Planning for shortages? Net Present Value analysis for a deteriorating item with partial backlogging

This paper develops inventory models to help answer strategic questions concerning whether planning for shortages offers financial benefits. A production-inventory system producing a deteriorating product in batches at a finite production rate with partial backordering is considered. Customers pay a deposit when placing a backorder. Backordered items receive a discount on the sales price. As lost sales may lead to customers not returning, the demand rate may depend on the fraction of lost sales. We develop a cash-flow based profit maximising Net Present Value (NPV) model without the inventory cost parameters commonly used in this context: unit holding cost, unit backorder cost, unit deterioration cost, and unit lost sales cost. The model finds the optimal inventory policy just like NPV models that discount the traditional parameters but has the advantage of not needing to estimate the value of the traditional parameters. It is shown that in models based on discounting the traditional parameters, the parameters are not exogenously determinable but are non-trivial functions of non-financial endogenous system parameters such as the production rate, annual demand rate, and backorder rate. Extensive numerical experiments illustrate how cash-flow NPV models provide insights into the value of planning for shortages and strategic choices about the design of the production-inventory system. It also provides insight into the classical problem of how to interpret unit backorder cost and unit lost sales cost. The study indicates that these insights cannot be reliably obtained from NPV models based on discounting unit backorder costs and unit lost sales costs.