Determining optimal production-inventory control policies for an inventory system with partial backlogging (Q1096522)

A mathematical model is developed for an inventory system in which the demand during the stockout period is partially backlogged and the items are replenished at a uniform rate. It is shown that by defining a time proportional backordered cost and a penalty cost per unit lost, a convex cost function can be obtained if a suitable set of decision variables is used in the analysis. The determination of optimal production-inventory control policies is thus greatly simplified since it is not necessary to use any ad hoc optimization procedure in the analysis. A numerical example is used to illustrate the theory. Computational results indicate that optimal policies are sensitive to the nature of the demand during the stockout period, and that erroneous assumption of the fraction of the unsatisfied demand that can be backlogged leads to a higher annual operating cost.