Degeneracy in inventory models

In order-quantity reorder-point formulations for inventory items where backordering is allowed, some of the more common ways to prevent excessive stockouts in an optimal solution are to impose either a cost per unit short, a cost per stockout occasion, or a target fill rate. We show that these popular formulations, both exact and approximate, can become ‘degenerate’ even with quite plausible parameters. By degeneracy we mean any situation in which the formulation either cannot be solved, leads to nonsensical ‘optimal’ solutions, or becomes equivalent to something substantially simpler. We explain the reasons for the degeneracies, yielding new insight into these models, and we provide practical advice for inventory managers.