A Stackelberg Location Problem on a Tree Network with Fuzzy Random Demands

This paper focuses on a new 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 the tree network, the distance between a facility and a customer can be defined as a fuzzy random number. For solving the Stackelberg location problem with the fuzzy random distances, first we introduce the α-level set for fuzzy random numbers and transfer it to the Stackelberg location problem with random demands. Next, the randomness of demands is represented as scenarios for each demand. Then, by using their expectations and variances, it can be reformulated as a version of conventional Stackelberg location problem on a tree network. Its complexity and solution method are shown based upon the characteristics of the facility location.