Optimal order quantity for deterministic demand with piecewise amount discount by genetic algorithm

With regards to the features of supply chain components in a sales company, the paper proposes the problem of allocating the replenishment orders of multiple products in several periods with deterministic demands of downstream customers. The optimization model aims to minimize the operational costs considering constraints of purchase quantity, inventory capacity and current capitals, i.e., an Economic Order Quantity optimization model based on the piece-wise discounts with respect to total purchase amount. To solve the model, a Genetic Algorithm is designed in terms of its characteristics; the chromosome coding with purchase quantity of periods. A heuristic method is employed to initialize the evolutionary population; the interchange-oriented crossover and the heuristic mutation are designed based on single-point or genes segment; and infeasible chromosomes are revised by means of a special repair strategy. The simulation experiments are implemented with practical data of a sales company and the results verified the effectiveness and efficiency of the proposed model and the solving algorithm.