Two metaheuristics to solve a multi-item multiperiod inventory control problem under storage constraint and discounts

In this paper, a multi-item multiperiod inventory control problem with all-unit and/or incremental quantity discount policies under limited storage capacity is presented. The independent random demand rates of the items in the periods are known and the items are supplied in distinct batch sizes. The cost consists of ordering, holding, and purchasing. The objective is to find the optimal order quantities of all items in different periods such that the total inventory cost is minimized and the constraint is satisfied. A mixed binary integer programming model is first developed to model the problem. Then, a parameter-tuned genetic algorithm (GA) is employed to solve it. Since there is no benchmark available in the literature, a memetic algorithm (MA) is utilized as well to validate and verify the results obtained. The model implementation is next presented using some numerical examples and finally the performances of the proposed GA and MA are compared using two statistical tests and a simple additive weighting method. The results show that GA has better performance than MA in terms of average objective function value and average run time using the two comparison procedures.

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