Simple Expressions for Safety Factors in Inventory Control

The literature on inventory control discusses many methods to establish the level of decision parameters -like reorder levels or safety factors-, necessary to attain a prescribed service level. In general, however, these methods are not easy applicable: they often use time-consuming iterations, requiring specific software. In particular, large-scale application on huge numbers of stock keeping items are a heavy burden on the computer system. In this paper, we consider a periodic review fully back-ordered order up-to level (R,S)-system with stationary gamma distributed demand, and constant lead time. Two service level constraints are treated simultaneously: the stock-out probability and the fill rate. For the case that, in addition, the demand distribution parameters are known, we (i) calculate exact safety factors, depending on three model parameters, (ii) present simple expressions that give nearly exact safety factors. The latter expressions are valid for a wide range of parameter values; since implementation is straightforward, our method is appropriate for routine operational use. For unknown demand parameters, estimates obtained from past observations can be plugged in. The behaviour of the resulting order up-to levels is studied by simulation and appears to be quite satisfactory. A comparison with the standard - normality based - approach is made; an indication of the robustness of our method is given. Our most important message, however, is that this two-step procedure turns out to be applicable to a much wider range of inventory problems; to illustrate this remark, preliminary results on a specific (R,s,S)-system are mentioned.