Exponentially decaying inventory with partial back-ordering

Most of the research in decaying inventory models considers either complete back-ordering or complete lost sale. The analysis on partial back-ordering has received relatively little attention. In this study, a partial back-ordered inventory model for an item which deteriorates exponentially is developed. It is demonstrated that models with complete back-ordering and complete lost sales are special cases of the general model. Also, a lower bound on the back-ordered ratio is obtained to ensure convexity of the total cost function. A numerical example to illustrate the theory is provided.