A hybrid method of fuzzy simulation and genetic algorithm to optimize constrained inventory control systems with stochastic replenishments and fuzzy demand

Multi-periodic inventory control problems are mainly studied by employing one of two assumptions. First, the continuous review, where depending on the inventory level, orders can happen at any time, and next the periodic review, where orders can only be placed at the beginning of each period. In this paper, we relax these assumptions and assume the times between two replenishments are independent random variables. For the problem at hand, the decision variables (the maximum inventory of several products) are of integer-type and there is a single space-constraint. While demands are treated as fuzzy numbers, a combination of back-order and lost-sales is considered for the shortages. We demonstrate the model of this problem is of an integer-nonlinear-programming type. A hybrid method of fuzzy simulation (FS) and genetic algorithm (GA) is proposed to solve this problem. The performance of the proposed method is then compared with the performance of an existing hybrid FS and simulated annealing (SA) algorithm through three numerical examples containing different numbers of products. Furthermore, the applicability of the proposed methodology along with a sensitivity analysis on its parameters is shown by numerical examples. The comparison results show that, at least for the numerical examples under consideration, the hybrid method of FS and GA shows better performance than the hybrid method of FS and SA.