A Multi-objective Competitive Location Problem under Queuing Framework

Document Type : Research Paper

Authors

1 Department of Industrial Engineering, Faculty of Technology and Engineering, University of Qom, Qom, Iran

2 Department of Industrial Engineering, University of Kashan, Kashan, Iran

Abstract

This paper addresses a situation in which a firm is willing to locate several new multi-server facilities in a geographical area to provide a service to his customers within the M/M/m/K queue system. As a new assumption, it is also considered that there is already operating competitors in such system. This paper is going to find the location of facilities in a way that the market share of entering firm is maximized. For this purpose, simultaneous minimization of total cost and maximum idle time in each facility is considered as two objective functions in the model. The total cost consists of two parts: (1) the fixed cost for opening a new facility, and (2) the operational costs regarding to the customers, which depends on travel time to the facility and the waiting time at the facility. In addition, in order to make the problem more adapted to real-world situations, two new constraints on budget and number of the servers in each facility are added to the model. Eventually, to tackle the suggested problem, a non-dominated sorting genetic algorithm (NSGA-II) and a non-dominated ranked genetic algorithm (NRGA) are utilized. Finally, the performance of algorithms are investigated via analyzing a set of test problems.

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Main Subjects


A. Weber, (1929), Uber den Standort der Industrien (Alfred Weber's Theory of the Location of Industries), University of Chicago, USA.
Aboolian R, Berman O, Krass D, (2007), Competitive facility location and design problem. European Journal of Operational Research, Vol. 182, pp. 40–62.
Al Jadaan, O, Rao, C R, Rajamani, L. (2008). Non-dominated ranked genetic
algorithm for solving multi-objective optimization problems: NRGA. Journal of Theoretical and Applied Information Technology, Vol. 4, pp. 60–67.
Bashiri M, Hosseininezhad SJ, (2009), A fuzzy group decision support system for multi-facility location problems. International Journal of Advanced Manufacturing Technology, Vol. 42, pp. 533–543.
Benati S, (1999), The maximum capture problem with heterogeneous customers. Computers & Operations Research, Vol. 26, pp. 1351–1367.
Benati S, Hansen P, (2002), The maximum capture problem with random utilities: Problem formulation and algorithms. European Journal of Operational Research, Vol. 143, pp. 518–530.
Beresnev V, (2013), Branch-and-bound algorithm for a competitive facility location problem. Computers & Operations Research, Vol. 40, pp. 2062–2070.
Biesinger B, Hu B, Raidl G, (2016), Models and algorithms for competitive facility location problems with different customer behavior. Springer, Annals of Mathematics and Artificial Intelligence, Vol. 76, pp. 93–119
Brandeau M, Chiu S, (1994), Location of competing facilities in a user-optimizing environment with market externalities. Transportation Science, Vol. 28, pp. 125–140.
Church R, ReVelle C, (1974), the maximal covering location problem. Regional science association international, Vol.  32, pp. 101–118.
Deb K, Agrawal S, Pratap A, Meyarivan T, (2000), A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II.  Proceedings of the parallel problem solving from nature VI (PPSN-VI), Vol. 1917, pp. 849–858.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester, U.K: Wiley.
Dobson G, Karmarkar U, (1987), Competitive location on a network. Operational Research, Vol. 35, pp. 565–574.
Drezner T, Drezner Z, Salhi S, (2002), solving the multiple competitive facilities location problem. European Journal of Operational Research, Vol. 142, pp. 138–151.
Eiselt H, Laporte G, Thisse J, (1993), Competitive location models: a framework and bibliography, Transportation Science, Vol. 27, pp. 44–54.
Hajipour V, Rahmati S.H.A, Pasandideh S.H.R, Akhavan Niaki S.T, (2014), A multi-objective harmony search algorithm to optimize multi-server location–allocation problem in congested systems. Computers & Industrial Engineering, Vol. 72, pp. 187–197.
Hakimi SL, (1964), Optimal locations of switching centers and the absolute centers and medians of a graph. Operations Research, Vol. 12, pp. 450–459.
Hakimi SL, (1983), on locating new facilities in a competitive environment. European Journal of Operational Research, Vol. 12, pp. 29–35.
Hillier F, Lieberman G (1986) Introduction to operations research. Holden-Day, Oakland.
Hotelling H, (1929), Stability in competition, Economic Journal, Vol. 39, pp. 41–57.
Loghmanian S.M.R, Jamaluddin H, Ahmad R, Yusof R, Khalid M, (2012), Structure optimization of neural network for dynamic system modeling using multi-objective genetic algorithm. The Natural Computing Applications, Vol. 21, pp. 1281–1295.
Maleki H. R, Khanduzi R, Akbari R. (2016), A novel hybrid algorithm for solving continuous single-objective defensive location problem. The Natural Computing Applications, Vol. 28 (No. 11), pp. 3323-3340.
Marianov V, Ríos M, Icaza MJ, (2008), Facility location for market capture when users rank facilities by shorter travel and waiting times. European Journal of Operational Research, Vol. 191, pp. 32–44.
McFadden D, (1974), Conditional logit analysis of qualitative choice behavior. In: Zarembka P (Ed) Frontiers in econometrics. Academic, New York.
Memari A, Abdul Rahim A.R, Hassan A, Ahmad R, (2016), A tuned NSGA-II to optimize the total cost and service level for a just-in-time distribution network.springer. The Natural Computing Applications, Vol. 28 (No. 11), pp. 3413-3427.
Michalewicz, Z., and Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, Vol. 4, pp. 1–32.
Rahmati S.H.A, Ahmadi A, Sharifi M, Chambari A, (2014), A multi-objective model for facility location–allocation problem with immobile servers within queuing framework. Computer and Industrial Engineering, Vol. 74, pp. 1-10.
Rezapour S, Farahani RZ, Fahimnia B, Govindan K, Mansouri Y, (2015) Competitive Closed-Loop Supply Chain Network Design with Price-Dependent Demands. Journal of Cleaner Production, Vol. 93, pp. 251–272.
Shiode S, Drezner Z, (2003), A competitive facility location problem on a tree network with stochastic weights. European Journal of Operational Research, Vol. 149, pp. 47–52.
Suárez-Vega R, Santos-Penate D.R, Dorta-Gonzalez P, Rodriguez-Diaz M, (2011), A multi-criteria GIS based procedure to solve a network competitive location problem. Applied Geography, Vol. 93, pp. 282-291.
Toregas C, Swain R, ReVelle C, Bergman L, (1971),The location of emergency service facilities. Operations Research, Vol. 19, pp. 1363–1373.
Vahdani B, Veysmoradi D, Shekari N, Mousavi S. M, (2016), Multi-objective, multi period location-routing model to distribute relief after earthquake by considering emergency roadway repair. The Natural Computing Applications, pp. 1–20.
Zarrinpoor N, Seifbarghy M, (2011), A competitive location model to obtain a specific market share while ranking facilities by shorter travel time. International Journal of Advanced Manuf Technol, Vol. 55, pp. 807–816.
Zitzler, E., Thiele, L. (1998). Multiobjective optimization using evolutionary algorithms a comparative case study. In: A. E. Eiben, T. Back, M. Schoenauer, H. P. Schwefel (Eds.), Fifth International Conference on Parallel Problem Solving from Nature (PPSN-V) ,Vol. 1498, pp. 292–301.