A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model

In this research, an economic order quantity (EOQ) model is first developed for a two-level supply chain system consisting of several products, one supplier and one-retailer, in which shortages are backordered, the supplier’s warehouse has limited capacity and there is an upper bound on the number of orders. In this system, the supplier utilizes the retailer’s information in decision making on the replenishments and supplies orders to the retailer according to the well known (R, Q) policy. Since the model of the problem is of a non-linear integer-programming type, a genetic algorithm is then proposed to find the order quantities and the maximum backorder levels such that the total inventory cost of the supply chain is minimized. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology and to evaluate and compare its performances to the ones of a penalty policy approach that is taken to evaluate the fitness function of the genetic algorithm.