The CVaR-based Optimal Ordering Problems Of The Retailer In A Backorder Setting

With the increase of market competition and improvement of the customer service level, backlogging the unsatisfied demands of the customers for the retailer in a stock-out situation becomes more and more popular in reality, especially in e-commerce. For the retailers, it is obvious that backlogging the excess demands can save the opportunity loss the from the lost sales and be helpful to maintain long-term relationships with the customers. However, it is natural that not all the customers accept the backordering invitation and backlogging the excess demands always produces soem associated costs, such as the ordering and transportation costs. Then if the backordering rate is very low or the backordering cost is very high, there will be certain losses for the retailer. Moreover, over-reliance on backordering will have a negative effect on the retailer’s reputation, which may adversely affect the long-term interests of retailer. Then, with the market demand becoming more complex and the market competition becoming more fierce, how to give the optimal decisions to reduce the potential risk from the uncertainty of the market demand for the retailer with a backordering case has important consequences.For the risk control problem of the retailer with backordering, this paper applies the Conditional Value-at-Risk(CVaR) measure to study the optimal ordering problem of the retailer. In view of the diversity of the retailer in practice, we study the cases when the objectives of the retailer are profit maximization, opportunity loss minimization and loss-averse utility maximization, respectively. The following conclusions are obtained. i) the retailer who aims maximize the CVaR objective of profit will order fewer than the retailer who aims maximize the expected profit and the loss-averse retailer who aims maximize the CVaR objective of utility will order fewer than the loss-averse retailer who aims maximize the expected utility, while the retailer who aims minimize the CVaR objective of opportunity loss may order more or fewer than the retailer who aims minimize the expected opportunity loss. This implies the optimal order decisions of the retailers with different CVaR objectives will be different. ii) the optimal order quantities of the retailers with the above objectives will increase when the backorder rate increases or the backorder costs decreases. iii) the optimal order quantities of the retailers with the CVaR objective of profit maximization and utility maximization will increase, while the optimal order quantity of the retailer with the CVaR objective of opportunity loss minimization may increase or decrease when the confidence level increases. iv) with the increase of the confidence level, the retailer’s expected profit and the loss-averse retailer’s expected utility will decrease, while the retailer’s expected opportunity loss will increase. This confirms the fact that high risk implies high return and low risk comes with low return.With the increase of market competition and fluctuation of market demand, our results will provide some theoretical foundations and management insights for the optimal ordering decisions and risk management of the retailer with backordering, and give some suggestions and advices for the retailer in practice to improve the risk management of inventory and procurement.