We compare two inventory systems, one in which excess demand is lost and the other in which excess demand is back-ordered. Both systems are reviewed periodically. They experience the same sequence of identically and independently distributed random demands. Holding and shortage costs are considered. The holding cost parameter is identical; however, the cost of a lost sale could be different from the per-period cost of backlogging a unit sale. When these costs are equal, we prove that the optimal expected cost for managing the system with lost sales is lower. When the cost of a lost sale is greater, we establish a relationship between these parameters that ensures that the reverse inequality is true. These results are useful for designing inventory systems. We also introduce a new stochastic comparison technique in this paper.
- Production: stochastic
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research