Abstract
Facility location-allocation problem aims at determining the locations of some facilities to serve a set of spatially distributed customers and the allocation of each customer to the facilities such that the total transportation cost is minimized. In real life, the facility location-allocation problem often comes with uncertainty for lack of the information about the customers’ demands. Within the framework of uncertainty theory, this paper proposes an uncertain facility location-allocation model by means of chance-constraints, in which the customers’ demands are assumed to be uncertain variables. An equivalent crisp model is obtained via the \(\alpha \)-optimistic criterion of the total transportation cost. Besides, a hybrid intelligent algorithm is designed to solve the uncertain facility location-allocation problem, and its viability and effectiveness are illustrated by a numerical example.
Similar content being viewed by others
References
Badri, M. A. (1999). Combining the analytic hierarchy process and goal programming for global facility location-allocation problem. International Journal of Production Economic, 62, 237–248.
Charnes, A., & Cooper, W. (1961). Management models and industrial applications of linear programming. New York: Wiley.
Cooper, L. (1963). Location-allocation problems. Operational Research, 11, 331–344.
Darzentas, J. (1987). A discrete location model with fuzzy accessibility measures. Fuzzy Sets and Systems, 23, 149–154.
Gao, Y. (2012). Uncertain models for single facility location problems on networks. Applied Mathematical Modelling, 36(6), 2592–2599.
Gong, D., Gen, M., Xu, W., & Yamazaku, G. (1995). Hybrid evolutionary method for obstacle location-allocation problem. International Journal of Computers and Industrial Engineering, 29, 525–530.
Hodey, M., Melachrinoudis, E., & Wu, X. (1997). Dynamic expansion and location of an airport: A multiple objective approach. Transportation Research: Part A-Policy and Practice, 31, 403–417.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–292.
Logendran, R., & Terrell, M. P. (1988). Uncapacitated plant location-allocation problems with price sensitive stochastic demands. Computers and Operations Research, 15, 189–198.
Li, X., & Liu, B. (2009). Hybrid logic and uncertain logic. Journal of Uncertain Systems, 3(2), 83–94.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.
Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2009). Theory and practice of uncertain programming (2nd ed.). Berlin: Springer.
Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.
Liu, B. (2010). Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems, 4(3), 163–170.
Liu B. & Chen X. W. (2013). Uncertain multi-objective programming and uncertain goal programming, http://orsc.edu.cn/online/131020.
Liu, B., & Yao, K. (2012). Uncertain multilevel programming: Algorithm and application, http://orsc.edu.cn/online/120114.
Liu, Y. H., & Ha, M. H. (2010). Expected value of function of uncertain variables. Journal of Uncertain Systems, 13, 181–186.
Murray, A. T., & Church, R. L. (1996). Applying simulated annealing to location-planning models. Journal of Heuristics, 2, 31–53.
Murtagh, B. A., & Niwattisyawong, S. R. (1982). Efficient method for the muti-depot location em dash allocation problem. Journal of the Operational Research Society, 33, 629–634.
Qin, Z., & Kar, S. (2013). Single-period inventory problem under uncertain environment. Applied Mathematics and Computation, 219(18), 9630–9638.
Wang, G., Tang, W., & Zhao, R. (2013). An uncertain price discrimination model in labor market. Soft Computing, 17(4), 579–585.
Wen, M., & Iwamura, K. (2008). Fuzzy facility location-allocation problem under the Hurwicz criterion. European Journal of Operational Research, 184, 627–635.
Yao, K., & Ji, X. (2014). Uncertain decision making and its application to portfolio selection problem. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(1), to be published.
Zeng, Z., Wen, M., & Kang, R. (2013). Belief reliability: A new metrics for products’ reliability. Fuzzy Optimization and Decision Making, 12(1), 15–27.
Zhou, J., & Liu, B. (2003). New stochastic models for capacitated location-allocation problem. Computers & Industrial Engineering, 4, 111–125.
Zhou, J., & Liu, B. (2007). Modeling capacitated location-allocation problem with fuzzy demands. Computers & Industrial Engineering, 53(3), 454–468.
Acknowledgments
This work was supported by National Natural Science Foundation of China (Nos. 71201005, 71371019, 61104132), and in part by the Program for New Century Excellent Talents in University (No. NCET-12-0026).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Wen, M., Qin, Z. & Kang, R. The \(\alpha \)-cost minimization model for capacitated facility location-allocation problem with uncertain demands. Fuzzy Optim Decis Making 13, 345–356 (2014). https://doi.org/10.1007/s10700-014-9179-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10700-014-9179-z