A multi-product continuous review inventory system with stochastic demand, backorders, and a budget constraint

Common characteristics of inventory systems include uncertain demand and restrictions such as budgetary or storage space constraints. Several authors have examined budget constrained multi-item stochastic inventory systems controlled by continuous review policies without considering marginal shortage costs. Existing models assume that purchasing costs are paid at the time an order is placed, which is not always the case since in some systems purchasing costs are paid when orders arrive. In the latter case the maximum investment in inventory is random since the inventory level when an order arrives is a random variable. Hence payment of purchasing costs on delivery yields a stochastic budget constraint for inventory. This paper models a multi-term stochastic inventory system with backordered shortages when estimation of marginal backorder cost is available, and payment is due upon order arrival. The budget constraint can easily be converted into a storage constraint.