A bi-objective inventory model to minimize cost and stock out time under backorder shortages and screening

Although minimizing costs is the main objective in inventory models, meeting customer's needs is another basic goal of many companies. Especially in the case shortages are allowed, the waiting time a customer spends to receive his/her backlogged shortage is an important factor that affects maintaining with the company. As defining an accurate shortage cost which includes cost of losing customers and cost of damaging brand image is not possible for many companies, the above two objectives are considered in this paper to develop a bi-objective inventory model, in which the total cost of a retailer and his customers’ stock out times are minimized. In this model, the order size, the maximum backordering quantity, and the number of inspectors are defined as the decision variables, where a 100% screening process with the rate higher than the demand rate is used to screen out the items. After screening, the non-conforming items are stored in the warehouse, where they will be exchanged with new items when a new order is arrived at the end of the cycle. The bi-objective optimization problem is solved using the non-dominated sorting genetic algorithm (NSGA-II). As there is no benchmark available in the literature, another multi-objective optimization algorithm called the multi-objective particle swarm optimization (MOPSO) is employed to validate the result and to evaluate the performance of NSGA-II. Computational results of solving some randomly generated numerical examples are in favor of MOPSO.