Facility location problem with stochastic demand and multi-objective considering queuing theory framework

Abstract

In this paper, the facility location problem with immobile servers is studied. In proposed model, tow objective functions have been considered: (1) minimizing the average customer waiting time and (2) minimizing the fixed cost of facility installation. The M/M/K queuing system has been used to formulate the problem. Also Customers are assumed to visit the closest open facility. Simulated Annealing algorithm with LP metric framework has been used to solve the proposed model. Several examples are presented to demonstrate the applications of the proposed methodology.

Keywords


[1] Pasandideh, H.R., Akhavan Niaki, T., "Genetic application in a facility location problem with random demand within queuing framework", Journal of Intelligent manufacturing, Vol. 23, No. 3, pp. 651-659, 2012.
[2] Zanjirani Farahani R., Hekmatfar M., "Facility Location", Springer, 2009.
[3] Larson R.C., "A hypercube queueing model for facility location and redistricting in urban emergency services", Computers and Operations Research, Vol. 1, pp. 67-95, 1974.
[4] Daskin M.S., "A maximum expected covering location model: formulation, properties and heuristic solutions", Transportation Science, Vol. 17, pp. 48-70, 1983.
[5] Berman O., Larson R., Chiu S., "Optimal server location on a network operating as an M/G/1 queue", Operations Research, Vol. 12, No. 4, pp. 746-771, 1985.
[6] Batta R., "Single server queueing–location models with rejection", Transportation Science, Vol. 22, pp. 209-216, 1988.
[7] Batta R., Larson R., Odoni A., "A single-server priority queueing–location model", Networks, Vol. 8, pp. 87-103, 1988.
[8] Wang Q., Batta R., Rump CH.M., "Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers", Annals of Operations Research, Vol. 111, pp. 17-34, 2002.
[9] Berman O., Larson R.C., Fouska, N., "Optimal location of discretionary facilities", Transportation Science, Vol. 26, pp. 201-211, 1992.
[10] Marianov V., ReVelle C., "The queuing maximal availability location problems: a model for the sitting of emergency vehicles", European Journal of Operational Research, Vol. 93, pp. 110-120, 1996.
[11] Marianov V., Serra D., "Probabilistic maximal covering location–allocation models for congested systems", Journal of Regional Science, Vol. 38, No. 3, pp. 401-424, 1998.
[12] Drezner T., Drezner Z., "The gravity multiple server location problem", Computers and Operations Research, Vol. 38, pp. 694-701, 2011.
[13] زرین­ پور، ن.، "چارچوب مدل مکان­یابی حداکثر پوشش با امکان ایجاد ازدحام پایان­نامه کارشناسی ارشد مهندسی صنایع، دانشکده مهندسی صنایع دانشگاه الزهرا، 1389.
[14] اصغرپور، م. ج.، "تحقیق در عملیات پیشرفته"، چاپ ششم، انتشارات دانشگاه تهران، تهران، 1388
[15] Aarts E., Korst J., Michiels W., "Simulated annealing", Springer Verlag, 2005.