Developing a New Bi-Objective Functions Model for a Hierarchical Location-Allocation Problem Using the Queuing Theory and Mathematical Programming

Journal of Optimization in Industrial Engineering

مقاله 12، دوره 12، شماره 2، مهر 2019، صفحه 149-154   

نوع مقاله: Original Manuscript

شناسه دیجیتال (DOI): 10.22094/joie.2018.350.0

نویسندگان

Parham Azimi^* ؛ Abulfazl Asadollahi

Department of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

چکیده

In this research, a hierarchical location-allocation problem is modeled in a queue framework. The queue model is considered as M/M/1/k, in which system capacity is finite, equals to k. This is the main contribution of the current research. Customer's enters to the system in order to find the service according to a Poisson. In this problem, the hierarchical location-allocation model is considered in two levels. Also, the model has two objective functions: maximizing the total number of demand coverage and minimizing the waiting time of customers in queues to receive services. After modeling and verifying the validity of the presented model, it is solved using NSGA II and MOPSO meta-heuristics.

کلیدواژه‌ها

Location-Allocation Problems؛ Hierarchical Models؛ M/M/m Queuing Model؛ Multi-objective programming؛ Taguchi Method؛ NSGA-II algorithm

مراجع

Başar, A., Kabak O., İlker Topçu, Y. Bozkaya, B. Location Analysis in Banking: A New Methodology and Application for a Turkish Bank. Volume 232 of the series International Series in Operations Research & Management Science pp. 25-54

 Bell, J.E., Griffis, S.E. Military Applications of Location Analysis. Volume 232 of the series International Series in Operations Research & Management Science pp. 403-433

Boffey, B., Galva˜o, R. Espejo,L. (2007). A review of congestion models in the location of facilities with immobile servers, European Journal of Operational Research 178, 643–662.

Chan, Y. Mahan, J. M.,  Chrissis, J.W., Drake, D.W.& Wang, D. (2008). Hierarchical maximal-coverage location–allocation: Case of generalized search-and-rescue, Computers & Operations Research 35,1886 – 1904.

Collette Y, Siarry P (2003). Multi-objective optimization: principlesand case studies. Springer, New York.

Galvao, R. D., Gonzalo Acosta Espejo, L., Boffey, B.  (2003). Dual-based heuristics for a hierarchical covering location problem, Computers & Operations Research 30, 165–180.

Galvao, R. D., Gonzalo Acosta Espejo, L., Boffey, B. (2002). A hierarchical model for the location of perinatal facilities in the municipality of Rio de Janeiro, European Journal of Operational Research 138,495–517.

Galvao, R. D., Gonzalo Acosta Espejo, L., Boffey, B., Yates, D. (2006). Load balancing and capacity constraints in a hierarchical location model, European Journal of Operational Research 172, 631–646.

Gama, M., Santos, B.F. & Paola Scaparra, M. (2015). A multi-period shelter location-allocation model with evacuation orders for flood disasters. EURO Journal on Computational Optimization, pp. 1-25

Hodgson, M.J. & Kruse Jacobsen, s. (2009). A hierarchical location-allocation model with travel based on expected referral distances, Ann Oper Res 167,271–286.

Hodgson, M.J. (1986). A Hierarchical Location-Allocation Model with Allocations Based On Facility Size, Annals of Operations Research 6,273-289.

Jayaraman, V., Gupta, R. Pirkul, H. (2003). Selecting hierarchical facilities in a service-operations environment, European Journal of Operational Research 147, 613–628.

 Khodaparasti, S.,  Jahedi, S., Bruni, M. E. & Beraldi. P. Enhancing community based health programs in Iran: a multi-objective location-allocation model. Health Care Management Science, pp. 1-15

Lee, J.M. & Lee, Y.H. (2012). Facility location and scale decision problem with customer preference, Computers & Industrial Engineering 63,184–191.

Marianov, M. & Serra, D. (1998). Probabilistic maximal covering location-allocation models for congested systems, Journal of Regional Science, Vol. 38, NO. 3,401-424.

Marianov, V., Serra, D. (2001). Hierarchical location allocation models for congested systems, European Journal of Operational Research 135,195-208.

Mohammadi, M., Jolai, F.& Rostami, H. (2011). An M/M/c queue model for hub covering location problem, Mathematical and Computer Modelling 54, 2623–2638.

NARUL, C. (1981). Hierarchical location-allocation problems: A classification scheme.

Rabieyan, R. & Seifbarghy, M. (2010). Maximal Benefit Location Problem for a Congested System, Journal of Industrial Engineering 5,73-83.

Sahin, G. & Sural, H. (2007). A review of hierarchical facility location models, Computers & Operations Research 34,2310 – 2331.

Teixeira, J. C. &. Antunes, A.P. (2008). A hierarchical location model for public facility planning, European Journal of Operational Research 185,92–104.

Vilcapoma Ignacio, A.A., Ferreira Filho, J.M. V. & Diéguez Galvao, R. (2008). Lower and upper bounds for a two-level hierarchical location.Problem in computer networks, Computers & Operations Research 35,1982 – 1998.

Zitzler E (1999) Evolutionary algorithm for multi-objective optimization: methods and applications. Ph.D. Dissertation, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.