Production and Transportation Planning - A fuzzy Approach for Minimizing the Total Cost

In this paper, we deal with the production and transportation planning of a household appliances manufacturer that has production facilities and central stores for resellers in several sites in Europe. Each store can receive products from all production plants and it is not necessary that all products are produced in all production units. The transport between any two bases is done by trucks. For simplicity we assume, that each truck has the same capacity of M EURO-pallets, and for each product the unit is EURO-pallet. The target of this paper is to determine a production and transportation plan that minimize the total sum of the production cost and the transportation cost. For working in a realistic environment we assume that the production capacities in the different plants and the demand in the sales bases are not known exactly but the management can describe the data in form of fuzzy numbers. By using an inter-active algorithm for solving the fuzzy linear programming system we achieve a stable production and a satisfactory supply of the products. Moreover, we demonstrate that this integer programming problem can adequately be solved without using computation-intensive integer programming algorithms. Additionally, in the course of the inter-active solution process the production bottlenecks get clearly visible. A numerical example illustrates the efficiency of the proposed procedure.