Optimizing material procurement planning problem by two-stage fuzzy programming

Abstract

This paper presents a new class of two-stage fuzzy material procurement planning (MPP) models with minimum-risk criteria, in which the material demand, the spot market material unit price and the spot market material supply quantity are uncertain and assumed to be fuzzy variables with known possibility distributions. We formulate the two-stage MPP model with the objective of maximizing the credibility of the total material procurement costs less than a given allowable investment level, and the credibility can be regarded as the material procurement risk criteria in a fuzzy environment. Since the fuzzy material demand, the fuzzy spot market material unit price and the fuzzy spot market material supply quantity are usually continuous fuzzy variables with infinite supports, the proposed MPP model belongs to an infinite-dimensional optimization problem that cannot be solved directly. To avoid this difficulty, we apply an approximation approach (AA) to the proposed two-stage fuzzy MPP model, and turn it into an approximating finite-dimensional optimization one. The convergence about the objective function of the approximating two-stage MPP model to that of the original two-stage MPP one is also discussed. Since the exact analytical expression for the objective function in the approximating fuzzy MPP model is unavailable, and the approximating MPP model is a mixed-integer program that is neither linear nor convex, traditional optimization algorithms cannot be used to solve it. Therefore, we develop two heuristic algorithms to solve the approximating MPP model. The first is a particle swarm optimization (PSO) algorithm based on the AA, and the second is a hybrid PSO algorithm which based on the AA and a neural network (NN). Finally, we provide an actual optimization problem about the fuel procurement to compare the effectiveness of the designed algorithms.