The Optimal Order Size and the Maximum Shortage Level Decision under an Order Driven Model

Abstract

Abstract. This paper mainly studies the retailer how to decision his order size and the maximum shortage level to maximize his profits. To end this, we establish an order driven model which consists of a vender and a buyer. In this model, we consider the three reality factors simultaneously: inspection errors, imperfect quality, multiple screening and shortage backordering. Based on it, we derive the optimal order size and the maximum shortage level. We also obtain three useful managerial insights. First, when the backordering cost increases, the buyer should decrease the order size and the shortage level simultaneously. Second, when freight transportation cost increases, the buyer should also increase the order size and the shortage level simultaneously. Third, the cost of accepting a defective item and the cost of rejecting a non-defective item have no impact on order size and the shortage level. Finally, we conduct numerical studies to complement our analytic findings and gain more managerial insights.