Economic order quantity model for items with imperfect quality and multiple suppliers

Economic order/production quantity (EOQ/EPQ) models for imperfect items have received great attention in the last decade. The main common feature of these models is the incorporation of the imperfect items into the problem. While in real-world problems, buyers usually work with multiple suppliers, the focus of the existing literature has been on a single-supplier variant of the problem. In this study, we formulate an EOQ model for items with imperfect quality when considering multiple suppliers, which is a particular type of supplier selection and EOQ models. The initial formulated problem is a mixed integer nonlinear programming that aims to maximize the total annual profit of the buyer such that customer demand is completely met and suppliers’ capacity constraints are satisfied. Since proposed model is nonlinear, first by using the unique property of model, it is converted to mixed integer linear programming then solved by GAMS/CPLEX software to obtain optimal solution. We then use a numerical example to illustrate the problem, and conduct a sensitivity analysis to study the sensitivity of the objective function and the decision variables to the imperfect rate of the items supplied by the selected suppliers.