Application of Fuzzy Programming with Recourse in Material Requirement Planning Problem

Material requirement planning (MRP) is a popular approach used in production processes for planning. Many forms of uncertainly in practice affect the production process and different approaches have been presented for MRP with uncertainty. In order to model MRP problem under fuzzy uncertainly, we present a fuzzy programming model with recourse based on credibility theory. We consider fuzzy variables coefficients related to the market demand and the unit price of material on spot market. The objective value is minimizing the expected value of total material procurement cost. This proposed MRP problem belongs to an infinite-dimensional optimization problem that cannot be solved directly and it is 0-1 mix integer program, neither linear nor convex, traditional optimization algorithms cannot be used to solve it. So to solve the presented MRP model, we design a hybrid algorithm which combines approximation approach (AA) and particle swarm optimization (PSO). We also present one numerical example to illustrate the effectiveness of the designed algorithm.

1. Introduction

Most of manufacturing firms and trading companies spend more than half of their sales dollar in the purchase of material. Consequently, purchase material at right quality from right suppliers is very important to them. However, due to the uncertainty involved in material's price, market's demand and the uncertainty of changing raw material to finished product and so on, the MRP problem is hard to solve. But in order to enhance the validity of the decision made in MRP problem, we should consider these uncertainty factors when making decision in MRP problem.