A fuzzy model for operational supply chain optimization problems

A supply chain is a network of suppliers, manufacturing plants, warehouses, and distribution channels organized to acquire raw materials, to convert these raw materials to finished products, and to distribute these products to customers. Linear Programming is a widely used technique to optimize Supply Chain decisions. In the crisp approach to a supply chain problem, every parameter value is certain whereas in real life, the data are rather fuzzy than crisp. The fuzzy set theory has the capability of modelling the problems with vague information. In this paper, a fuzzy optimization model for supply chain problems is developed under vague information. The first objective of this model is to minimize cost associated with producing, distributing and inventorying of products under a variety constraints such as capacity, quality etc. The second objective of the model is to minimize the delivery times. The model considers the cost and time needed for supply of raw materials from different suppliers, production in different plants and distribution to different markets. The crisp version of the problem is utilized to determine aspiration levels for the fuzzy case where both objectives and constraints are fuzzy. A numerical example is given to show the usability of the fuzzy model.