Fuzzy two-stage material procurement planning problem

Material procurement planning (MPP) deals with the problem that purchasing the right quantity of material from the right supplier at the right time, a purchaser can reduce the material procurement costs via a reasonable MPP model. In order to handle the MPP problem in a fuzzy environment, this paper presents a new class of two-stage fuzzy MPP models, in which the material demand, the spot market material unit price and the spot market material supply quantity are assumed to be fuzzy variables with known possibility distributions. In addition, the procurement decisions are divided into two groups. Some procurement decisions, called first-stage decisions, must be taken before knowing the the particular values taken by the fuzzy variables; while some other decisions, called second-stage decisions, can be taken after the realizations of the fuzzy variables are known. The objective of the proposed fuzzy MPP model is to minimize the expected material procurement costs over the two stages. On other hand, 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 whose objective function cannot be computed exactly. To avoid this difficulty, we suggest an approximation approach (AA) to evaluating the objective function, and turn the original MPP model into an approximating finite-dimensional one. To show the credibility of the AA, the convergence about the objective function of the approximating MPP model to that of the original MPP one is 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, the traditional optimization algorithms cannot be used to solve it. Therefore, we design an AA-based particle swarm optimization to solve the approximating two-stage fuzzy MPP model. Finally, we apply the two-stage MPP model to an actual fuel procurement problem, and demonstrate the effectiveness of the designed algorithm via numerical experiments.

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