Two-stage fuzzy generalized assignment problem with value-at-risk criteria

This paper presents a new type of two-stage fuzzy generalized assignment problem (FGAP) models with critical value-at-risk (VaR) criteria based on credibility theory and two-stage fuzzy optimization method. Since the proposed FGAP model often includes fuzzy coefficients defined through known possibility distributions, it is inherently an infinite-dimensional optimization problem that can rarely be solved directly. Thus, algorithm procedures for solving such an optimization problem must rely on intelligent computing and approximation schemes. In this paper, we employ an approximation approach (AA) to calculate the objective function of the two-stage FGAP, and discuss the convergence about the use of the approximation method. Considering that the approximating FGAP model is neither linear nor convex, we design a hybrid particle swarm optimization (PSO) algorithm. Finally, one numerical example with six tasks and three agents is given to demonstrate the feasibility of the designed algorithm.