Allocation of Buses to Depots : A Case Study R Sridharan Minimizing dead kilometres is an important operational objective of an urban road transport undertaking as dead kilometres mean additional losses. This can be achieved by formulating the underlying decision problem of allocating the buses to depots as a transportation problem. Using data from an urban road transport undertaking, R Sridharan shows how such a modelling can lead to significant reduction in dead kilometres. Given the need for fuel conservation under the current circumstances in our country, this will mean considerable saving in petrol consumption. R Sridharan is a faculty member in the Production and Quantitative Methods Area of the Indian Institute of Management, Ahmedabad. Urban passenger road transport undertakings in India are mostly state owned. These undertakings are expected to provide efficient, economical and safe transport services for urban populations. However, the decisions related to fare fixation and fare increases are controlled by the government. Managements of the undertakings have very little influence in determining the fare or in changing it upward in response to rising operational costs. More often than not, in order to be profitable or in order to reduce losses, managements need to spend their efforts in keeping an eagle's eye on costs. Any measure which can contribute to the reduction of operating costs could result in improved profitability. It is also relevant to note here that most urban transport undertakings are heavily subsidized and almost all urban transport undertakings in India (and probably anywhere in the world) are incurring losses. Since undertakings have no flexibility in deciding changes in fares, costs should become the primary objective of the managements of urban passenger road transport undertakings. The Problem A typical urban passenger road transport undertaking has a large fleet of buses operating on different routes. Usually, the buses are operated between 5 am and 11 pm. When the buses are not under operation (i.e. between 11 pm and 5 am), they are sent to a depot where basic servicing and parking facilities are provided. Every day, a bus leaves the depot in the morning to its starting terminal for its daily operation, and at the end of the last trip is brought back to the depot from its ending terminal. The trip from the terminal to the depot as well as from the depot to the terminal does not carry any passengers. Therefore, the distance covered by the bus (between its terminal and the depot) without carrying any passengers is called 'dead kilometres.' The dead kilometre is fairly high for urban passenger road transport undertakings and it results in losses to the organization. The losses may be either opportunity losses or direct losses. The opportunity loss is equal to the loss in revenue that could have been earned by the bus had it been carrying passengers, and the direct loss is the cost of fuel and wear and tear on the bus(see Box). Vol.l6,No.2, April-June 1991 27
Is it possible to eliminate dead kilometres completely? The answer is no. However, it is possible to orient the organization's effort towards the progressive minimization of dead kilometres to the extent possible. This is possible if the undertaking directs attention to the efficient (optimal) allocation of buses to depots. It is observed that in most transport organizations, this decision is made almost entirely on gut feeling or on the.basis of "good judgements." The effort is to haul a bus from the terminal to the nearest depot. If the nearest depot does not have any space to accommodate the bus, then it is allocated to the next closest depot, and so on. It can easily be verified that such an assignment does not result in an overall optimum, Minimization of Dead Kilometres as a Transportation Model The problem of allocating buses to depots in order to minimize dead kilometres can be formulated as a Transportation model (as shown in the Appendix) which can be solved in order to obtain the optimal allocation. A case study is presented in this paper to illustrate the use of such a model for obtaining the optimal allocation of buses to depots. The input data needed for the parameters of the model were obtained from an urban road transport undertaking. Let us call it the MDK Corporation. The model was used to identify the allocation of buses to depots and the results from the model indicated substantial savings in dead Box: Terminology Dead Kilometre: The distance travelled by a bus from its terminal to the depot after ending its operations for the day, and from the depot to its terminal before commencing operations for the day without carrying any passengers. Trip : A journey undertaken by the bus from a starting terminal to an ending terminal with the intention of earning revenue. Terminal: Starting or ending point of a trip. Route: A specific path between two terminals. Routes are referred to by alphanumerals, e.g. 12,12A, 41B. Service: A bus assigned to a specific route. A service will normally mean a bus. Depot : Locations where the buses are parked and serviced when they are not in operation. kilometres for MDK compared to its existing allocation. An attempt has been made in this paper to demonstrate the utility of the model in decision making with particular focus on the ability to provide the decision maker with a high degree of flexibility in analysing and evaluating various options. MDK: A Profile MDK Corporation is a wholly government owned urban transport corporation serving a major city in India. At the time of this study (1988), MDK had a fleet of 2,089 buses served by 18 depots. Thirteen of these 18 depots were located within the city limit. MDK was operating 355 routes touching 172 terminals (69 within the city limits) in the entire metro area. The total cost per kilometre of running was Rs 5.39 while the variable cost per kilometre was Rs 1.82. The revenue per kilometre was Rs 4.80. The Case Study The data for the case study were collected from MDK Corporation. Depot-wise data related to the allocation of buses to depots located within the city limit were collected. Table 1 gives the format in which the data were received. The depot-wise data were related to the terminals from which the buses were allocated, the number of buses thus allocated, and the distance between the terminal and the depot. Though this data provided the distance between the terminals and the depots to which allocations were made currently, the complete distance matrix from depots to terminals was not available from this data. From the depot-wise data, we identified that allocations were made to the 13 depots from 34 terminals covering a total of 1,438 buses. This covers about 50 per cent of the city terminals and 69 per cent of the buses in operation in the city. The 34 by 13 distances matrix between terminals and depots was then completed by taking the distances from a city map. To validate these "map" distances, they were compared with the known terminal depot distances as given by MDK corporation in its depot-wise data. The depot capacities and terminal requirements of buses were also obtained from the depot-wise data. (The depot capacities are shown in Table 4 while the terminal requirements can be obtained by taking the row total in either Table 2 or Table 3.) The existing allocation as used by MDK corporation for the 13 depots resulted in dead kilometres of 4909.6 km per day. 28 Vikalpa
Table 2: Allocation of Buses to Depots by MDK Corporation Depots A B C D E F G H I J K L M 1 59 2 122 3 24 4 76 5 43 6 1 7 1 8 1 9 6 10 8 11 20 T 12 7 2 13 14 e 14 13 r 15 118 m 16 12 i 17 8 n 18 39 a 19 11 1 20 14 s 21 4 7 22 24 75 23 33 24 6 25 9 19 99 26 7 27 1 81 28 58 47 29 67 7 30 67 31 161 32 25 33 22 14 34 6 The optimization model was used within the framework of the existing routes as provided by the depot-wise data given by MDK corporation. However, if we could alter some of these parameters, particularly the number of buses that are required to start from each terminal, then the savings are expected to be even higher. the package is menu-driven and PC based, the initial effort needed in adapting the model is minimal. Also, the resources needed to instal the model can easily be recovered within a month. The model can also be used to study the impact of increasing depot capacities, opening new depots, increasing/decreasing of the number of terminals and changing the location of terminals. It is this kind of flexibility provided by the model for a "what if" analysis which makes it very attractive. The PC based package developed for this case study can be used by any urban road transport undertaking to minimize its dead kilometre distances. Since 30 Vikalpa
Table 3: Allocation of Buses to Depots by the Model Depots A B C D E F C H 1 J K L M 1 59 2 122 3 24 4 76 5 43 6 1 7 1 8 1 9 6 10 7 1 11 20 12 9 T 13 14 e 14 13 r 15 118 12 m 17 8 i 18 39 n 19 11 a 20 14 1 21 11 s 22 1 98 23 18 15 24 6 25 22 100 5 26 7 27 82 28 105 29 18 56 30 67 31 161 32 25 33 9 27 34 6 Capa- Depot cities Table 4: Summary of Allocation of Buses to Depots No of buses MDK Allocation Dead km. per day No of buses Allocation as per Model Dead km. per day A 150 147 736.4 144 634.4 B 179 168 632.0 179 588.4 C 154 146 936.4 121 430.6 D 36 33 184.8 36 257.4 E 167 158 416.0 140 220.0 F 57 55 58.0 57 91.6 G 113 108 799.8 113 747.0 H 100 99 158.4 100 160.0 I 84 73 145.2 84 109.8 J 86 81 0.0 82 0.0 K 156 146 369.8 156 578.4 L 67 56 280.8 56 89.6 M 183 168 192.0 170 76.8 Total 1438 4909.6 1438 3984.0 Savings in dead kilometres 925.6 Vol.16,No.2, April-June 1991 31