Possibilistic Mixed Integer Linear Programming Approach for Production Allocation and Distribution Supply Chain Network Problem in the Consumer Goods Industry

In the consumer goods industry there is an ongoing trend towards an increased product variety and shorter replenishment cycle times. Hence, manufacturers seek a better coordination of production and distribution activities. Our study is motivated by the production-distribution problem encountered by a soft-drink company operating in consumer goods industry. The problem is to determine the optimal allocation of products and routing decisions for a multi-echelon supply chain to minimize the total supply chain cost comprising of production, setup, inventory and distribution costs. A mixed integer linear programming (MILP) model is proposed to describe the optimization problem. However, a real supply chain operates in a highly dynamic and uncertain environment. The ambiguity of cost parameters is considered in the objective function of the model. The proposed approach uses the strategy of minimizing the most possible cost, maximizing the possibility of obtaining lower cost, and minimizing the risk of obtaining higher cost. Zimmermann’s fuzzy multi objective programming method is then applied for achieving an overall satisfactory compromise solution. The applicability of the proposed model is illustrated through a case study in consumer goods industry.