A Mathematical Model for Fire Station Locating with Maximal Covering Location and Multi Period Approach

Document Type : Original Article

Authors

1 Associate Professor, Department of Industrial Engineering, Alzahra University, Tehran, Iran

2 M.Sc of Industrial Engineering, Bu-Ali Sina University, Hamedan, Iran

3 M.Sc Student of Industrial Engineering, Kharazmi University, Tehran, Iran.

Abstract

In this study, a model is presented for fire station’s locating and facilities allocating to stations in different periods and emergency situations. This model is designed, considering amount of demands and facilities coverage radius, being dynamic (based on traffic and type of region) in different periods. According to fact, in the presented model, amount of demand for each demand point depends on number of coverage by facilities and amount of demand of demand point .in this model , location of stations is determined once in different periods. The numbers of facilities which are allocated to stations are allocated dynamically and can be relocated in different periods. In the model, each strategic demand point (arsenal, food storage and so on) can be potential point for facilities. This is a complicated model so to solve this model, particle swarm optimization algorithm and combinatorial matrix have been suggested. In the suggested algorithm, method of making matrix is such that locating matrix and early and final allocation are presented in a single matrix. Finally the results of proposed algorithm with artificial bee colony were compared the results show that this algorithm is better in terms of quality of answers and solving time.

Keywords

References

[1]      Church R., ReVelle C.S., (1974) "The maximal covering location problem", Papers of the Regional Science Association 32, 101–118.
[2]      ReVelle C.S., Eiselt H.A., (2005)" Location analysis: a synthesis and survey", European Journal of Operational Research 165 (1) ,1–19.
[3]      ReVelle C.S., Eiselt H.A., M.S. (2008)" Daskin, A bibliography for some fundamental problem categories in discrete location science", European Journal of Operational Research 184(3) 817–848.
[4]      Corrêa F.d.A., Lorena L.A.N, Ribeiro, G.M. (2009)."A decomposition approach for the probabilistic maximal covering location–allocation problem", Computers & Operations Research 36 (10), 2729–2739.
[5]      Batanovic V., Petrovic D., Petrovic R., (2009). "Fuzzy logic based algorithms for maximum covering location problems", Information Sciences 179 (1–2), 120–129.
[6]      Berman O., Wang J., (2011) "The minmax regret gradual covering location problem on a network with incomplete information of demand weights", European Journal of Operational Research 208 (3), 233–238.
[7]      ReVelle C., Scholssberg, M., Williams J., (2008) "Solving the maximal covering location problem with heuristic concentration", Computers & Operations Research 35 (2) ,427–435.
[8]      Curtin K.M., Hayslett K., Qiu F., (2007) " Determining optimal police patrol areas with maximal covering and backup covering location models", Networks and Spatial Economics 10 ,125–14.
[9]      Rajagopalan H.K., Saydam C., Xiao J., (2008) "A multiperiod set covering location model for dynamic redeployment of ambulances", Computers & Operations Research 35 (3), 814–826.
[10]   Schilling D.A., (1980) "Dynamic location modeling for public-sector facilities: a multicriteria approach", Decision Sciences 11 (4), 714–724.
[11]   Gunawardane G., (1982) "Dynamic versions of set covering type public facility location problems", European Journal of Operational Research 10 (2), 190–195.
[12]   Repede J.F., Bernardo J.J., (1994)"Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky", European Journal of Operational Research 75 (3), 567–581.
[13]   Marianov V., Revelle C., (1994) "The queuing probabilistic location set covering problem and some extensions", Socio-Economic Planning Sciences 28 (3), 167–178.
[14]   Gendreau M., Laporte G., Semet F., "(2001) A dynamic model and parallel tabu search heuristic for real-time ambulance relocation", Parallel Computing 27 (12), 1641–1653.      
[15]   Basar A., Catay B., Unluyurt T., (2011) "A multi-period double coverage approach for locating the emergency medical service stations in Istanbul", Journal of the Operational Research Society 62, 627–637.
[16]   Ghaderi, A., & Jabalameli, M.S. (2013) "Modeling the budget-constrained dynamic uncapacitated facility location–network design problem and solving it via two efficient heuristics: a case study of healthcare", Mathematical and Computer Modeling, 57(3), 382–400.
[17]   Nickel, S., & Saldanha da Gama, F. (2015) "Multi-period facility location. In Location science" (pp.289–310). Springer.
[18]   Correia, I., & Saldanha da Gama, F. (2015). Facility location under uncertainty. In Location science (pp.177203). Springer.
[19]   Taghavifard M., Dehghani M.H., Aghaei M, (2015). Development model to determine the optimal order with a choice of preferred suppliers and solved using genetic algorithm, NSGA-II, Management Researches in Iran, 19(2):66-89 (in Persian).
[20]   Schutte J.F., Reinbolt J.A., Frgly B.J, Haftka, R.T., & George, A.D. (2004). Parallel global optimization with the particle swarm algorithm, International Journal for numerical Methods in Engineering, 61(13): 2296-2315.
[21]   Parsopoulos K.E., & Vrahabits, M.M. (2004). On the computation of all global minimizers through particle swarm optimization, Evolutionary computation IEEE Transaction, 211-224.
[22]   Mansori F., Abbasnejad T., Asgarpour H., (2016). Agile supply chain network design condition dependence on demand to price, Modern Researches in
Decision Making, 2(1):180-206, (in Persian).

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