Competitive Facilities Location Problems with Fuzzy Random Demand

This paper proposes a new location problem of competitive facilities, e.g. shops and stores, with uncertainty and vagueness including demands for the facilities in a plain. By representing the demands for facilities as fuzzy random variables, the location problem can be formulated as a fuzzy random programming problem. For solving the fuzzy random programming problem, first the α-level sets for fuzzy numbers are used for transforming it to a stochastic programming problem, and secondly, by using their expectations and variances, it can be reformulated to a deterministic programming problem. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic oscillation. The efficiency of the solution method is shown by applying it to numerical examples of the facility location problems.