Optimal Location of Bus Depots in an Urban Area Enrico Musso & Anna

Transactions on the Built Environment vol 30, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509 Optimal location of bus depots in an urban area Enrico Musso & Anna Sciomachen akg/z Abstract This paper deals with the so-called "plant location problem" and aims to set up a methodology for determining the optimal location and size of bus depots. Location and size of bus depots are usually not efficient, mainly because of: - the subsequent growth of the city, or significant changes in location patterns (causing possible inefficiencies in terms of land use); - the growing demand for public transport over time (causing ineficiencies in exploiting economies of scale). Nevertheless, any "present" location is usually very difficult to change, due to: - the lack of an appropriate methodology to find out better locations; - the unpopularity of any decision concerning new locations for bus depots. The poposed methodology aims to investigate the overall costs connected with depots (land use costs + operational costs + journey-to-depot costs) and to minimize them by determining the optimal combination of number, size and location of depots, given the urban transportation network and the overall number of buses. A case study is then developed for the city of Genoa. The present scenario is analyzed with respect to several decision constraints, (geography, feasible depot sizes, resource allocation, bus types, time of investment and budget restrictions). Then, the shortest path between any pair of possible bus stops is computed together with the average number of trips for each bus line and the location, handling and managing costs for each depot. Finally. a Mixed Integer Programming (MIP) model is derived for solving the problem on the basis of the average daily traffic data in the city of Genoa. The model is solved using an optimization software library on a personal computer. 1 Purpose of the paper This papers aims to point out a methodology for optimizing size and location of bus depots in an urban transit company. Sizes and locations of bus depots are often a result of choices taken in the past, no longer efficient with respect to the present technological and market conditions. For example, after a significant urban growth the depot location Transactions on the Built Environment vol 30, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509 94 Urban Transport and the Environment for the 21st Century has possibly become too central, and the area has now a greater economic potential. Or, the oldest depots may be too small for present need, so that the company may be induced to set up additional smaller depots. Besides, the potential opposition of resident population makes it politically difficult to move a depot toward any new site. So that, as a result, the previous location is more acceptable and eventually very stable, despite of its possible inefficiency. It should also be said that land values of nearby areas are negatively affected by the new depot, while land values of previous neighbourhood will be positively affected. Both changes will be included only in future prices, and result in unfair damages for present landowners. Thus, the overall number of relocation should be reduced to the minimum. The lack of satisfactory methods to find out the optimal solution in terms of number/size/location of depots often causes urban planning to be almost completely ineffective. These methods are needed in order to: - achieve higher long-term efficiency in land use; - reduce speculations deriving from discretionary choices on depot location. 2 Some specifications In the proposed methodology, we have assumed that the overall number of buses, the busline network, and the frequency on each line, are given (since depot supply must be optimized with respect to service supply, and not the opposite). It could be objected that location and size of depots are tipical long term choices. But on the other side, since the transit network depends on demand, no reliable forecasts can be developed on future demand over the whole life of the depot (at least 50 years). Obvoiusly, some overcapacity of depots with respect to present number of bus should be considered, but this just means a different overall capacity, and does not implies adjustments in methodology. We have assumed that costs to be minimized are the costs of the transit company. No external costs (like pollution of empty-journeys from/to the depot) have been considered, since: - transit companies deficit are presently so relevant that this should be considered a priority goal; - given the network and the frequency (which means, given the level of efficacy), any further gaps between social and company costs are basicly connected to congestion and pollution, which are implicitly minimized since the proposed method sets up a trade off between minimum empty journeys and economies of scale in depot management. 3 The cost function Basicly, the problem is to minimize a cost function including: Transactions on the Built Environment vol 30, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509 Urban Transport and the Environment for the 21st Century 95 - the costs of space (the pontential land value of the area where the depot is expected to be located); - the costs of depot (the cost of depot management and of all functions and activities taking place inside the depot); - the costs of empty journeys (from/to the depot: mainly staff costs and fuel costs); without reducing the performance of the network (i.e.: same network, same number of vehicles, same frequency). 3.1 The costs of space We could consider two different criteria: - a "potential" value criterium, where land value is basicly determined by the demand for alternative use of the space, and is influenced by features such as central location, accessibility, environmental quality, etc.; - an "actual" value criterium, where land value is strongly affected by urban planning regulations concerning the area. Quite often, planners follow the latter, and just confirm the present location of depots, thus keeping low the value of those areas. Clearly, decisions concerning location of depots, instead of being influenced by present location, should come first, and should only be influenced by the potential value of the areas, determined by alternative land uses. In any application of the proposed model a given number of alternative sites will be considered, and for each of them the total cost includes the value of the objective function (costs of depot + costs of journeys to/from depots) and the specific potential value of the area. The model allows to rank the alternatives from the point of view of all costs related to depots. We have not included the cost of space in the objective function of the model, since it is easier to estimate and add the potential value of the area only for best potential locations. So, the objective function to minimize is a cost function including the costs of depots and the costs of journey to/from depots. A trade off is clearly to be stated between possible economies of scale in depots management and costs of journey to/from depots, which are higher if the number of depots is lower. 3.2 The depot costs The depot costs include: - labour costs: the bigger part of the depot costs (in the study case - Genoa, Italy - they weigh over 75%); - consumption: electric power, fuel, water, telephone, etc.; - disposable and spare parts. Cost categories rank from general and sundry expenses, contract works, bus preparation, servicing expenses, cleaning, plant servicing. Transactions on the Built Environment vol 30, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509 96 Urban Transport and the Environment for the 21st Century The analysis of depot costs for the transit company of the city of Genoa shows the existence of economies of scale up to a size of 180-200 vehicles per depot (the total number of vehicles is 848). For bigger depots, average costs appear more or less constant, without relevant diseconomies of scale. These results are confirmed by a productivity index (namely: number of vehicles per staff unit), which increases until the depot sizes reach the above mentioned number of buses. Obviously, total depot costs can be minimized only if the number of depots is minor or equal to the ratio between the total number of buses and the minimum optimal size, and if no depot is below that size. For example, the depot costs related to the 848 Genoa buses are properly minimized with 1,2,3 or 4 depots (provided that none of them is smaller than 180-200 units), while costs increase if the number is higher (they are presently 7). 3.3 The jouney to/from depot costs The jouney to/from depot costs are those costs that are necessary for buses to reach the terminus of the correspondind bus line from the depots, and viceversa. Note that during this journey buses cannot offer any transportation to the users, so that only pure costs can be considered in this case to be added to the overall costs connected with depots. These costs consist of: - labour costs; - fuel and consumption costs. The above costs can be considered as a function of the distance between depots and bus termina, that is denoted as "empty path". The "empty path" is usually as shorter as greater is the number of depots (and then as smaller is their size), and as shorter as the path followed by buses is the optimal one. Therefore, the journey from/to depots are as smaller as the bus terminus is closer to the depot. Moreover, the journey from/to depots cost are also a function of the number, say F, of input/out daily entries of each bus.

Load more