8:00-- at 6:00 PM. 636 00:31:43,850 --> 00:31:47,440 So you do an hour in the PM. 637 00:31:47,440 --> 00:31:49,250 And you can have longer ones too. 638 00:31:49,250 --> 00:31:52,094 There will be some rules that prevent excessively long ones. 639 00:31:52,094 --> 00:31:53,510 AUDIENCE: And when you were saying 640 00:31:53,510 --> 00:31:55,896 I get paid 50% more as that bus driver, do 641 00:31:55,896 --> 00:31:58,430 I get paid 50% more for the-- 642 00:31:58,430 --> 00:31:59,820 only the hours that I'm working? 643 00:31:59,820 --> 00:32:01,070 GABRIEL SANCHEZ-MARTINEZ: Yes. 644 00:32:01,070 --> 00:32:02,000 AUDIENCE: OK, got it. 645 00:32:02,000 --> 00:32:04,490 GABRIEL SANCHEZ-MARTINEZ: And that will vary by agreement. 646 00:32:04,490 --> 00:32:08,086 So that's specific to this labor agreement. 647 00:32:08,086 --> 00:32:11,650 AUDIENCE: And during in between the shifts? 648 00:32:11,650 --> 00:32:14,470 GABRIEL SANCHEZ-MARTINEZ: So you are paid the spread penalty. 649 00:32:14,470 --> 00:32:16,006 And you are paid-- 650 00:32:16,006 --> 00:32:17,380 there are a bunch of rules. like, 651 00:32:17,380 --> 00:32:19,296 No matter how many hours you work, you're paid 652 00:32:19,296 --> 00:32:21,660 a minimum of eight. 653 00:32:21,660 --> 00:32:22,897 There's a swing pay bonus. 654 00:32:22,897 --> 00:32:24,730 So if you start your day somewhere different 655 00:32:24,730 --> 00:32:26,980 than you end the day, then you have to pay the person, 656 00:32:26,980 --> 00:32:31,690 I think, 30 minutes extra for their driving time, 657 00:32:31,690 --> 00:32:34,180 or whatever, for getting to the other location 658 00:32:34,180 --> 00:32:36,920 where you potentially left your car. 659 00:32:36,920 --> 00:32:40,640 So there are compensations for all of these things. 660 00:32:40,640 --> 00:32:43,960 And the point here in this cost modeling lecture 661 00:32:43,960 --> 00:32:49,050 is that these drivers with spread, with large spreads, 662 00:32:49,050 --> 00:32:49,890 cost more. 663 00:32:49,890 --> 00:32:52,320 So we want to build a cost model that 664 00:32:52,320 --> 00:32:54,930 recognizes those differences, especially 665 00:32:54,930 --> 00:32:56,940 with regards to driver hours. 666 00:32:56,940 --> 00:32:59,730 So we extend service and require more driver hours 667 00:32:59,730 --> 00:33:01,770 more in the peak than in the off-peak. 668 00:33:01,770 --> 00:33:05,250 Then we need to account for those differences. 669 00:33:05,250 --> 00:33:09,570 Here is a graph by time of day of the wage cost per platform 670 00:33:09,570 --> 00:33:13,780 hour, just by hour, divided by the base pay rate. 671 00:33:13,780 --> 00:33:19,760 So off-peak, you see that the average is variables to one. 672 00:33:22,800 --> 00:33:26,130 But if you go to the peak, then you're 673 00:33:26,130 --> 00:33:29,790 paying an average of, say, 25% higher, 674 00:33:29,790 --> 00:33:32,490 because some of the drivers are straight shifts, 675 00:33:32,490 --> 00:33:33,990 but there's a mix of drivers that 676 00:33:33,990 --> 00:33:37,490 are spread, large spread, and being paid some spread 677 00:33:37,490 --> 00:33:38,280 penalties. 678 00:33:38,280 --> 00:33:40,970 So that drives the costs up. 679 00:33:40,970 --> 00:33:46,212 OK, here's an exercise to solidify this concept. 680 00:33:46,212 --> 00:33:47,670 Oh, before that we have a question. 681 00:33:47,670 --> 00:33:53,040 AUDIENCE: Sorry, is it uncommon that the employees, they night 682 00:33:53,040 --> 00:33:54,360 [INAUDIBLE] price. 683 00:33:54,360 --> 00:33:58,140 I mean that someone starts working at night 684 00:33:58,140 --> 00:34:01,600 and drives some buses or trains. 685 00:34:01,600 --> 00:34:06,500 And they go to sleep, and after the day, 686 00:34:06,500 --> 00:34:10,120 restart their work in the morning? 687 00:34:10,120 --> 00:34:12,120 GABRIEL SANCHEZ-MARTINEZ: So for safety reasons, 688 00:34:12,120 --> 00:34:14,400 a lot of labor agreements require-- 689 00:34:14,400 --> 00:34:17,550 and any work rules require a minimum amount 690 00:34:17,550 --> 00:34:20,760 of break between the end of a run 691 00:34:20,760 --> 00:34:23,313 and the start of the next one. 692 00:34:23,313 --> 00:34:26,810 And that could be 12 hours. 693 00:34:26,810 --> 00:34:30,630 So you know, where that person sleeps is up to them. 694 00:34:30,630 --> 00:34:32,070 I suppose most of them go home. 695 00:34:35,790 --> 00:34:38,100 Normally the rules won't allow you 696 00:34:38,100 --> 00:34:43,290 to have a run that, if you end service at 5:00, 697 00:34:43,290 --> 00:34:46,360 you won't be able to check in at 8:00 again. 698 00:34:46,360 --> 00:34:48,865 If you did a full day that end at 5:00 AM, 699 00:34:48,865 --> 00:34:50,489 you're probably not going to be allowed 700 00:34:50,489 --> 00:34:52,955 to start the next full day at 8:00 AM, 701 00:34:52,955 --> 00:34:54,580 because that's not a long enough break. 702 00:34:54,580 --> 00:34:55,790 And that would be unsafe. 703 00:34:55,790 --> 00:34:59,100 AUDIENCE: Yeah, I said this because in Japan, 704 00:34:59,100 --> 00:35:04,770 it is very common to have some place to stay and provide them. 705 00:35:04,770 --> 00:35:10,426 And also it enable us to run the very late night 706 00:35:10,426 --> 00:35:14,220 [INAUDIBLE] services. 707 00:35:14,220 --> 00:35:15,762 So yeah, I'm just curious about this. 708 00:35:15,762 --> 00:35:17,886 GABRIEL SANCHEZ-MARTINEZ: I didn't know about that. 709 00:35:17,886 --> 00:35:19,590 I'm interested to learn more about it. 710 00:35:19,590 --> 00:35:21,660 AUDIENCE: Would people want to do that every day? 711 00:35:21,660 --> 00:35:24,680 Or would they, like, maybe expect to do that once a week? 712 00:35:24,680 --> 00:35:26,290 AUDIENCE: It depends on the shift, 713 00:35:26,290 --> 00:35:28,744 but no one continue that kind of-- 714 00:35:28,744 --> 00:35:29,660 AUDIENCE: Yeah you'd-- 715 00:35:29,660 --> 00:35:30,409 AUDIENCE: --shift. 716 00:35:30,409 --> 00:35:32,304 AUDIENCE: --live at work. 717 00:35:32,304 --> 00:35:33,220 AUDIENCE: Sorry, what? 718 00:35:33,220 --> 00:35:36,863 AUDIENCE: You would just live at work and do your whole life 719 00:35:36,863 --> 00:35:38,282 just not doing anything else. 720 00:35:38,282 --> 00:35:39,228 AUDIENCE: [INAUDIBLE] 721 00:35:40,985 --> 00:35:42,610 GABRIEL SANCHEZ-MARTINEZ: I mean, these 722 00:35:42,610 --> 00:35:46,980 are maybe cultural differences for work rules 723 00:35:46,980 --> 00:35:48,220 differences across cultures. 724 00:35:48,220 --> 00:35:49,685 I'd love to learn more about it. 725 00:35:49,685 --> 00:35:51,660 If you have any reference that you can send me, 726 00:35:51,660 --> 00:35:52,860 that would be great. 727 00:35:52,860 --> 00:35:54,074 AUDIENCE: Sure. 728 00:35:54,074 --> 00:35:55,990 GABRIEL SANCHEZ-MARTINEZ: Any other questions? 729 00:35:55,990 --> 00:35:56,810 Ari, I think you had a question. 730 00:35:56,810 --> 00:35:59,351 AUDIENCE: Oh, I was going to say that based on Chicago, which 731 00:35:59,351 --> 00:36:01,651 runs overnight service, there is so few enough shifts 732 00:36:01,651 --> 00:36:03,400 that, basically, everything is [INAUDIBLE] 733 00:36:03,400 --> 00:36:04,870 as a straight shift. 734 00:36:04,870 --> 00:36:06,870 But I think when you bid for an overnight shift, 735 00:36:06,870 --> 00:36:08,490 you basically get all overnight shifts. 736 00:36:08,490 --> 00:36:10,115 You keep on that rhythm so you wouldn't 737 00:36:10,115 --> 00:36:13,020 have an overnight and a day. 738 00:36:13,020 --> 00:36:16,050 And there are some operators that really like the overnight 739 00:36:16,050 --> 00:36:19,560 shift, because it provides-- they can care for kids during 740 00:36:19,560 --> 00:36:21,809 the day, or just they like that-- 741 00:36:21,809 --> 00:36:23,100 like working outside the peaks. 742 00:36:23,100 --> 00:36:24,540 GABRIEL SANCHEZ-MARTINEZ: I don't know what the labor rules 743 00:36:24,540 --> 00:36:27,404 are there, but some, personally, they also get a premium 744 00:36:27,404 --> 00:36:28,070 for taking the-- 745 00:36:28,070 --> 00:36:28,946 AUDIENCE: [INAUDIBLE] 746 00:36:28,946 --> 00:36:30,736 GABRIEL SANCHEZ-MARTINEZ: There are usually 747 00:36:30,736 --> 00:36:33,600 premiums for running on holidays or running late at night. 748 00:36:33,600 --> 00:36:38,100 So the least desirable runs might have an extra premium 749 00:36:38,100 --> 00:36:40,740 associated to compensate for the inconvenience 750 00:36:40,740 --> 00:36:44,010 or the undesirability thereof. 751 00:36:44,010 --> 00:36:49,980 Great, so we have an example here 752 00:36:49,980 --> 00:36:52,890 where we've done this exercise and we've looked 753 00:36:52,890 --> 00:36:54,030 at all periods of the day. 754 00:36:54,030 --> 00:36:57,360 We've looked at the minimum, the average, and the maximum unit 755 00:36:57,360 --> 00:37:02,010 costs for drivers, so screw, for peak, off-peak, 756 00:37:02,010 --> 00:37:05,140 and the combination of peak and off-peak. 757 00:37:05,140 --> 00:37:08,920 And we have six different scenarios. 758 00:37:08,920 --> 00:37:11,860 And we want to choose the unit cost for each of these. 759 00:37:11,860 --> 00:37:15,350 So let's go one by one. 760 00:37:15,350 --> 00:37:17,860 So what happens if we want to increase the peak 761 00:37:17,860 --> 00:37:20,540 and off-peak service proportionally? 762 00:37:20,540 --> 00:37:24,148 Which unit cost from this matrix would you use? 763 00:37:24,148 --> 00:37:25,460 AUDIENCE: Combined. 764 00:37:25,460 --> 00:37:27,940 GABRIEL SANCHEZ-MARTINEZ: So we're hearing combined-- 765 00:37:27,940 --> 00:37:30,030 agreement, yeah? 766 00:37:30,030 --> 00:37:32,330 And from combining, would you take minimum, average, 767 00:37:32,330 --> 00:37:33,372 or maximum? 768 00:37:33,372 --> 00:37:34,790 AUDIENCE: Average. 769 00:37:34,790 --> 00:37:36,581 GABRIEL SANCHEZ-MARTINEZ: Average combined? 770 00:37:38,180 --> 00:37:40,820 Yeah, OK, and why is that? 771 00:37:40,820 --> 00:37:43,420 Because it's proportional on both ends. 772 00:37:43,420 --> 00:37:46,231 And we don't actually need the temporal variation model 773 00:37:46,231 --> 00:37:46,730 for this. 774 00:37:46,730 --> 00:37:47,839 So we can go without. 775 00:37:47,839 --> 00:37:49,880 What if it's a proportional decrease in both peak 776 00:37:49,880 --> 00:37:51,940 and off-peak? 777 00:37:51,940 --> 00:37:54,056 Would we use the same one? 778 00:37:54,056 --> 00:37:56,940 AUDIENCE: Minimum combined? 779 00:37:56,940 --> 00:37:59,523 GABRIEL SANCHEZ-MARTINEZ: Some people are saying the same one. 780 00:37:59,523 --> 00:38:01,150 AUDIENCE: [INAUDIBLE] 781 00:38:01,150 --> 00:38:03,525 GABRIEL SANCHEZ-MARTINEZ: You're saying minimum combined. 782 00:38:03,525 --> 00:38:05,545 We have one minimum combined. 783 00:38:05,545 --> 00:38:07,128 What's your idea for minimum combined? 784 00:38:09,876 --> 00:38:10,800 AUDIENCE: [INAUDIBLE] 785 00:38:10,800 --> 00:38:12,000 GABRIEL SANCHEZ-MARTINEZ: Retracting, OK. 786 00:38:12,000 --> 00:38:14,166 AUDIENCE: When you say minimum cost or average cost, 787 00:38:14,166 --> 00:38:16,600 is that for the peak period or is that for [INAUDIBLE]?? 788 00:38:16,600 --> 00:38:17,850 GABRIEL SANCHEZ-MARTINEZ: So if it's peak, 789 00:38:17,850 --> 00:38:19,200 it will be for the peak hours. 790 00:38:19,200 --> 00:38:20,980 If it's off-peak, it's for off-pea, hours. 791 00:38:20,980 --> 00:38:22,110 AUDIENCE: No, I mean the-- 792 00:38:22,110 --> 00:38:24,526 GABRIEL SANCHEZ-MARTINEZ: But minimum maximum hours, like, 793 00:38:24,526 --> 00:38:27,330 within the peak hours, then there are some drivers that are 794 00:38:27,330 --> 00:38:31,319 paid more on average and others that are paid less, 795 00:38:31,319 --> 00:38:33,360 because some of them are-- have spread penalties, 796 00:38:33,360 --> 00:38:34,450 and others don't. 797 00:38:34,450 --> 00:38:37,170 So even in the peaks, are straight shifts. 798 00:38:37,170 --> 00:38:40,810 And those are on the low end. 799 00:38:40,810 --> 00:38:41,340 Question? 800 00:38:41,340 --> 00:38:42,881 AUDIENCE: Well, I guess, wouldn't you 801 00:38:42,881 --> 00:38:45,471 want to use-- like, if were going to add to the peak, 802 00:38:45,471 --> 00:38:47,220 is it a bad assumption to assume that it's 803 00:38:47,220 --> 00:38:48,960 going to be more expensive than your most [INAUDIBLE]?? 804 00:38:48,960 --> 00:38:49,810 GABRIEL SANCHEZ-MARTINEZ: We're getting to that. 805 00:38:49,810 --> 00:38:52,615 So the third one is, increases in peak period services only, 806 00:38:52,615 --> 00:38:53,115 so-- 807 00:38:53,115 --> 00:38:54,390 AUDIENCE: But I guess, even combined, 808 00:38:54,390 --> 00:38:56,431 like, wouldn't you want to use the max or the min 809 00:38:56,431 --> 00:38:58,644 because it's incremental? 810 00:38:58,644 --> 00:39:00,060 GABRIEL SANCHEZ-MARTINEZ: The idea 811 00:39:00,060 --> 00:39:05,222 is that, if you increase things proportionally, then 812 00:39:05,222 --> 00:39:07,180 you're going to have the same mix that you have 813 00:39:07,180 --> 00:39:11,770 now but a little more each. 814 00:39:11,770 --> 00:39:16,450 If you add service both peak and off-peak in proportion, which 815 00:39:16,450 --> 00:39:19,060 means that, if there is twice as much peak service, then 816 00:39:19,060 --> 00:39:22,000 you're going to have twice much more peak service, 817 00:39:22,000 --> 00:39:26,570 then you're going to have the same distribution of spread 818 00:39:26,570 --> 00:39:30,330 penalties, and therefore, the same average costs. 819 00:39:30,330 --> 00:39:33,060 But now we go to the next question, which 820 00:39:33,060 --> 00:39:36,687 is, increases in peak period services only, which of these 821 00:39:36,687 --> 00:39:37,270 would you use? 822 00:39:40,490 --> 00:39:41,417 AUDIENCE: The max. 823 00:39:41,417 --> 00:39:43,250 GABRIEL SANCHEZ-MARTINEZ: We're hearing max. 824 00:39:43,250 --> 00:39:46,130 And I assume for peak, max for peak? 825 00:39:46,130 --> 00:39:46,755 AUDIENCE: Yeah. 826 00:39:46,755 --> 00:39:48,504 GABRIEL SANCHEZ-MARTINEZ: Any other ideas? 827 00:39:48,504 --> 00:39:49,734 AUDIENCE: Peak average. 828 00:39:49,734 --> 00:39:52,410 GABRIEL SANCHEZ-MARTINEZ: Peak average, two ideas-- 829 00:39:52,410 --> 00:39:53,370 OK, let's debate. 830 00:39:58,864 --> 00:40:00,280 AUDIENCE: All right, so basically, 831 00:40:00,280 --> 00:40:03,490 if we're increasing in the peak period only, 832 00:40:03,490 --> 00:40:09,830 we're going to have to do more of these spread shifts 833 00:40:09,830 --> 00:40:10,330 to do that. 834 00:40:10,330 --> 00:40:11,579 GABRIEL SANCHEZ-MARTINEZ: Yes. 835 00:40:11,579 --> 00:40:13,784 AUDIENCE: And those are our most expensive shifts. 836 00:40:13,784 --> 00:40:15,825 GABRIEL SANCHEZ-MARTINEZ: Yes, are you convinced? 837 00:40:15,825 --> 00:40:16,825 AUDIENCE: I'm convinced. 838 00:40:16,825 --> 00:40:23,950 GABRIEL SANCHEZ-MARTINEZ: OK, good so great, so $45 right, 839 00:40:23,950 --> 00:40:25,760 the maximum of the peak-- 840 00:40:25,760 --> 00:40:29,760 what if it's a decrease in peak period service? 841 00:40:29,760 --> 00:40:32,740 So now we're coming back here and we're only 842 00:40:32,740 --> 00:40:37,360 taking the top of the top off and we're not giving anything 843 00:40:37,360 --> 00:40:40,035 to the off-peak [INAUDIBLE]. 844 00:40:40,035 --> 00:40:41,306 AUDIENCE: The inverse. 845 00:40:41,306 --> 00:40:42,281 AUDIENCE: [INAUDIBLE] 846 00:40:42,281 --> 00:40:43,780 GABRIEL SANCHEZ-MARTINEZ: Same, 45-- 847 00:40:43,780 --> 00:40:44,488 AUDIENCE: Maximum 848 00:40:44,488 --> 00:40:46,940 GABRIEL SANCHEZ-MARTINEZ: --going down now, OK, great-- 849 00:40:46,940 --> 00:40:52,400 OK, increases in off-peak period services only, 850 00:40:52,400 --> 00:40:54,830 so now we're leaving the peak where it is. 851 00:40:54,830 --> 00:40:58,140 And we're decreasing service off-peak-- so here and maybe 852 00:40:58,140 --> 00:41:00,919 at night. 853 00:41:00,919 --> 00:41:02,210 AUDIENCE: Increasing, you said? 854 00:41:02,210 --> 00:41:03,320 GABRIEL SANCHEZ-MARTINEZ: Decreasing-- 855 00:41:03,320 --> 00:41:04,315 is it decreasing or increasing? 856 00:41:04,315 --> 00:41:04,590 AUDIENCE: Increase. 857 00:41:04,590 --> 00:41:05,381 AUDIENCE: Increase. 858 00:41:05,381 --> 00:41:09,086 GABRIEL SANCHEZ-MARTINEZ: Let's start with increasing. 859 00:41:09,086 --> 00:41:13,000 AUDIENCE: Then maybe minimum in off-peak? 860 00:41:13,000 --> 00:41:14,640 GABRIEL SANCHEZ-MARTINEZ: OK, that's 861 00:41:14,640 --> 00:41:17,220 actually the high end of what it could be. 862 00:41:17,220 --> 00:41:20,100 So of the cells here, yes, that's 863 00:41:20,100 --> 00:41:21,496 the one that you should pick. 864 00:41:21,496 --> 00:41:24,570 You should use the minimum off-peak. 865 00:41:24,570 --> 00:41:27,600 But it could actually be closer to 0. 866 00:41:27,600 --> 00:41:30,020 If you're depending on the cost structure and the spread 867 00:41:30,020 --> 00:41:32,520 penalties, you will be able to convert 868 00:41:32,520 --> 00:41:35,160 some of the drivers that are peak to spread-- 869 00:41:35,160 --> 00:41:36,390 to a non-spread shift. 870 00:41:36,390 --> 00:41:39,570 So you'll get straight shifts from these drivers. 871 00:41:39,570 --> 00:41:42,210 And that may actually compensate so much 872 00:41:42,210 --> 00:41:45,050 that it's a free conversion. 873 00:41:48,050 --> 00:41:54,476 So what about decreases in off-peak period service? 874 00:41:58,940 --> 00:42:03,020 So now we are actually decreasing the off-peak 875 00:42:03,020 --> 00:42:05,400 and leaving everything the same. 876 00:42:05,400 --> 00:42:08,840 So what two things happen? 877 00:42:08,840 --> 00:42:10,940 Presumably, off-peak services are straight runs. 878 00:42:10,940 --> 00:42:12,380 They're not spread. 879 00:42:12,380 --> 00:42:15,710 So if you remove those but keep the peak level 880 00:42:15,710 --> 00:42:19,430 operation the same, then for any of those that you remove, 881 00:42:19,430 --> 00:42:20,030 you have to-- 882 00:42:20,030 --> 00:42:20,685 AUDIENCE: Add in the most expensive-- 883 00:42:20,685 --> 00:42:23,330 GABRIEL SANCHEZ-MARTINEZ: --add in the most expensive ones. 884 00:42:23,330 --> 00:42:25,785 So what is the net effect? 885 00:42:25,785 --> 00:42:26,660 AUDIENCE: Adding $15. 886 00:42:29,495 --> 00:42:31,120 GABRIEL SANCHEZ-MARTINEZ: It's probably 887 00:42:31,120 --> 00:42:36,629 going to be close to 0 again because of this effect. 888 00:42:36,629 --> 00:42:37,920 AUDIENCE: But can you explain-- 889 00:42:37,920 --> 00:42:39,628 GABRIEL SANCHEZ-MARTINEZ: And again, this 890 00:42:39,628 --> 00:42:42,234 depends on the specific costs for the labor agreement 891 00:42:42,234 --> 00:42:43,900 and the spread penalties and everything. 892 00:42:43,900 --> 00:42:45,590 But it gives you an idea. 893 00:42:45,590 --> 00:42:49,141 So if you only decrease off-peak service-- 894 00:42:49,141 --> 00:42:51,410 AUDIENCE: You're getting rid of those. 895 00:42:51,410 --> 00:42:53,785 GABRIEL SANCHEZ-MARTINEZ: --then you have to remove a few 896 00:42:53,785 --> 00:42:56,950 of the straight runs and not pay them the full day, 897 00:42:56,950 --> 00:42:58,610 but you have to then get-- 898 00:42:58,610 --> 00:43:03,830 you have to convert some of the existing spread runs to-- 899 00:43:03,830 --> 00:43:05,230 AUDIENCE: [INAUDIBLE] straight. 900 00:43:05,230 --> 00:43:07,810 GABRIEL SANCHEZ-MARTINEZ: --from straight to spread. 901 00:43:07,810 --> 00:43:10,900 AUDIENCE: Well wait, why is it at a cost of 0 then? 902 00:43:10,900 --> 00:43:12,850 GABRIEL SANCHEZ-MARTINEZ: Because you-- 903 00:43:12,850 --> 00:43:17,820 even though you are reducing the number of driver hours, 904 00:43:17,820 --> 00:43:21,430 you will increase the proportion of the most expensive ones 905 00:43:21,430 --> 00:43:22,954 only in the peak. 906 00:43:22,954 --> 00:43:25,120 AUDIENCE: So you might not wind up saving any money. 907 00:43:25,120 --> 00:43:25,980 GABRIEL SANCHEZ-MARTINEZ: Exactly. 908 00:43:25,980 --> 00:43:27,939 AUDIENCE: Where would you put it in the matrix? 909 00:43:27,939 --> 00:43:30,230 GABRIEL SANCHEZ-MARTINEZ: Well, it's not in the matrix. 910 00:43:30,230 --> 00:43:32,560 But if anything, you would look at off-peak minimum. 911 00:43:32,560 --> 00:43:34,826 But it's going to be in the range of 0 to 30. 912 00:43:34,826 --> 00:43:36,700 And again, depending on the specific numbers, 913 00:43:36,700 --> 00:43:39,670 it could even be that you have to pay more. 914 00:43:39,670 --> 00:43:41,377 Or many things can happen. 915 00:43:41,377 --> 00:43:42,210 [INTERPOSING VOICES] 916 00:43:42,210 --> 00:43:44,585 AUDIENCE: --thinking it was going to be like the occupant 917 00:43:44,585 --> 00:43:45,907 minimum and the peak maximum. 918 00:43:45,907 --> 00:43:47,740 GABRIEL SANCHEZ-MARTINEZ: Yeah, it could be. 919 00:43:47,740 --> 00:43:49,240 That's a good idea. 920 00:43:49,240 --> 00:43:51,010 But again, it depends on the specifics. 921 00:43:51,010 --> 00:43:53,480 And this is a cost model that isn't so precise. 922 00:43:55,774 --> 00:43:57,940 AUDIENCE: You're saying, because you're not actually 923 00:43:57,940 --> 00:44:00,370 increasing peak service, but you're proportionally 924 00:44:00,370 --> 00:44:01,210 increasing it. 925 00:44:01,210 --> 00:44:02,140 GABRIEL SANCHEZ-MARTINEZ: Not proportionally, we're 926 00:44:02,140 --> 00:44:04,300 just decreasing the off-peak and not touching the peak. 927 00:44:04,300 --> 00:44:06,466 AUDIENCE: OK, but then, I mean, proportionally, more 928 00:44:06,466 --> 00:44:07,820 of your hours are on the peak. 929 00:44:07,820 --> 00:44:08,800 GABRIEL SANCHEZ-MARTINEZ: Yes, exactly. 930 00:44:08,800 --> 00:44:09,680 AUDIENCE: [INAUDIBLE] 931 00:44:09,680 --> 00:44:12,141 GABRIEL SANCHEZ-MARTINEZ: Exactly, yeah. 932 00:44:12,141 --> 00:44:12,640 All right-- 933 00:44:12,640 --> 00:44:13,990 AUDIENCE: [INAUDIBLE] 934 00:44:15,340 --> 00:44:17,780 GABRIEL SANCHEZ-MARTINEZ: So that was a good. 935 00:44:17,780 --> 00:44:19,180 There's a mistake in this slide. 936 00:44:19,180 --> 00:44:19,960 Please fix it. 937 00:44:19,960 --> 00:44:21,510 It says here, "see page 8." 938 00:44:21,510 --> 00:44:22,870 It should be, "see page 6." 939 00:44:25,650 --> 00:44:29,630 OK, so from page six, the total fixed cost to be allocated 940 00:44:29,630 --> 00:44:34,730 is $44.6 million. 941 00:44:34,730 --> 00:44:37,770 And that is the sum of-- 942 00:44:37,770 --> 00:44:39,472 we want to allocate fixed costs. 943 00:44:39,472 --> 00:44:40,930 So that is the sum of all the fixed 944 00:44:40,930 --> 00:44:42,460 costs that appear on page six. 945 00:44:42,460 --> 00:44:45,790 There's 5.7, 3, and 35.9. 946 00:44:45,790 --> 00:44:48,970 That adds up to 44.6. 947 00:44:48,970 --> 00:44:54,380 And now we have here number of buses operating on the peak, 948 00:44:54,380 --> 00:44:56,330 on the base, on the evening, Saturday 949 00:44:56,330 --> 00:44:58,250 and Sunday, the number of hours-- 950 00:44:58,250 --> 00:45:01,820 so peak average, 4.5, 6 base hours, 951 00:45:01,820 --> 00:45:06,050 4 evening hours for a total of 14.5 hours per week day, 952 00:45:06,050 --> 00:45:10,010 12 hours operating Saturday, 12 hours operating Sunday. 953 00:45:10,010 --> 00:45:12,470 And the objective of this model is 954 00:45:12,470 --> 00:45:16,310 to take the fixed costs incurred by the agency 955 00:45:16,310 --> 00:45:22,460 and allocate them to vehicle hours. 956 00:45:22,460 --> 00:45:24,180 So let's do that. 957 00:45:24,180 --> 00:45:25,620 We have to do this allocation. 958 00:45:25,620 --> 00:45:29,690 And we can start with-- 959 00:45:29,690 --> 00:45:32,720 one way of looking at this is, these evening buses, 960 00:45:32,720 --> 00:45:36,440 250 evening buses are also operating in the base 961 00:45:36,440 --> 00:45:38,840 and in the peak. 962 00:45:38,840 --> 00:45:41,720 Then there's an additional 125 buses 963 00:45:41,720 --> 00:45:46,410 that are operating only in the base and at Saturdays, 964 00:45:46,410 --> 00:45:48,360 during Saturdays. 965 00:45:48,360 --> 00:45:50,760 And then there's an additional 400 buses 966 00:45:50,760 --> 00:45:54,640 that are operating only in the peak during the weekday. 967 00:45:54,640 --> 00:46:00,450 So let's allocate costs to the 250, the additional 125, 968 00:46:00,450 --> 00:46:04,330 and the additional 400 according to how long they operate 969 00:46:04,330 --> 00:46:07,300 and how much it costs based on the unit costs 970 00:46:07,300 --> 00:46:10,370 that we calculated in this example. 971 00:46:10,370 --> 00:46:15,760 So we start with 250 buses across all time periods. 972 00:46:15,760 --> 00:46:18,100 What's the share of fixed cost to be allocated to them? 973 00:46:18,100 --> 00:46:19,040 It's 32%. 974 00:46:19,040 --> 00:46:22,150 It's 250 buses divided by the total number 975 00:46:22,150 --> 00:46:24,580 of buses, which is 775. 976 00:46:24,580 --> 00:46:26,520 That's 32%. 977 00:46:26,520 --> 00:46:29,660 32% of the total cost is $14.4 million. 978 00:46:29,660 --> 00:46:33,970 That's how much money we want to allocate to these buses. 979 00:46:33,970 --> 00:46:37,610 And how many bus hours are operated in the whole year? 980 00:46:37,610 --> 00:46:40,180 Well, there's 250 buses. 981 00:46:40,180 --> 00:46:42,580 And we want to add up the hours operated 982 00:46:42,580 --> 00:46:45,040 during weekdays, during Saturdays, and during Sundays 983 00:46:45,040 --> 00:46:46,070 for the whole week. 984 00:46:46,070 --> 00:46:48,410 So there are roughly 250 weekdays 985 00:46:48,410 --> 00:46:51,460 in a year, 58 Saturdays, and 57 Sundays. 986 00:46:51,460 --> 00:46:54,010 Those add up to 365 days. 987 00:46:54,010 --> 00:46:56,810 And there are 14.5 hours during the weekday 988 00:46:56,810 --> 00:46:58,570 and 12 on the weekends. 989 00:46:58,570 --> 00:46:59,795 So we add those up. 990 00:46:59,795 --> 00:47:01,690 We multiply by the number of buses. 991 00:47:01,690 --> 00:47:08,560 And we get 1.25 million bus hours for the whole year. 992 00:47:08,560 --> 00:47:13,360 And if we divide the $14.4 million 993 00:47:13,360 --> 00:47:17,500 by 1.25 million bus hours, we get an average cost 994 00:47:17,500 --> 00:47:20,650 per bus hour of $11.52. 995 00:47:20,650 --> 00:47:24,430 And that's the base, which is the only thing that applies 996 00:47:24,430 --> 00:47:26,290 in the evening and Sundays. 997 00:47:26,290 --> 00:47:28,540 And it is a portion of what applies 998 00:47:28,540 --> 00:47:33,080 in Saturday, weekday days, and peak, so only a portion. 999 00:47:33,080 --> 00:47:37,420 So now let's move to the next 125 buses 1000 00:47:37,420 --> 00:47:41,890 operating on all time periods except Sundays and weekday 1001 00:47:41,890 --> 00:47:43,060 evenings. 1002 00:47:43,060 --> 00:47:45,820 So how much money do we have to allocate? 1003 00:47:45,820 --> 00:47:51,250 The $44.6 million total divided by the additional 125 buses 1004 00:47:51,250 --> 00:47:53,110 divided by the total number of buses. 1005 00:47:53,110 --> 00:47:55,930 That's $7.2 million. 1006 00:47:55,930 --> 00:48:00,040 How many total bus hours are operated by those 125 buses? 1007 00:48:00,040 --> 00:48:05,200 Well, this is 10.5 hours excluding 1008 00:48:05,200 --> 00:48:10,210 the evening during the weekdays times 250 weekdays plus the 12 1009 00:48:10,210 --> 00:48:13,390 hours on Saturdays times the 58 Saturdays. 1010 00:48:13,390 --> 00:48:16,630 So that's 0.42 million bus hours. 1011 00:48:16,630 --> 00:48:23,260 And 7.2 divided by 0.42 is $17.14 average cost 1012 00:48:23,260 --> 00:48:24,220 per bus hour. 1013 00:48:24,220 --> 00:48:25,355 Do you follow? 1014 00:48:25,355 --> 00:48:27,350 Any questions on this? 1015 00:48:27,350 --> 00:48:29,350 OK, now let's do the peak. 1016 00:48:29,350 --> 00:48:31,210 That's the most expensive part. 1017 00:48:31,210 --> 00:48:33,690 So how much do we have to allocate? 1018 00:48:33,690 --> 00:48:34,750 It's $23 million. 1019 00:48:34,750 --> 00:48:35,770 How do we get that? 1020 00:48:35,770 --> 00:48:44,800 44.6 total times 400 divided by 725. 1021 00:48:44,800 --> 00:48:47,950 And how many annual bus hours do we need to-- 1022 00:48:47,950 --> 00:48:49,600 do we operate during the peak? 1023 00:48:49,600 --> 00:48:54,130 It's 400 additional buses only in the peak times 4.5 hours 1024 00:48:54,130 --> 00:48:57,310 of the peak times 250 weekdays. 1025 00:48:57,310 --> 00:49:00,610 And that's 0.45 million hours. 1026 00:49:00,610 --> 00:49:07,270 And 23 million by 0.45 is $51.11 average cost 1027 00:49:07,270 --> 00:49:10,110 per bus hour, or per peak bus hour, in this case. 1028 00:49:10,110 --> 00:49:17,560 OK, so now we have unit costs for peak, for the base, 1029 00:49:17,560 --> 00:49:21,430 and then the off-peak, for the evenings' and Sundays' 1030 00:49:21,430 --> 00:49:24,110 operation, which is great. 1031 00:49:24,110 --> 00:49:29,530 So the variable vehicle cost was $37.13. 1032 00:49:29,530 --> 00:49:32,020 We had calculated that from the previous model 1033 00:49:32,020 --> 00:49:34,030 that you can find on page six. 1034 00:49:34,030 --> 00:49:37,870 And now we can adjust these costs 1035 00:49:37,870 --> 00:49:41,150 by time period, which is what we want to do. 1036 00:49:41,150 --> 00:49:44,540 We want to have a model that is sensitive to time periods. 1037 00:49:44,540 --> 00:49:50,320 So for Sunday evening service, we will increase the $37.13 1038 00:49:50,320 --> 00:49:52,750 by $11.52. 1039 00:49:52,750 --> 00:49:54,670 For Saturday and weekday service, 1040 00:49:54,670 --> 00:49:58,690 we want to increase the cost, the base cost of $37.13, 1041 00:49:58,690 --> 00:50:01,300 by $13.97. 1042 00:50:01,300 --> 00:50:07,420 And for weekday peak, we want to increase it by $32.86. 1043 00:50:07,420 --> 00:50:11,110 And notice that when we look at Saturday and weekday, 1044 00:50:11,110 --> 00:50:13,630 we have to combine the two unit costs, 1045 00:50:13,630 --> 00:50:18,280 because we have a portion of Saturday 1046 00:50:18,280 --> 00:50:23,410 and weekday-based service is from the first 375 buses. 1047 00:50:23,410 --> 00:50:25,990 And the portion of it is from the additional more expensive 1048 00:50:25,990 --> 00:50:27,540 125 buses. 1049 00:50:27,540 --> 00:50:29,560 And when we do peak, the same thing applies. 1050 00:50:29,560 --> 00:50:35,590 So we start with the 250 base buses at $11.52. 1051 00:50:35,590 --> 00:50:38,260 Then we have 125 at $17.14. 1052 00:50:38,260 --> 00:50:40,510 And then we have the peak of the peak buses, which 1053 00:50:40,510 --> 00:50:43,570 are 400 times the unit cost for those buses, which 1054 00:50:43,570 --> 00:50:45,230 is much higher. 1055 00:50:45,230 --> 00:50:47,740 And that's the total cost, the total unit cost 1056 00:50:47,740 --> 00:50:51,230 for a weekday peak service. 1057 00:50:51,230 --> 00:50:52,010 Questions on this? 1058 00:50:55,090 --> 00:50:56,235 You have a question, Eli? 1059 00:50:58,810 --> 00:51:00,310 This is all sort of written here. 1060 00:51:00,310 --> 00:51:04,820 And all the numbers are copied from previous slides, 1061 00:51:04,820 --> 00:51:07,220 so you should be able to follow this on your own 1062 00:51:07,220 --> 00:51:08,601 if you're a little lost. 1063 00:51:08,601 --> 00:51:10,100 But if not, come see me after class, 1064 00:51:10,100 --> 00:51:12,130 then we can talk about it. 1065 00:51:12,130 --> 00:51:14,440 OK, so now let's compare the models. 1066 00:51:14,440 --> 00:51:17,020 We started out with a very traditional simple model, 1067 00:51:17,020 --> 00:51:21,370 and the first one we gave, which was full annual cost. 1068 00:51:21,370 --> 00:51:24,970 And it had this factor which accounted for the fact 1069 00:51:24,970 --> 00:51:28,780 that we weren't including the peak vehicle, the costs 1070 00:51:28,780 --> 00:51:30,730 associated with peak vehicles. 1071 00:51:30,730 --> 00:51:33,610 So that was the first example. 1072 00:51:33,610 --> 00:51:37,990 We also had in that page a variable cost model, which 1073 00:51:37,990 --> 00:51:39,780 only accounts for variable costs, 1074 00:51:39,780 --> 00:51:42,340 so it excludes fixed costs. 1075 00:51:42,340 --> 00:51:44,920 And now we can look at the peak period model 1076 00:51:44,920 --> 00:51:46,150 and off-peak period model. 1077 00:51:46,150 --> 00:51:57,790 So we make an adjustment to the first model, which-- 1078 00:51:57,790 --> 00:52:01,700 to this variable cost model with the unit 1079 00:52:01,700 --> 00:52:02,920 cost that we just calculated. 1080 00:52:02,920 --> 00:52:08,800 So if we take the $37.13 of revenue vehicle hours 1081 00:52:08,800 --> 00:52:11,200 that was in our initial variable cost model 1082 00:52:11,200 --> 00:52:17,590 and we add the unit cost for peak revenue hours, 1083 00:52:17,590 --> 00:52:26,360 which is $32.86 from right here-- 1084 00:52:26,360 --> 00:52:30,200 so that's the weekday peak service unit cost-- 1085 00:52:30,200 --> 00:52:34,370 then we get $69.99. 1086 00:52:34,370 --> 00:52:38,570 Now that becomes our unit cost in the peak. 1087 00:52:38,570 --> 00:52:46,280 And we have the 2.41. 1088 00:52:46,280 --> 00:52:48,810 Give me a second here. 1089 00:52:48,810 --> 00:52:51,600 That comes from page six directly, I believe. 1090 00:52:54,430 --> 00:52:58,530 Yes, so that's the combination of 2.27 and 0.14. 1091 00:52:58,530 --> 00:53:03,960 Because we're not counting the temporal difference 1092 00:53:03,960 --> 00:53:06,830 on peak vehicle or revenue vehicle miles. 1093 00:53:06,830 --> 00:53:10,310 We're only doing it for revenue vehicle hours. 1094 00:53:10,310 --> 00:53:11,810 It's for driver cost. 1095 00:53:11,810 --> 00:53:14,730 And driver costs were associated with hours, not miles. 1096 00:53:14,730 --> 00:53:17,770 So that stays the same. 1097 00:53:17,770 --> 00:53:21,450 So this is our full annual peak cost model. 1098 00:53:21,450 --> 00:53:24,810 And if we want to increase peak-only service, 1099 00:53:24,810 --> 00:53:26,550 we use this model, not the other one. 1100 00:53:26,550 --> 00:53:28,980 And it will reflect more faithfully 1101 00:53:28,980 --> 00:53:31,032 what the costs will be. 1102 00:53:31,032 --> 00:53:32,740 We can do the same with off-peak service. 1103 00:53:32,740 --> 00:53:37,140 So we take the $37.13. 1104 00:53:37,140 --> 00:53:42,060 And we can add the combination of the portion of it 1105 00:53:42,060 --> 00:53:46,170 that is $11.52 and the portion of it that is $13.97. 1106 00:53:46,170 --> 00:53:47,290 Let's do that. 1107 00:53:47,290 --> 00:53:49,162 So let me have-- 1108 00:53:49,162 --> 00:53:51,510 let's do that on the board so that we have the example. 1109 00:53:54,790 --> 00:54:17,440 So for off-peak period model, we start out 1110 00:54:17,440 --> 00:54:26,080 with the base cost of $37.13. 1111 00:54:26,080 --> 00:54:32,380 And then we add $11.52. 1112 00:54:32,380 --> 00:54:35,800 And that's going to apply only for the fraction 1113 00:54:35,800 --> 00:54:44,780 of off-peak hours that are sort of Sunday and weekday evening. 1114 00:54:44,780 --> 00:54:49,870 So if we go back to $11.52, this is Sunday and evening service 1115 00:54:49,870 --> 00:54:51,050 only. 1116 00:54:51,050 --> 00:54:53,630 So the question is, how many Sunday and evening service 1117 00:54:53,630 --> 00:54:55,020 hours are there in a whole year? 1118 00:55:00,830 --> 00:55:02,900 The proportion is this one that I'm writing here, 1119 00:55:02,900 --> 00:55:12,890 1684 divided by 3,880. 1120 00:55:12,890 --> 00:55:17,580 And I'll calculate that too in a second. 1121 00:55:17,580 --> 00:55:25,640 We also want to add the other cost, which is $13.97. 1122 00:55:25,640 --> 00:55:41,060 And the proportion of that is 2,196 divide by 3,880. 1123 00:55:41,060 --> 00:55:54,630 So that's 37.13 plus about 5 plus about 7.91. 1124 00:55:54,630 --> 00:56:01,800 And that comes out to 50.04. 1125 00:56:01,800 --> 00:56:09,210 OK, so where do we get 1,684 and 2,196 from? 1126 00:56:09,210 --> 00:56:10,710 It's similar to before, right? 1127 00:56:10,710 --> 00:56:12,960 We just count how many hours there are. 1128 00:56:12,960 --> 00:56:16,270 So let's just do it quickly here for the record. 1129 00:56:16,270 --> 00:56:20,820 So let's just compute the bottom one, actually. 1130 00:56:20,820 --> 00:56:22,650 And you'll get the idea for the others, 1131 00:56:22,650 --> 00:56:25,040 because it doesn't make sense to do all of them. 1132 00:56:25,040 --> 00:56:33,670 So off peak hours-- 1133 00:56:33,670 --> 00:56:41,700 so we have 10 off-peak hours in the weekday times 250 weekdays 1134 00:56:41,700 --> 00:56:44,550 per year plus-- 1135 00:56:44,550 --> 00:56:47,307 so this is weekdays-- 1136 00:56:50,440 --> 00:56:53,740 plus 12 hours on Saturdays. 1137 00:56:53,740 --> 00:56:55,210 And we said there are 7-- 1138 00:56:55,210 --> 00:56:56,770 or 58 Saturdays per year-- 1139 00:57:00,400 --> 00:57:05,220 plus 12 hours on Sundays, and we said 57 Sundays per year. 1140 00:57:08,210 --> 00:57:22,230 And that comes out to 3,880 hours. 1141 00:57:22,230 --> 00:57:28,122 So that's combinations of these to get the 1,684 and the 2,196. 1142 00:57:28,122 --> 00:57:29,460 Yeah? 1143 00:57:29,460 --> 00:57:34,050 AUDIENCE: So for the 1,684, that's 1144 00:57:34,050 --> 00:57:37,159 Sunday evening service, right? 1145 00:57:37,159 --> 00:57:39,200 GABRIEL SANCHEZ-MARTINEZ: Right, so yes, exactly. 1146 00:57:39,200 --> 00:57:41,500 So that's Sunday and evenings, right. 1147 00:57:41,500 --> 00:57:44,180 AUDIENCE: And then the other is Saturday and weekend base? 1148 00:57:44,180 --> 00:57:45,805 GABRIEL SANCHEZ-MARTINEZ: Yes, exactly. 1149 00:57:52,430 --> 00:57:55,550 So did people follow this allocation example? 1150 00:57:55,550 --> 00:57:59,570 So what we're doing is taking-- dividing the day into periods. 1151 00:57:59,570 --> 00:58:02,120 Some periods, we recognize are more expensive than others 1152 00:58:02,120 --> 00:58:03,020 throughout. 1153 00:58:06,080 --> 00:58:07,080 Now, we have fixed cost. 1154 00:58:07,080 --> 00:58:10,710 And we want to allocate them across periods. 1155 00:58:10,710 --> 00:58:13,220 And we want to allocate more cost to the peak, 1156 00:58:13,220 --> 00:58:15,440 because that sort of costs more. 1157 00:58:15,440 --> 00:58:20,840 So we then use these unit costs to-- 1158 00:58:20,840 --> 00:58:24,020 and we count how many hours we provide off-peak 1159 00:58:24,020 --> 00:58:25,040 and during the peak. 1160 00:58:25,040 --> 00:58:30,620 And we do things in proportions to that, essentially. 1161 00:58:30,620 --> 00:58:32,307 These are not the only cost models 1162 00:58:32,307 --> 00:58:33,390 that you can come up with. 1163 00:58:33,390 --> 00:58:35,840 These are not the only ways of allocating cost. 1164 00:58:35,840 --> 00:58:38,150 But they provide an example of how you 1165 00:58:38,150 --> 00:58:39,770 can go about allocating costs. 1166 00:58:39,770 --> 00:58:43,520 Allocating cost is a science. 1167 00:58:43,520 --> 00:58:44,450 It's also an art. 1168 00:58:44,450 --> 00:58:48,350 And you encounter it in agencies, 1169 00:58:48,350 --> 00:58:51,245 because you have these huge budgets, and huge expenditures. 1170 00:58:51,245 --> 00:58:55,400 And many projects require you to allocate to a portion 1171 00:58:55,400 --> 00:58:56,750 or allocate costs. 1172 00:58:56,750 --> 00:58:59,120 And if you want to have a cost model, you have to do it, 1173 00:58:59,120 --> 00:59:01,240 because your cost model should reflect 1174 00:59:01,240 --> 00:59:07,980 these different variables, explanatory variables. 1175 00:59:07,980 --> 00:59:10,830 The third and last type of model that we are going to discuss 1176 00:59:10,830 --> 00:59:16,500 is the incremental fixed variable model. 1177 00:59:16,500 --> 00:59:19,120 It's somewhat similar to the ones that we saw before, 1178 00:59:19,120 --> 00:59:24,540 but now we classify costs as being variable, semi-variable, 1179 00:59:24,540 --> 00:59:26,080 and fixed. 1180 00:59:26,080 --> 00:59:29,235 So we have a little more 1181 00:59:29,235 --> 00:59:30,570 AUDIENCE: [INAUDIBLE] 1182 00:59:30,570 --> 00:59:31,200 GABRIEL SANCHEZ-MARTINEZ: --precision-- 1183 00:59:31,200 --> 00:59:33,180 AUDIENCE: ----[INAUDIBLE] marked by-- 1184 00:59:33,180 --> 00:59:36,500 GABRIEL SANCHEZ-MARTINEZ: --a little more precision in how-- 1185 00:59:36,500 --> 00:59:38,940 in what we consider fixed or variable. 1186 00:59:38,940 --> 00:59:40,830 We also have the same explanatory variables 1187 00:59:40,830 --> 00:59:43,280 that we had before, so vehicle hours, vehicle miles, 1188 00:59:43,280 --> 00:59:44,850 and peak vehicles. 1189 00:59:44,850 --> 00:59:47,480 So now, the combination of these are 1190 00:59:47,480 --> 00:59:50,350 nine different explanatory variables. 1191 00:59:50,350 --> 00:59:53,760 And we do the same thing as we have done before. 1192 00:59:53,760 --> 00:59:55,660 We have a schedule of expenses. 1193 00:59:55,660 --> 00:59:58,330 These are our accounts in your ledger, 1194 00:59:58,330 --> 01:00:01,230 so crew wages, vehicle servicing, fuel, tires, 1195 01:00:01,230 --> 01:00:05,460 insurance, traffic stuff, things like publicity, and rent, 1196 01:00:05,460 --> 01:00:06,510 and building maintenance. 1197 01:00:06,510 --> 01:00:07,676 Everything is included here. 1198 01:00:07,676 --> 01:00:11,220 So all of your budget is going to fall into some category. 1199 01:00:11,220 --> 01:00:12,960 It's divided among these categories. 1200 01:00:12,960 --> 01:00:21,030 So now you decide, for each of these, 1201 01:00:21,030 --> 01:00:23,040 which of these three resources apply 1202 01:00:23,040 --> 01:00:26,340 and which cost type you consider this to be. 1203 01:00:26,340 --> 01:00:29,000 So for example, crew wages, let's associate 1204 01:00:29,000 --> 01:00:30,870 that with bus hours, as we did before. 1205 01:00:30,870 --> 01:00:32,820 And that's fully variable. 1206 01:00:32,820 --> 01:00:35,520 So that, we should feel comfortable with. 1207 01:00:35,520 --> 01:00:41,380 Things like building utilities, that shouldn't be variable. 1208 01:00:41,380 --> 01:00:42,400 So that's a fixed cost. 1209 01:00:42,400 --> 01:00:44,108 And we'll associate that with peak buses, 1210 01:00:44,108 --> 01:00:46,420 because peak buses is the one that we 1211 01:00:46,420 --> 01:00:49,780 say is a good proxy for how big the agency is. 1212 01:00:49,780 --> 01:00:54,590 So peak buses is, again, like agency size, if you will. 1213 01:00:54,590 --> 01:00:57,050 So then there are things in the middle. 1214 01:00:57,050 --> 01:01:01,930 So publicity, well, semi-variable, because if you-- 1215 01:01:01,930 --> 01:01:03,970 so the extent that you increase service, 1216 01:01:03,970 --> 01:01:06,345 there is going to be some amount of additional publicity. 1217 01:01:06,345 --> 01:01:09,430 It's not going to be necessarily a linear proportion 1218 01:01:09,430 --> 01:01:12,590 increase with as you-- you know, we add one more bus, 1219 01:01:12,590 --> 01:01:18,760 then you have that much more marketing or publicity expense. 1220 01:01:18,760 --> 01:01:21,850 Some of those expenses are having an office and staff, so 1221 01:01:21,850 --> 01:01:24,730 some salaries, so that portion is fixed. 1222 01:01:24,730 --> 01:01:26,530 But then there is extra space that you 1223 01:01:26,530 --> 01:01:30,020 have to cover on each additional bus, so that part is variable. 1224 01:01:30,020 --> 01:01:32,320 So now we have a semi-variable cost. 1225 01:01:32,320 --> 01:01:37,270 And you can associate that, in this case, with peak buses, 1226 01:01:37,270 --> 01:01:39,460 because for each peak bus you have, then 1227 01:01:39,460 --> 01:01:43,990 that's how many buses you have to plaster with ads. 1228 01:01:43,990 --> 01:01:45,730 That gives you an example. 1229 01:01:45,730 --> 01:01:47,800 So you can go through each of these. 1230 01:01:47,800 --> 01:01:50,830 Again, this requires judgment, and therefore, each person 1231 01:01:50,830 --> 01:01:52,450 may do it slightly differently. 1232 01:01:52,450 --> 01:01:55,930 But you use a schedule. 1233 01:01:55,930 --> 01:01:59,200 And you then build your-- 1234 01:01:59,200 --> 01:02:01,300 you calculate your unit costs, much like we 1235 01:02:01,300 --> 01:02:03,370 did with the earlier examples. 1236 01:02:03,370 --> 01:02:04,959 And you then apply the model. 1237 01:02:04,959 --> 01:02:06,250 But now we have more precision. 1238 01:02:06,250 --> 01:02:12,190 So if you have some kind of new expense, 1239 01:02:12,190 --> 01:02:15,220 or you decide you're going to save some money somehow, 1240 01:02:15,220 --> 01:02:18,490 then you decide, what-- how am I going 1241 01:02:18,490 --> 01:02:20,740 to spend less or spend more? 1242 01:02:20,740 --> 01:02:23,481 Would that be a variable, semi-variable, or fixed cost? 1243 01:02:23,481 --> 01:02:25,855 Would I associate that with vehicle hours, vehicle miles, 1244 01:02:25,855 --> 01:02:27,310 or peak vehicles? 1245 01:02:27,310 --> 01:02:29,320 And then you would use that unit cost 1246 01:02:29,320 --> 01:02:35,800 to bring the total costs up or down from the agency. 1247 01:02:35,800 --> 01:02:38,080 Even more detailed models, you could just 1248 01:02:38,080 --> 01:02:43,840 go by expense category and do your engineering-style sort 1249 01:02:43,840 --> 01:02:47,170 of budget if you want to really calculate 1250 01:02:47,170 --> 01:02:48,670 exactly how much cost you'll save, 1251 01:02:48,670 --> 01:02:53,240 or exactly how much extra cost you'll incur. 1252 01:02:53,240 --> 01:02:56,750 But these cost models are applied more-- 1253 01:02:56,750 --> 01:02:59,360 a little more bluntly in projects 1254 01:02:59,360 --> 01:03:01,250 where you are evaluating, especially 1255 01:03:01,250 --> 01:03:03,775 at an early stage, what it would cost. 1256 01:03:03,775 --> 01:03:05,150 And you have different scenarios. 1257 01:03:05,150 --> 01:03:08,832 And you want to quickly know how much it would cost. 1258 01:03:08,832 --> 01:03:11,550 OK, so questions on cost modeling? 1259 01:03:16,480 --> 01:03:17,710 No questions on cost-- 1260 01:03:17,710 --> 01:03:18,680 yeah, one question? 1261 01:03:18,680 --> 01:03:23,330 AUDIENCE: So in this case, you would have more reliability 1262 01:03:23,330 --> 01:03:28,040 on the proportion of each expense assigned 1263 01:03:28,040 --> 01:03:29,044 to each category? 1264 01:03:29,044 --> 01:03:30,710 GABRIEL SANCHEZ-MARTINEZ: Yeah, so you-- 1265 01:03:30,710 --> 01:03:33,620 essentially, you're lumping things a little less. 1266 01:03:33,620 --> 01:03:34,650 You have more variables. 1267 01:03:34,650 --> 01:03:36,545 So your unit costs are more precise. 1268 01:03:40,450 --> 01:03:45,070 And I think the ability to move to more sophisticated models 1269 01:03:45,070 --> 01:03:49,680 is increasing now that everything is computer-based. 1270 01:03:49,680 --> 01:03:51,680 [INAUDIBLE], you had a question? 1271 01:03:51,680 --> 01:03:52,600 AUDIENCE: [INAUDIBLE] 1272 01:03:53,365 --> 01:03:54,240 AUDIENCE: [INAUDIBLE] 1273 01:03:54,240 --> 01:03:54,906 GABRIEL SANCHEZ-MARTINEZ: Oh, the three of you 1274 01:03:54,906 --> 01:03:55,910 had a question. 1275 01:03:55,910 --> 01:03:56,640 No, not you? 1276 01:03:56,640 --> 01:03:57,140 OK. 1277 01:03:57,140 --> 01:03:57,610 AUDIENCE: I had a question. 1278 01:03:57,610 --> 01:03:58,570 GABRIEL SANCHEZ-MARTINEZ: OK, Ethan. 1279 01:03:58,570 --> 01:04:00,550 AUDIENCE: Back on Slide 11, you said 1280 01:04:00,550 --> 01:04:04,210 it's possible that reducing driver 1281 01:04:04,210 --> 01:04:09,790 hours in off-peak periods might have no effect 1282 01:04:09,790 --> 01:04:12,310 or could even potentially actually increase costs. 1283 01:04:12,310 --> 01:04:14,650 AUDIENCE: It could-- well, yeah, it shouldn't increase. 1284 01:04:14,650 --> 01:04:15,940 It shouldn't increase costs. 1285 01:04:15,940 --> 01:04:18,190 AUDIENCE: Well, I was going to ask, is there-- 1286 01:04:18,190 --> 01:04:20,875 is it ever the case that off-peak service, when 1287 01:04:20,875 --> 01:04:24,010 there is really low demand, exists simply 1288 01:04:24,010 --> 01:04:26,440 for the convenience of scheduling shifts rather 1289 01:04:26,440 --> 01:04:30,867 than meeting maximum headways, or anything like that? 1290 01:04:30,867 --> 01:04:32,450 GABRIEL SANCHEZ-MARTINEZ: Potentially, 1291 01:04:32,450 --> 01:04:36,020 but because driver costs are not the only cost of operating 1292 01:04:36,020 --> 01:04:40,670 service, you would then also agree to spend extra fuel 1293 01:04:40,670 --> 01:04:42,390 and extra maintenance costs. 1294 01:04:42,390 --> 01:04:47,600 And that is also a significant portion of a cost. 1295 01:04:47,600 --> 01:04:48,920 It's not just free. 1296 01:04:48,920 --> 01:04:51,920 Or it's only-- only this part may be free, 1297 01:04:51,920 --> 01:04:53,735 not the whole thing. 1298 01:04:53,735 --> 01:04:57,860 But yeah, I think, if you find yourself in a situation 1299 01:04:57,860 --> 01:05:04,790 where your labor agreement requires you to have-- 1300 01:05:04,790 --> 01:05:07,430 maybe there is a cap on how much spread you can have. 1301 01:05:07,430 --> 01:05:08,930 So you have all these straight runs. 1302 01:05:08,930 --> 01:05:11,390 And they're only working for four hours. 1303 01:05:11,390 --> 01:05:15,500 And then you say, well, you know, let's add service. 1304 01:05:15,500 --> 01:05:18,530 And let's make the off-peak service very good. 1305 01:05:18,530 --> 01:05:21,170 So yeah, that could happen, but it's a management decision. 1306 01:05:21,170 --> 01:05:22,780 That's not something with the science. 1307 01:05:22,780 --> 01:05:27,060 It's a policy managerial decision. 1308 01:05:27,060 --> 01:05:28,980 Yeah? 1309 01:05:28,980 --> 01:05:32,076 AUDIENCE: On the last slide when you were talking about peak 1310 01:05:32,076 --> 01:05:34,940 buses, if we're decreasing [INAUDIBLE],, 1311 01:05:34,940 --> 01:05:36,450 is it indicative of agency size? 1312 01:05:36,450 --> 01:05:37,700 GABRIEL SANCHEZ-MARTINEZ: Yes. 1313 01:05:37,700 --> 01:05:40,640 So in this example, we only have three-- 1314 01:05:40,640 --> 01:05:42,420 well, we have nine exploratory variables, 1315 01:05:42,420 --> 01:05:45,500 which are the combination of the three resource variables 1316 01:05:45,500 --> 01:05:46,710 and the three cost types. 1317 01:05:46,710 --> 01:05:49,970 But if you go back to the first example in this lecture, 1318 01:05:49,970 --> 01:05:52,250 we had three explanatory variables-- bus hours, 1319 01:05:52,250 --> 01:05:53,910 bus miles, and peak buses. 1320 01:05:53,910 --> 01:05:56,910 And we have to assign everything to one of these three. 1321 01:05:56,910 --> 01:06:03,260 So of those three, peak buses is something 1322 01:06:03,260 --> 01:06:07,820 that most closely relates to how large your agency is, much more 1323 01:06:07,820 --> 01:06:10,350 so than bus hours or bus miles. 1324 01:06:10,350 --> 01:06:13,100 And if you had other variables, then 1325 01:06:13,100 --> 01:06:15,980 maybe those would be even closer to agency size. 1326 01:06:15,980 --> 01:06:18,960 But in this example, we only have these three-- 1327 01:06:18,960 --> 01:06:19,460 yeah. 1328 01:06:22,730 --> 01:06:24,170 And why peak buses? 1329 01:06:24,170 --> 01:06:25,760 Well, because if you have more buses, 1330 01:06:25,760 --> 01:06:27,510 you need a bigger parking garage for them. 1331 01:06:27,510 --> 01:06:30,920 You need a bigger refueling and maintenance facility. 1332 01:06:30,920 --> 01:06:33,050 You might need more mechanics and more-- right? 1333 01:06:33,050 --> 01:06:36,200 So the many costs that are mostly 1334 01:06:36,200 --> 01:06:37,970 fixed scale up with how many vehicles 1335 01:06:37,970 --> 01:06:43,390 you have on your garage, and how many garages you 1336 01:06:43,390 --> 01:06:46,790 have, and all those things. 1337 01:06:46,790 --> 01:06:49,360 Another detail which I want to emphasize 1338 01:06:49,360 --> 01:06:52,310 is that, with regards to the variable 1339 01:06:52,310 --> 01:06:56,380 and fixed, so again, if you have to incur an expense that 1340 01:06:56,380 --> 01:07:00,350 is more marginal, then you might want to use a variable cost 1341 01:07:00,350 --> 01:07:06,170 model, because you may not need another garage, for example, 1342 01:07:06,170 --> 01:07:08,390 for a few extra buses. 1343 01:07:08,390 --> 01:07:10,670 But at some point, you do incur on-- 1344 01:07:10,670 --> 01:07:13,790 you reach an investment threshold, where, well, 1345 01:07:13,790 --> 01:07:15,860 now you've crossed the line. 1346 01:07:15,860 --> 01:07:19,250 And you do need an extra facility. 1347 01:07:19,250 --> 01:07:22,149 And you have to hire people to run the facility. 1348 01:07:22,149 --> 01:07:23,690 And that's going to be-- that's going 1349 01:07:23,690 --> 01:07:25,230 to increase your fixed cost. 1350 01:07:25,230 --> 01:07:30,320 So that happens in lumpy fashion rather than variable 1351 01:07:30,320 --> 01:07:33,106 and scaling up [INAUDIBLE]. 1352 01:07:33,106 --> 01:07:34,480 We have an additional 10 minutes. 1353 01:07:34,480 --> 01:07:36,750 And maybe it would be a good opportunity 1354 01:07:36,750 --> 01:07:40,350 to discuss the first assignment, which 1355 01:07:40,350 --> 01:07:42,910 I have not finished grading. 1356 01:07:42,910 --> 01:07:44,080 I'm sorry about that. 1357 01:07:44,080 --> 01:07:46,170 I hope to have that back to you soon. 1358 01:07:46,170 --> 01:07:52,470 But we might as well go over it and just discuss the solution. 1359 01:07:52,470 --> 01:07:53,940 So let me switch to that. 1360 01:07:56,450 --> 01:08:01,080 OK, so does everybody remember the first assignment? 1361 01:08:01,080 --> 01:08:05,780 Or is that sort of back in your [INAUDIBLE]---- 1362 01:08:05,780 --> 01:08:10,090 you had some sample data in a spreadsheet. 1363 01:08:10,090 --> 01:08:12,260 And you had to calculate-- the first question was, 1364 01:08:12,260 --> 01:08:15,820 calculate statistics by direction. 1365 01:08:15,820 --> 01:08:22,640 So this is the spreadsheet, and time of day, and running time. 1366 01:08:22,640 --> 01:08:24,740 This data was given to you. 1367 01:08:24,740 --> 01:08:30,000 And I like to use the indirect function. 1368 01:08:30,000 --> 01:08:33,060 I don't know if people will know it or not, but it's convenient. 1369 01:08:33,060 --> 01:08:36,979 So if you type the range name in a cell, 1370 01:08:36,979 --> 01:08:40,660 then you can compute things as a function of that range name. 1371 01:08:40,660 --> 01:08:42,510 And that's very convenient. 1372 01:08:42,510 --> 01:08:48,580 So I selected the range B2 to B751. 1373 01:08:48,580 --> 01:08:51,260 And that corresponds to all the data 1374 01:08:51,260 --> 01:08:56,350 on this, all the data on this first sheet. 1375 01:08:56,350 --> 01:08:59,450 And then I did the same for direction, too. 1376 01:08:59,450 --> 01:09:01,279 So therefore, when I go to mean, I say, 1377 01:09:01,279 --> 01:09:03,590 equals average indirect of B4. 1378 01:09:03,590 --> 01:09:08,101 And I'm pointing the mean to the range, 1379 01:09:08,101 --> 01:09:09,350 which is a variable in itself. 1380 01:09:09,350 --> 01:09:10,399 That's very neat. 1381 01:09:10,399 --> 01:09:13,359 So you can do that for average mean, again, 1382 01:09:13,359 --> 01:09:17,240 min, max, and percentile, and then fill to the right, 1383 01:09:17,240 --> 01:09:20,850 because you have a different range here. 1384 01:09:20,850 --> 01:09:24,122 So it'll reflect that. 1385 01:09:24,122 --> 01:09:26,394 So it's a little trick. 1386 01:09:26,394 --> 01:09:27,560 So these are the statistics. 1387 01:09:27,560 --> 01:09:30,390 This was very straightforward. 1388 01:09:30,390 --> 01:09:33,459 Then Question 4, it starts getting more at transportation 1389 01:09:33,459 --> 01:09:35,540 itself. 1390 01:09:35,540 --> 01:09:36,960 This requires some judgment. 1391 01:09:36,960 --> 01:09:38,350 So we're saying, what's the running time? 1392 01:09:38,350 --> 01:09:39,425 What's the recovery time? 1393 01:09:39,425 --> 01:09:40,550 What's the half cycle time? 1394 01:09:40,550 --> 01:09:42,200 And what's the cycle time? 1395 01:09:42,200 --> 01:09:46,399 So running time should be something 1396 01:09:46,399 --> 01:09:48,470 that happens typically, because this is what 1397 01:09:48,470 --> 01:09:49,850 you publish on your schedule. 1398 01:09:49,850 --> 01:09:51,975 This is what's going to go on your journey planner. 1399 01:09:51,975 --> 01:09:55,460 So people need to know what to expect. 1400 01:09:55,460 --> 01:09:57,860 And therefore, running time should be based 1401 01:09:57,860 --> 01:09:59,300 on the average or the median. 1402 01:10:02,150 --> 01:10:06,030 Of these statistics, that you computed before, 1403 01:10:06,030 --> 01:10:08,390 these should be the two that you use. 1404 01:10:08,390 --> 01:10:11,150 I usually prefer the median, because the average 1405 01:10:11,150 --> 01:10:15,710 is affected by outliers and by heavy tails on the right 1406 01:10:15,710 --> 01:10:17,180 quite a bit. 1407 01:10:17,180 --> 01:10:21,050 So I usually go for the median, or the 50th percentile. 1408 01:10:21,050 --> 01:10:23,812 Recovery time-- so what is recovery time for? 1409 01:10:27,179 --> 01:10:28,460 AUDIENCE: For making up-- 1410 01:10:28,460 --> 01:10:30,410 well, first of all, so the drivers can go to the bathroom 1411 01:10:30,410 --> 01:10:31,600 and things like that [INAUDIBLE]---- 1412 01:10:31,600 --> 01:10:32,790 GABRIEL SANCHEZ-MARTINEZ: Sure, yeah. 1413 01:10:32,790 --> 01:10:34,880 AUDIENCE: --and then second of all, to make up 1414 01:10:34,880 --> 01:10:37,670 for problems in the schedule. 1415 01:10:37,670 --> 01:10:39,700 So say I'm driving out on this bus route. 1416 01:10:39,700 --> 01:10:42,242 And it takes me eight minutes longer than I thought it would. 1417 01:10:42,242 --> 01:10:44,408 GABRIEL SANCHEZ-MARTINEZ: I wouldn't characterize it 1418 01:10:44,408 --> 01:10:46,350 as a problem with the schedule per se, but-- 1419 01:10:46,350 --> 01:10:48,890 so the schedule is a deterministic decision 1420 01:10:48,890 --> 01:10:50,320 about how long it will take you. 1421 01:10:50,320 --> 01:10:53,015 And the reality is that the running time 1422 01:10:53,015 --> 01:10:54,530 is a stochastic variable. 1423 01:10:54,530 --> 01:10:56,420 It varies from run to run. 1424 01:10:56,420 --> 01:10:59,720 So you want to say-- 1425 01:10:59,720 --> 01:11:01,550 you want to make a claim about what 1426 01:11:01,550 --> 01:11:03,650 the typical running time is. 1427 01:11:03,650 --> 01:11:06,230 But then you have to have some recovery time to account 1428 01:11:06,230 --> 01:11:08,010 for anything later than that. 1429 01:11:08,010 --> 01:11:10,400 And you recognize-- it's a way of recognizing 1430 01:11:10,400 --> 01:11:12,800 that these running times are stochastic. 1431 01:11:12,800 --> 01:11:17,810 So the half cycle time is how much 1432 01:11:17,810 --> 01:11:19,700 time you budget for the run, including 1433 01:11:19,700 --> 01:11:20,990 those late ones, right? 1434 01:11:20,990 --> 01:11:24,190 So I set that to a high percentile, the 95th, 1435 01:11:24,190 --> 01:11:25,310 in this case. 1436 01:11:25,310 --> 01:11:26,960 The reading was suggesting that you 1437 01:11:26,960 --> 01:11:30,380 could use 15% times the average, or things like that. 1438 01:11:30,380 --> 01:11:33,230 When you have data, then you should use the data. 1439 01:11:33,230 --> 01:11:37,760 So the technique of taking an average 1440 01:11:37,760 --> 01:11:39,290 and multiplying it by a percentage 1441 01:11:39,290 --> 01:11:42,659 is what the industry typically does 1442 01:11:42,659 --> 01:11:44,450 when you don't have automatically collected 1443 01:11:44,450 --> 01:11:47,180 data, when you essentially send someone 1444 01:11:47,180 --> 01:11:51,200 out to drive behind the bus or to do-- or a ride checker 1445 01:11:51,200 --> 01:11:53,060 to collect data on the bus. 1446 01:11:53,060 --> 01:11:57,485 And you do five, or six, maybe 10 trips. 1447 01:11:57,485 --> 01:11:58,790 And then you get an average. 1448 01:11:58,790 --> 01:12:01,675 And that's not enough to estimate your high percentiles, 1449 01:12:01,675 --> 01:12:03,800 because you probably didn't see the high percentile 1450 01:12:03,800 --> 01:12:05,300 in those only 10 trips. 1451 01:12:05,300 --> 01:12:09,737 So therefore, you have to rely on a different method. 1452 01:12:09,737 --> 01:12:11,570 And then you could multiply by a percentage. 1453 01:12:11,570 --> 01:12:14,840 But if you have data, then you should use the data. 1454 01:12:14,840 --> 01:12:19,580 And 10%, 15%, 20%, whatever you use 1455 01:12:19,580 --> 01:12:22,571 might not be adequate for a specific bus route. 1456 01:12:22,571 --> 01:12:24,320 So because you have data, you can actually 1457 01:12:24,320 --> 01:12:26,720 measure how variable it is. 1458 01:12:26,720 --> 01:12:30,860 And therefore, high percentile is a better choice. 1459 01:12:30,860 --> 01:12:34,940 95% is 1 in 20, right? 1460 01:12:34,940 --> 01:12:38,870 So if you think of there being 20 weekdays in a month, 1461 01:12:38,870 --> 01:12:42,020 then you're saying, well, about-- 1462 01:12:42,020 --> 01:12:46,300 for the 8:00 trip, I expect it to be late about once 1463 01:12:46,300 --> 01:12:47,284 in a month. 1464 01:12:47,284 --> 01:12:48,950 AUDIENCE: [INAUDIBLE] it start out late. 1465 01:12:48,950 --> 01:12:49,750 GABRIEL SANCHEZ-MARTINEZ: To start out late, 1466 01:12:49,750 --> 01:12:52,820 because it was-- yeah, for there to be a knock on effect 1467 01:12:52,820 --> 01:12:54,710 on my next trip, essentially. 1468 01:12:54,710 --> 01:12:56,990 And for every other time of the month, 1469 01:12:56,990 --> 01:12:58,440 I expect it to run smoothly. 1470 01:12:58,440 --> 01:13:01,250 So that's why 95 is a typical choice here. 1471 01:13:01,250 --> 01:13:03,940 Lower numbers of percentiles are common, especially 1472 01:13:03,940 --> 01:13:05,330 at high frequency service-- 1473 01:13:05,330 --> 01:13:07,610 90, 85. 1474 01:13:07,610 --> 01:13:09,052 Question in the back, yeah? 1475 01:13:09,052 --> 01:13:11,010 AUDIENCE: So how do you use the 95th percentile 1476 01:13:11,010 --> 01:13:13,270 for the recovery? 1477 01:13:13,270 --> 01:13:15,210 You said for the traffic-- 1478 01:13:15,210 --> 01:13:17,251 GABRIEL SANCHEZ-MARTINEZ: Exactly, the half cycle 1479 01:13:17,251 --> 01:13:18,170 is the 95. 1480 01:13:18,170 --> 01:13:20,120 And the recovery time is the difference 1481 01:13:20,120 --> 01:13:22,990 between the half cycle and the typical. 1482 01:13:22,990 --> 01:13:24,776 So on your journey planner, you only 1483 01:13:24,776 --> 01:13:26,650 put the running time, but then between trips, 1484 01:13:26,650 --> 01:13:29,350 you add the recovery time. 1485 01:13:29,350 --> 01:13:32,680 And then the cycle time is the sum of both half cycle times. 1486 01:13:32,680 --> 01:13:34,420 So that's pretty straightforward. 1487 01:13:34,420 --> 01:13:35,940 Question 5 was, how many vehicles 1488 01:13:35,940 --> 01:13:38,160 do you need to operate this? 1489 01:13:38,160 --> 01:13:41,200 And there is an equation, which is maybe 1490 01:13:41,200 --> 01:13:43,740 the most important equation in the whole course-- 1491 01:13:43,740 --> 01:13:48,070 number of vehicles equals cycle time divided by headway. 1492 01:13:48,070 --> 01:13:51,500 And you need to round up. 1493 01:13:51,500 --> 01:13:55,000 So cycle time is 84 minutes. 1494 01:13:55,000 --> 01:13:57,250 The headway we said was 10 minutes. 1495 01:13:57,250 --> 01:13:59,050 So that's 84 divided by 10. 1496 01:13:59,050 --> 01:13:59,940 It's 8.4. 1497 01:13:59,940 --> 01:14:01,580 Round up, that's 9 vehicles. 1498 01:14:01,580 --> 01:14:04,380 OK, you need nine vehicles to operate the bus route. 1499 01:14:04,380 --> 01:14:09,390 Question 6 asks you to plot the times. 1500 01:14:09,390 --> 01:14:14,250 Hopefully you labeled your axes and did everything 1501 01:14:14,250 --> 01:14:15,140 like you should. 1502 01:14:15,140 --> 01:14:18,040 And so here's time of day. 1503 01:14:18,040 --> 01:14:20,220 And here is running times in direction one, 1504 01:14:20,220 --> 01:14:22,080 running times in direction two. 1505 01:14:22,080 --> 01:14:28,422 And we identify that not all of these running times 1506 01:14:28,422 --> 01:14:30,130 come from the same operating environment. 1507 01:14:30,130 --> 01:14:33,620 We can see that there are some peaks and some off-peaks. 1508 01:14:33,620 --> 01:14:35,966 And uh oh, we just calculated everything wrong, 1509 01:14:35,966 --> 01:14:37,340 because we mixed up all the data. 1510 01:14:37,340 --> 01:14:38,900 And we shouldn't have. 1511 01:14:38,900 --> 01:14:43,370 So the question was, what are these periods? 1512 01:14:43,370 --> 01:14:45,680 So AM peak going from 7:00 to 9:00, 1513 01:14:45,680 --> 01:14:48,780 midday from 9:00 to 16:00, and PM from 16:00 to 18:00. 1514 01:14:48,780 --> 01:14:51,710 And we assume a 24-hour format. 1515 01:14:51,710 --> 01:14:54,950 And now we have to redo all the work. 1516 01:14:54,950 --> 01:14:57,080 We have to compute the same statistics. 1517 01:14:57,080 --> 01:15:01,280 I've just changed the ranges and copied the formulas from below, 1518 01:15:01,280 --> 01:15:02,379 and the fill to the right. 1519 01:15:02,379 --> 01:15:03,670 And we have all the statistics. 1520 01:15:03,670 --> 01:15:05,720 So that's great. 1521 01:15:05,720 --> 01:15:08,400 We repeat the calculation. 1522 01:15:08,400 --> 01:15:12,230 And we get the vehicle requirement by period now. 1523 01:15:12,230 --> 01:15:16,280 We still need nine vehicles in the AM and PM peaks, 1524 01:15:16,280 --> 01:15:19,070 but it turns out that we only need seven 1525 01:15:19,070 --> 01:15:22,040 in the base, between peaks. 1526 01:15:22,040 --> 01:15:24,320 So that's great. 1527 01:15:24,320 --> 01:15:25,620 What's the cycle time? 1528 01:15:25,620 --> 01:15:28,950 The cycle time, once you've calculated, 1529 01:15:28,950 --> 01:15:30,380 you can flip this equation. 1530 01:15:30,380 --> 01:15:32,860 I could have an entire lecture on this equation. 1531 01:15:32,860 --> 01:15:35,720 Believe, it gets-- you can flip it around. 1532 01:15:35,720 --> 01:15:39,390 And there is many ways of interpreting this equation. 1533 01:15:39,390 --> 01:15:42,410 But if you solve for c, cycle time 1534 01:15:42,410 --> 01:15:44,840 equals number of vehicles times headway. 1535 01:15:44,840 --> 01:15:46,970 Now you don't round any direction. 1536 01:15:46,970 --> 01:15:50,360 So once you've decided what n is, then 1537 01:15:50,360 --> 01:15:55,474 you solve this equation for c and revise your cycle time. 1538 01:15:55,474 --> 01:15:57,890 Because you rounded up, your cycle time will have gone up. 1539 01:15:57,890 --> 01:16:00,056 And therefore, your recovery time will have gone up. 1540 01:16:03,890 --> 01:16:07,210 The revised cycle time is 90 minutes, AM and PM peaks, 1541 01:16:07,210 --> 01:16:09,196 70 minutes off-peak. 1542 01:16:09,196 --> 01:16:10,820 And the recovery time is the difference 1543 01:16:10,820 --> 01:16:15,540 between the typical running time and the cycle time. 1544 01:16:15,540 --> 01:16:19,430 So then I asked, what if you had done the mistake 1545 01:16:19,430 --> 01:16:22,050 of using all the data combined? 1546 01:16:22,050 --> 01:16:24,590 That means that you're fine on AM and PM peaks, 1547 01:16:24,590 --> 01:16:28,480 but you would be excessively provisioning resources 1548 01:16:28,480 --> 01:16:29,780 in the off-peak. 1549 01:16:29,780 --> 01:16:32,270 So your cycle time was 90, because you 1550 01:16:32,270 --> 01:16:33,770 said it was nine vehicles. 1551 01:16:33,770 --> 01:16:36,740 And that recovery time would be 30 minutes and a half, 1552 01:16:36,740 --> 01:16:38,690 which would be excessive. 1553 01:16:38,690 --> 01:16:40,970 AUDIENCE: It's fine if we used the average instead 1554 01:16:40,970 --> 01:16:41,890 of the median, right? 1555 01:16:41,890 --> 01:16:43,181 GABRIEL SANCHEZ-MARTINEZ: Yeah. 1556 01:16:43,181 --> 01:16:45,300 I prefer-- I think median is a better choice, 1557 01:16:45,300 --> 01:16:49,930 but both are fine, especially if you remove outliers 1558 01:16:49,930 --> 01:16:51,650 from the average. 1559 01:16:51,650 --> 01:16:53,480 And this data didn't have outliers. 1560 01:16:53,480 --> 01:16:55,040 As you can see on the graphs, it's 1561 01:16:55,040 --> 01:17:00,950 very suspiciously clean data, and very precise, 1562 01:17:00,950 --> 01:17:03,660 places where the period begins and ends. 1563 01:17:03,660 --> 01:17:05,540 The data you will get for Assignment 3 1564 01:17:05,540 --> 01:17:06,830 does not look like that. 1565 01:17:06,830 --> 01:17:12,460 So all right, Question 9 said, now imagine 1566 01:17:12,460 --> 01:17:14,570 that this bus runs in a loop. 1567 01:17:14,570 --> 01:17:16,080 It only has one turn. 1568 01:17:16,080 --> 01:17:18,490 And I provide data. 1569 01:17:18,490 --> 01:17:21,670 We have data here for that combined operation 1570 01:17:21,670 --> 01:17:25,030 of running inbound, then outbound, then coming back. 1571 01:17:30,830 --> 01:17:35,380 We said we have a headway of 7 minutes. 1572 01:17:35,380 --> 01:17:38,840 And we are running with a fleet size of 10 vehicles. 1573 01:17:38,840 --> 01:17:41,210 How reliable is this service? 1574 01:17:41,210 --> 01:17:43,600 So we can compute from the headway 1575 01:17:43,600 --> 01:17:46,910 the fleet size and cycle time using this equation right here. 1576 01:17:46,910 --> 01:17:49,490 And we have 70 minutes. 1577 01:17:49,490 --> 01:17:54,890 And what we want to do then is, from all these observations, 1578 01:17:54,890 --> 01:17:57,260 you can think of this as some sort of probability 1579 01:17:57,260 --> 01:17:58,460 distribution. 1580 01:18:02,240 --> 01:18:08,520 We have some distribution of running time. 1581 01:18:08,520 --> 01:18:09,780 This is probability density. 1582 01:18:14,030 --> 01:18:15,200 And this is running time. 1583 01:18:20,630 --> 01:18:22,900 And we said the cycle time is 70. 1584 01:18:22,900 --> 01:18:25,680 So 70 will fall somewhere around here it 1585 01:18:25,680 --> 01:18:28,489 turns out, if you look it up. 1586 01:18:28,489 --> 01:18:29,530 That's very close to 50%. 1587 01:18:33,610 --> 01:18:38,320 The way I computed it used the spreadsheets solver, 1588 01:18:38,320 --> 01:18:39,670 you will see. 1589 01:18:39,670 --> 01:18:41,500 There are different names for it. 1590 01:18:41,500 --> 01:18:45,540 So I said, calculate the percentile of whatever 1591 01:18:45,540 --> 01:18:48,240 percentile I give you here. 1592 01:18:48,240 --> 01:18:49,800 So initially, I set it to-- 1593 01:18:49,800 --> 01:18:53,600 I don't know, maybe I set it to 95. 1594 01:18:53,600 --> 01:18:56,310 And it gave me the percentile. 1595 01:18:56,310 --> 01:19:00,080 This percentile is running on the AM peak data, 1596 01:19:00,080 --> 01:19:02,120 or whatever it is on spreadsheet 9. 1597 01:19:02,120 --> 01:19:05,000 And then I said, change that percentile such 1598 01:19:05,000 --> 01:19:07,080 that the cell equals 70. 1599 01:19:07,080 --> 01:19:09,050 And it solved it. 1600 01:19:09,050 --> 01:19:15,740 And it gave 0.476 probability. 1601 01:19:15,740 --> 01:19:17,520 Is that reliable, yes or no? 1602 01:19:17,520 --> 01:19:18,144 No. 1603 01:19:18,144 --> 01:19:20,060 AUDIENCE: So what's that probability refer to? 1604 01:19:20,060 --> 01:19:22,060 GABRIEL SANCHEZ-MARTINEZ: That's the probability 1605 01:19:22,060 --> 01:19:27,000 that you can run in 70 minutes or less. 1606 01:19:27,000 --> 01:19:30,406 And therefore, you don't cause delays on the next trip. 1607 01:19:30,406 --> 01:19:31,780 Your next trip can begin on time. 1608 01:19:35,190 --> 01:19:35,690 Sorry? 1609 01:19:35,690 --> 01:19:36,440 AUDIENCE: Not reliable. 1610 01:19:36,440 --> 01:19:38,565 GABRIEL SANCHEZ-MARTINEZ: Not reliable, thank you-- 1611 01:19:38,565 --> 01:19:42,360 OK, so Question 10 is the challenge question. 1612 01:19:42,360 --> 01:19:46,610 And now we have two variables. 1613 01:19:46,610 --> 01:19:50,120 So now you have recovery. 1614 01:19:50,120 --> 01:19:52,940 You start at A. You go this way. 1615 01:19:52,940 --> 01:19:56,450 You reach B. You do recovery there. 1616 01:19:56,450 --> 01:19:58,520 And then you run back. 1617 01:19:58,520 --> 01:20:00,410 So you have recovery here and here. 1618 01:20:00,410 --> 01:20:03,680 And we're asking about times here. 1619 01:20:03,680 --> 01:20:06,110 So we're saying, what's the probability 1620 01:20:06,110 --> 01:20:08,200 with the same situation of 7-minute headway 1621 01:20:08,200 --> 01:20:14,600 and a fleet size of 10 that this trip can depart on time? 1622 01:20:14,600 --> 01:20:19,140 So for that-- there are different approaches for this. 1623 01:20:19,140 --> 01:20:20,630 How many of you tried the question? 1624 01:20:23,590 --> 01:20:27,450 And how many of you think that they solved the question? 1625 01:20:27,450 --> 01:20:28,965 Most of you, OK. 1626 01:20:28,965 --> 01:20:32,190 AUDIENCE: Now with that answer. 1627 01:20:32,190 --> 01:20:35,040 GABRIEL SANCHEZ-MARTINEZ: So it's 1628 01:20:35,040 --> 01:20:38,400 actually not that difficult. Essentially what 1629 01:20:38,400 --> 01:20:40,320 you have is a situation where you 1630 01:20:40,320 --> 01:20:41,760 have different cases, right? 1631 01:20:41,760 --> 01:20:49,500 So if you run here, and you reached terminal B early 1632 01:20:49,500 --> 01:20:52,390 before your half cycle time is completed, 1633 01:20:52,390 --> 01:20:56,490 then you will recover at B until you reach your half cycle time. 1634 01:20:56,490 --> 01:20:58,500 And in that case, the only thing that matters 1635 01:20:58,500 --> 01:21:00,360 is the running time coming back. 1636 01:21:00,360 --> 01:21:03,060 But there is a case where you run here and it's late. 1637 01:21:03,060 --> 01:21:06,115 And you depart immediately from B. So for those cases, 1638 01:21:06,115 --> 01:21:08,370 you have to compute the probability 1639 01:21:08,370 --> 01:21:12,060 that the combination of running this way and that way 1640 01:21:12,060 --> 01:21:13,810 is less than 70. 1641 01:21:13,810 --> 01:21:16,050 So you have those two cases. 1642 01:21:16,050 --> 01:21:19,590 One way of doing that is to take all the running times that 1643 01:21:19,590 --> 01:21:20,820 apply. 1644 01:21:20,820 --> 01:21:23,970 I think this said at AM peak. 1645 01:21:23,970 --> 01:21:30,360 So direction one is on column A. There are 200 of these. 1646 01:21:30,360 --> 01:21:33,550 Direction two is on row one. 1647 01:21:33,550 --> 01:21:37,150 So I've done the transpose and put it on a row. 1648 01:21:37,150 --> 01:21:38,950 And then, for each of the cells, we 1649 01:21:38,950 --> 01:21:41,960 can compute the combined running time. 1650 01:21:41,960 --> 01:21:45,520 So notice that, for the first one, we're saying, 1651 01:21:45,520 --> 01:21:48,590 max of 35, which is the half cycle time-- 1652 01:21:48,590 --> 01:21:54,400 I decided here arbitrarily to split the whole cycle 1653 01:21:54,400 --> 01:21:56,080 time of 70 minutes in half. 1654 01:21:56,080 --> 01:22:02,270 So I'm saying the half cycle for the first run is 35 minutes. 1655 01:22:02,270 --> 01:22:07,030 And so the time of departure from B 1656 01:22:07,030 --> 01:22:11,350 is going to be the maximum of 35 for cases where it was faster 1657 01:22:11,350 --> 01:22:15,670 than 35, or the running time if it was longer than 35. 1658 01:22:15,670 --> 01:22:19,870 And then we add the running time in the return direction. 1659 01:22:19,870 --> 01:22:22,430 So we combine these two distributions-- 1660 01:22:22,430 --> 01:22:25,570 that's called the convolution-- by adding all of these up. 1661 01:22:25,570 --> 01:22:27,140 And all of these are possibilities. 1662 01:22:27,140 --> 01:22:30,580 All the combinations of these observations are possibilities. 1663 01:22:30,580 --> 01:22:34,280 And then we repeat the same thing. 1664 01:22:34,280 --> 01:22:38,200 So we say, let's assume this is 50%. 1665 01:22:38,200 --> 01:22:40,940 And let's calculate the percentile 1666 01:22:40,940 --> 01:22:45,500 on all the cells in that matrix and ask the spreadsheet 1667 01:22:45,500 --> 01:22:50,420 to provide or solve for the percentile that gives you 70. 1668 01:22:50,420 --> 01:22:56,420 And the answer is 0.418, so a little over. 1669 01:22:56,420 --> 01:22:59,700 Then there was an 11th question, which is very important. 1670 01:22:59,700 --> 01:23:02,060 It's not a number question here. 1671 01:23:02,060 --> 01:23:04,520 But it said, there is this person 1672 01:23:04,520 --> 01:23:07,560 who is watching these vehicles recover at the terminal. 1673 01:23:07,560 --> 01:23:13,240 And this person is annoyed that service is not frequent enough. 1674 01:23:13,240 --> 01:23:15,940 And these drivers are wasting time. 1675 01:23:15,940 --> 01:23:17,810 And they're sitting there not working. 1676 01:23:17,810 --> 01:23:22,670 And that person proposes that you should run-- 1677 01:23:22,670 --> 01:23:23,821 this person is an activist. 1678 01:23:23,821 --> 01:23:25,070 And they've gotten on the bus. 1679 01:23:25,070 --> 01:23:27,920 And they've measured the average time. 1680 01:23:27,920 --> 01:23:29,880 And they say, you can run this much faster. 1681 01:23:29,880 --> 01:23:30,838 You don't have to wait. 1682 01:23:30,838 --> 01:23:32,620 They're budgeting for so much time, 1683 01:23:32,620 --> 01:23:34,810 so you should run this at average 1684 01:23:34,810 --> 01:23:36,380 with average running times. 1685 01:23:36,380 --> 01:23:39,030 And it's your turn to sort of argue back. 1686 01:23:39,030 --> 01:23:42,730 So hopefully you said that, no, recovery time is important. 1687 01:23:42,730 --> 01:23:47,950 If you don't have recovery time, then many trips will have-- 1688 01:23:47,950 --> 01:23:49,390 will start late. 1689 01:23:49,390 --> 01:23:52,700 And if you're trying to take your bus based on a schedule, 1690 01:23:52,700 --> 01:23:54,430 then it'll never be there on time. 1691 01:23:54,430 --> 01:23:56,390 And that would be-- that would mean that you 1692 01:23:56,390 --> 01:23:57,530 have to wait a lot longer. 1693 01:23:57,530 --> 01:23:59,480 And it will be very annoying for everyone. 1694 01:23:59,480 --> 01:24:02,780 So that's it for Assignment 1. 1695 01:24:02,780 --> 01:24:06,452 I hope you understood all of this. 1696 01:24:06,452 --> 01:24:07,910 If you have questions, let me know. 1697 01:24:07,910 --> 01:24:11,440 I will grade it and have it back to you as soon as possible.