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The Scientific World Journal
Volume 2015 (2015), Article ID 826363, 9 pages
Research Article

A Simulated Annealing Methodology to Multiproduct Capacitated Facility Location with Stochastic Demand

1School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China
2School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410076, China
3Business Administration College, Zhejiang University of Finance & Economics, Hangzhou 310018, China

Received 29 June 2014; Revised 23 November 2014; Accepted 28 November 2014

Academic Editor: Chih-Chou Chiu

Copyright © 2015 Jin Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A stochastic multiproduct capacitated facility location problem involving a single supplier and multiple customers is investigated. Due to the stochastic demands, a reasonable amount of safety stock must be kept in the facilities to achieve suitable service levels, which results in increased inventory cost. Based on the assumption of normal distributed for all the stochastic demands, a nonlinear mixed-integer programming model is proposed, whose objective is to minimize the total cost, including transportation cost, inventory cost, operation cost, and setup cost. A combined simulated annealing (CSA) algorithm is presented to solve the model, in which the outer layer subalgorithm optimizes the facility location decision and the inner layer subalgorithm optimizes the demand allocation based on the determined facility location decision. The results obtained with this approach shown that the CSA is a robust and practical approach for solving a multiple product problem, which generates the suboptimal facility location decision and inventory policies. Meanwhile, we also found that the transportation cost and the demand deviation have the strongest influence on the optimal decision compared to the others.