Optimizing a bi-objective multi-product EPQ model with defective items, rework and limited orders: NSGA-II and MOPSO algorithms

• A novel bi-objective multi-product EPQ model is developed.
• Number of orders is limited and imperfect re-workable items are produced.
• NSGA-II and MOPSO are proposed to solve the problem.
• The solution qualities of both algorithms do not differ statistically.
• The required CPU time of MOPSO is considerably lower than NSGA-II.

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.