Mathematical Modeling on EPQ Under Imperfect Production System and Shortages with Asynchronous Rework Rate — A Grey Wolf Optimization Approach

This paper presents an environmentally sustainable Economic Production Quantity (EPQ) model under the influence of imperfect production and shortages. The defective items are reworked under an asynchronous rework process, where the reworking starts just after the production process stops. In this study, we have proposed two models under shortages, one with shortages satisfied by perfect production, and the other with shortages satisfied by production permitting defective item production which are reworked under asynchronous approach. During the processes of production, transportation and storage of inventory items, significant amount of carbon emissions is generated. In order to minimize these emissions and to reduce the setup costs, this paper proposes the integration of investment in green technology. The primary objective of this paper is to obtain the optimal values of lot size, backordered quantities, setup costs and green investment amounts in order to minimize the total cost of the manufacturer. To find the optimal solution, we have employed a metaheuristic method, Grey Wolf Optimization (GWO). A numerical example is also presented, accompanied by a sensitivity analysis to illustrate and validate the outcomes of the proposed inventory models.