A Stackelberg Location Problem on a Network with Fuzzy Random Demands

Abstract

This paper proposes a competitive facility location between two decision-makers (DMs), one of who has a priority to decision-making on a network with demands whose sites are uncertainly and vaguely. For representing such uncertainness and vagueness, the distance between a demand's site and one point in the network is given as a fuzzy random variable. Then, an optimal location problem for the DM with the above priority can be formulated as a Stackelberg location problem (SLP) with the fuzzy random variables. By using the alpha-level set, expectation, and variance, the SLP is reformulated as a version of conventional Stackelberg location problem on a network. Although previous study has shown theorems for the optimality of the SLP on tree network, this paper shows theorems for the optimality of the SLP on general network.