Abstract
This paper focuses on a Stackelberg location problem on a tree network with demands whose sites are given uncertainly and vaguely. By representing their sites as fuzzy random variables on it, the distances from demands to facilities can be defined as fuzzy random numbers, and then the location problem can be formulated as a fuzzy random bilevel programming problem. For solving the problem, first we introduce the α-level set for fuzzy random numbers and transfer it to a random bilevel programming problem. Next, we consider the situation that a leader gives a guaranteed probability for her/his objective function value. Then, by adding the constraint under it to both decision makers, it can be reformulated as a bilevel programming problem, which is a version of conventional Stackelberg location problem. Finally its complexity is shown, and then a solution method for the problem if the leader locates one facility is also shown based upon the characteristics of facility location.
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