Abstract
Article history: Received July 11 2014 Received in Revised Format October 23 2014 Accepted October 26 2014 Available online October 26 2014 Vertex and p-center problems are two well-known types of the center problem. In this paper, a pcenter problem with uncertain demand-weighted distance will be introduced in which the demands are considered as fuzzy random variables (FRVs) and the objective of the problem is to minimize the maximum distance between a node and its nearest facility. Then, by introducing new methods, the proposed problem is converted to deterministic integer programming (IP) problems where these methods will be obtained through the implementation of the possibility theory and fuzzy random chance-constrained programming (FRCCP). Finally, the proposed methods are applied for locating bicycle stations in the city of Tabriz in Iran as a real case study. The computational results of our study show that these methods can be implemented for the center problem with uncertain frameworks. © 2015 Growing Science Ltd. All rights reserved
Highlights
The facility location-allocation problem plays an important role in many firms and organizations
This paper proposes the vertex p -center problem with uncertain demandweighted distance in which the demands are considered as fuzzy random variables (FRVs)
The most important aim of this paper is to introduce new approaches for the problem, by using possibility and necessity measures which are based on the possibility theory (Dubois & Prade, 2001) and fuzzy random chance-constrained programming (FRCCP)
Summary
The facility location-allocation problem plays an important role in many firms and organizations. In stochastic facility location problems, the uncertain parameters are distinguished by random variables where their probability distribution is available. Based on possibility theory and fuzzy set theory, which deals with ambiguous and imprecise concepts, other methods have been developed for solving the facility location problems with uncertain parameters. Fuzziness and randomness of parameters are mixed up with each other and defined a hybrid uncertain variable in the facility location problem. Wang and Watada (2012) studied a hybrid modified PSO approach to VaR-based facility location problems with variable capacity in the fuzzy random uncertainty. This paper proposes the vertex p -center problem with uncertain demandweighted distance in which the demands are considered as fuzzy random variables (FRVs).
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