Optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming

Abstract

In this paper, a multiproduct single vendor–single buyer supply chain problem is investigated based on the economic production quantity model developed for the buyer to minimize the inventory cost. The model to be more applicable for real-world supply chain problems contains five stochastic constraints including backordering cost, space, ordering, procurement, and available budget. The objective is to find the optimal order quantities of the products such that the total inventory cost is minimized while the constraints are satisfied. The recently-developed sequential quadratic programming (SQP), as one of the best optimization methods available in the literature, is used to solve the problem. Twenty numerical examples in 3 scales of small, medium, and large are solved in order to demonstrate the applicability of the proposed methodology and to evaluate its optimum performance. The results show that SQP has satisfactory performance in terms of optimum solutions, number of iterations to achieve the optimum solution, infeasibility, optimality error, and complementarity. Besides, the optimum performance of the SQP method is compared with the one of another exact method called interior point using the above numerical examples under similar conditions. The comparison results are in favor of the employed SQP. At the end, a sensitivity analysis is performed on the change rate of the objective function obtained based on the change rate of the variance of the order quantity.