Estimating the EOQ Shortage Cost Parameter: A Partial Backlogging Approach

This paper presents a simple deterministic EOQ with time-dependent partial backlogging. The penalty during stockout arises from lost sales rather than from the usual shortage cost parameter. The model has a unique minimum for a broad class of lost-sales behavior during stockout. The main result is that a special case corresponds to the traditional full backlogging model and provides a means to estimate an imputed shortage cost from readily available data. If management's empirical data suggest that the standard EOQ formulation is not appropriate in a particular situation, then other formulations may be used. Two examples are given, one based on assumptions about aggregate behavior and another based on individual level behavioral assumptions. The optimal solutions of these alternative formulations are in general necessarily different from the standard EOQ solutions, but numerical examples suggest that the cost difference is not large.