| 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. |
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