Integrated optimization of an inventory-distribution system with cooperation among distribution centers

A new optimization model for the commodity distribution system consisting of distribution centers and consumer points and its calculation procedure are discussed. In this paper, demand is assumed to be a random variable whose probability distribution is known and stationary, and an integrated model is built where both inventory control and transportation problems are considered simultaneously. The assignment of consumer points to distribution centers is not fixed. The problem is formulated as an optimization problem to minimize the expectation of total of inventory holding costs, shortage costs and transportation costs, where the decision variables are the target inventory and transportation amount. The techniques of simulation and linear programming are used to calculate the expected costs, and an original direct search method is developed in order to decide the optimum target inventory. A genetic algorithm is also tested and compared with the proposed direct search method. The meaning of the model in this paper, as well as the effectiveness of the proposed calculation procedure, is clarified by numerical examples and computational experiments.