Bi-objective optimization of multi-product EPQ model with backorders, rework process and random defective rate

In this paper a bi-objective multi-product EPQ model is developed where defective products produce with a random rate while shortage are allowed and backordered. The objective functions are aimed to minimize total inventory costs and total required warehouse space to store products, where inventory costs include ordering costs, holding costs, backordering costs and purchasing costs. Different technical and operational constraints are considered. Also, to develop more realistic mathematical model of the problem all constraints are considered stochastic. Due to nonlinearity of the proposed model, a solution method is developed to obtain efficient Pareto optimal solutions of the bi-objective constrained NLP model.