OPTIMAL AND APPROXIMATE (Q,R) INVENTORY POLICIES WITH LOST SALES AND GAMMA-DISTRIBUTED LEAD TIME

Citation
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
Citations number
NO
Categorie Soggetti
Engineering
ISSN journal
09255273
Volume
30-1
Year of publication
1993
Pages
179 - 194
Database
ISI
SICI code
0925-5273(1993)30-1:<179:OAA(IP>2.0.ZU;2-8
Abstract
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.