Combined optimisation and MCDA based solution of the tram depot location problem




tram depot location, MCDA, multiple criteria decision aid, combinatorial optimisation, AHP method, AHORNsimple application


This paper deals with an issue of technical facilities location in a public transport system. The decision problem is formulated as a selection of the most advantageous alternative, i.e. the location of a new tram depot among the already existing facilities of this type. The selection is preceded by the evaluation of the alternatives. The assessment is not a trivial task, because there are many groups of interest with usually contradictory points of view. Therefore, the evaluation of the new tram depot locations should represent different aspects, e.g., economical, technical, environmental, and organizational. To handle such a complex decision problem the authors propose a methodology, which is a composition of the optimisation and multiple criteria evaluation techniques. The developed methodology is experimentally applied to the selection of one out of five tram depot locations in the public transport system of the city of Poznan, Poland. All the computational experiments are performed by means of optimization and multiple criteria decision aiding (MCDA) methods and tools, i.e. a linear optimization engine Solver Premium Platform and AHP method with its application AHORNsimple. The calculations are the basis for recommending the location of a new depot in the central part of the transport system network, which is a reasonable solution taking into account, e.g. the proximity of the main railway line, the possibility of triple distribution of the transport means from depot. The proposed methodology of the decision problem solution gives also an opportunity to create the hierarchy of considered tram depot locations as well as to compare the position in the ranking of the best solution with the existing one. Since the proposed methodology assumes the selection of the most suitable MCDA method to the problem under consideration and the decision maker’s preferences, it guarantees that the result of analysis becomes reliable and the decision aiding process is credible.


Al Ali, F., & Hassan, N.M. (2018). Optimisation of bus depot location with consideration of maintenance center availability. Journal of Transportation Engineering, Part A: Systems, 144(2), 05017011, doi: 10.1061/JTEPBS.0000-114

Ayag, Z., & Özdemir, R.G. (2007). An intelligent approach to ERP software selection through fuzzy ANP. International Journal of Production Research, 45(10), 2169–2194.

Ball, M., Assad, A., Bodin, L., Golden, B., & Spielberg, F. (1984). Garage Location for an Urban Mass Transit System. Transportation Science, 18(1), 56–75, doi: 10.1287/trsc.18.1.56.

Belton, V., & Stewart, T.J. (2002). Multiple Criteria Decision Analysis. An Integrated Approach. Boston: Kluwer Academic Publisher.

Brans, J.P., Vincke, P., & Mareschal, B. (1986). How to Select and How to Rank Projects: The PROMETHEE Method. European Journal of Operational Research, 24(2), 228–238, doi: 10.1016/0377-2217(86)90044-5.

Canca, D., & Barrena, E. (2018). The integrated rolling stock circulation and depot location problem in railway rapid transit systems. Transportation Research, Part E, 109, 115–138, doi:10.1016/j.tre.2017.10.018.

Carrese, S., & Ottone, G. (2006). A model for the management of a tram fleet. European Journal of Operational Research, 175(3), 1628–1651, doi: 10.1016/j.ejor.2005.02.031.

Chen, C., Yao, B., Chen, G., & Tian, Z. (2021). A queuing-location-allocation model for designing a capacitated bus garage system. Engineering Optimisation, doi: 10.1080/0305215-X.2021.1897800.

Cheng, S., Chan, C.W., & Huang, G.H. (2003). An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management. Engineering Applications of Artificial Intelligence, 16, 543–554, doi: 10.1016/S0952-1976(03)00-069-1.

Drezner, Z., & Hamacher, H.W. (2004). Facility Location: Applications and Theory. New York: Springer.

Guitouni, A., & Martel, J.-M. (1998). Tentative guidelines to help choosing an appropriate MCDA method. European Journal of Operational Research, 109, 501–521, doi:10.1016/S-0377-2217(98)00073-3.

Hamdouni, M., Desaulniers, G., & Soumis, F. (2007). Parking buses in a depot using block patterns: A Benders decomposition approach for minimizing type mismatches. Computers and Operations Research, 34(11), 3362–3379, doi:10.1016/j.cor.2006.02.002.

Hamdouni, M., Soumis, F., & Desaulniers, G. (2007). Parking buses in a depot with stochastic arrival times. European Journal of Operational Research, 183, 502–515, doi: 10.1016/j.ejor.2006.10.004.

Haase, K., Knörr, L., Krohn, R., Müller, S., & Wagner, M. (2019). Facility location in the public sector. In Laporte, G., Nickel, S., & Saldanha da Gama, F. (Eds), Location Science, 745–764, Cham: Springer, doi:10.1007/978-3-030-32177-2_26.

He, S., Wang, Y., & Zhang, Z. (2019). Optimization of bus depot location with consideration of dead kilometers: A case study in Xi’an, China. 19th COTA International Conference of Transportation Professionals, Nanjing, China, doi:10.1061/9780784482292.429.

Jacyna, M. (2001). Modelowanie wielokryterialne w zastosowaniu do oceny systemów transportowych. Prace Naukowe Politechniki Warszawskiej. Transport, 47, 3–139.

Jacyna, M., Wasiak, M., Lewczuk, K., Chamier-Gliszczyński, N., & Dąbrowski, T. (2018). Decision problems in developing proecological transport system. Rocznik Ochrona Środowiska, 20(2), 1007–1025.

Jacquet-Lagreze, E., & Siskos, J. (1982). Assessing a Set of Additive Utility Functions for Multicriteria Decision-Making, the UTA Method. European Journal of Operational Research, 10, 151–164, doi:10.1016/0377-2217-(82)90155-2.

Kim, E.W., & Kim, S. (2021). Optimum Location Analysis for an Infrastructure Maintenance Depot in Urban Railway Networks. KSCE Journal of Civil Engineering, 25, 1919–1930, doi:10.1007/s12205-021-1496-5.

Kontou, E., Kepaptsoglou, K., Charalampakis, A.E., & Karlaftis, M.G. (2014). The bus to depot allocation problem revisited: a genetic algorithm. Public Transport, 6, 237–255, doi: 10.-1007/s12469-013-0078-4.

Kupka, P., & Sawicki, P. (2015). Optymalizacja lokalizacji zajezdni tramwajowej w systemie komunikacji miejskiej. Logistyka, 2, 462–472.

Laport, G., Nickel, S., & Saldanha da Gama, F. (2015). Location Science. Cham: Springer, doi:10.1007/978-3-319-13111-5.

Mahadikar, J., Mulangi, R.H., & Sitharam, T.G. (2015). Optimization of bus allocation to depots by minimizing dead kilometers. Journal of Advanced Transportation, 49, 901–912, doi: 10.1002/atr.1312.

Melo, M. T., Nickel, S., & Saldanha da Gama, F. (2009). Facility location and supply chain management - A review. European Journal of Operational Research, 196(2), 401–412, doi:10.1016/j.ejor.2008.05.007.

Musso, E., & Sciomachen, A. (1997). Optimal location of bus depot in an urban area. Transactions on the Built Environment, 30, 93–103, doi: 10.2495/UT970091.

Roy, B., & Słowiński, R. (2013). Questions guiding the choice of a multicriteria decision aiding method. EURO Journal on Decision Processes, 1, 69–97, doi:10.1007/s40070-013-0004-7.

Rudyk, T., Szczepański, E., & Jacyna, M. (2019). Safety factor in the sustainable fleet management model. Archives of Transport, 49(1), 103–114, doi:10.5604/01.3001.0013.2780.

Saaty, T.L (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.

Sawicka, H. (2012). Metoda reorganizacji systemu dystrybucji towarów. Politechnika Warszawska, Rozprawa doktorska, Warszawa.

Sawicka, H. (2020). The Methodology of Solving Stochastic Multiple Criteria Ranking Problems Applied in Transportation. Transportation Research Procedia, 47, 219–226, doi: 10.1016/j.trpro.2020.03.092.

Sawicki, P., & Fierek, S. (2017). Problem jednoczesnego wyznaczania przebiegu linii i lokalizacji zajezdni w systemie transportu zbiorowego. Prace Naukowe Politechniki Warszawskiej - Transport, Problemy transportu w inżynierii logistyki – część 3, 119, 429–444.

Sawicki, P., & Fierek, S. (2018a). Mixed public transport lines construction and vehicle’s depots location problems. In Macioszek E., Sierpiński G. (Eds.). Recent Advances in Traffic Engineering and Transport Networks and Systems. Lecture Notes in Networks and Systems, 21, (p. 213–224). Heidelberg: Springer, doi: 10.100-7/978-3-319-64084-6_20.

Sawicki, P., & Fierek, S. (2018b). The impact of long-term travel demand changes on mixed decision problems of mass transit lines construction and vehicles' depots location. Technical Transactions, 6, 103–112, doi: 10.4467/z23537-37XCT.18.090.8695.

Sawicki, P., & Kupka, P. (2016). Ustalanie lokalizacji zajezdni tramwajowej w systemie komunikacji miejskiej z zastosowaniem metody wspomagania decyzji. Transport Miejski i Regionalny, 6, 6–11.

Sawicki, P., & Sawicka, H. (2020). Manual - How to use AHORNsimple® to support multiple criteria decision process? Virtual Decision Lab, (

Szczepański, E., Jachimowski, R., Izdebski, M., & Jacyna-Gołda, I. (2019). Warehouse location problem in supply chain designing: a simulation analysis. Archives of Transport, 50(2), 101–110, doi:10.5604/01.3001.0013.5-752.

Vincke, P. (1992). Multicriteria Decision-Aid. Chichester: John Wiley & Sons.

Xi, B.D., Su, J., Huang, G.H., Qin, X.S., Jiang, Y.H, Huo, S.L., Ji, D.F., & Yao, B. (2010). An integrated optimization approach and multicriteria decision analysis for supporting the waste-management system of the City of Beijing, China. Engineering Applications of Artificial Intelligence, 23(4), 620–631, doi: 10.10-16/j.engappai.2010.01.002.

Żochowska, R., & Soczówka, P. (2018). Analysis of selected transportation network structures based on graph measures. Scientific Journal of Silesian University of Technology. Series Transport, 98, 223–233, doi:10.20858/sjsutst. 2018.98.21.






Original articles

How to Cite

Sawicki, P., & Sawicka, H. (2021). Combined optimisation and MCDA based solution of the tram depot location problem. Archives of Transport, 60(4), 88-103.


Similar Articles

1-10 of 280

You may also start an advanced similarity search for this article.