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 the cost of losing customers and cost of damaging brand image is not possible for many companies, the above two objectives are considered to develop a bi-objective inventory model, in which the total cost of a retailer and his customers’ stock out times are minimized. The main novelty of this research is to consider the stock out time as a separate objective to reduce the customers’ dissatisfaction besides the total cost. Moreover, the number of inspectors is defined as a decision variable besides other variables including the order size and the maximum back-ordering quantity.