Sg. Johansen et A. Thorstenson, OPTIMAL AND APPROXIMATE (Q,R) INVENTORY POLICIES WITH LOST SALES AND GAMMA-DISTRIBUTED LEAD TIME, International journal of production economics, 30-1, 1993, pp. 179-194
We consider the continuous review inventory control system with fixed
reorder point r and constant order quantity Q. Demands are assumed to
be generated by a Poisson process with one unit demanded at a time. De
mands not covered immediately from inventory are lost. For the case of
at most one order outstanding we derive and implement a model to obta
in exact solutions for the reorder point and the order quantity. The m
odel is formulated as a semi-Markov decision model and we show that if
it is profitable to issue orders then a (Q, r) policy is average-cost
optimal. In general neither a (Q, r) policy nor an (s, S) policy is o
ptimal if demand for more than one unit at a time is allowed in our mo
del. A policy-iteration algorithm is developed for finding the optimal
policy. We focus on the shape of the lead-time distribution by studyi
ng the optimal policy when the lead times are gamma distributed with d
ifferent shape parameters. The results are compared to those obtained
when applying approximate methods to the reorder-point inventory syste
m.