Analysis of an inventory system with exponential partial backordering

In this paper we study an inventory model with partial backlogging, where unsatisfied demand is partially backlogged according to an exponential function. In this model the total cost is the sum of the order cost, the holding cost, the backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general approach for finding the optimal policy is developed. Numerical examples are used to illustrate how the approach works.