Inventory System Subject to Disaster with General Interarrival Times

Abstract

We discuss a single commodity continuous review (s, S) inventory system in which commodities get damaged due to external disaster. Shortages are not permitted and lead time is assumed to be zero. The interarrival times of demands constitute a family of i.i.d. random variables with a common arbitrary distribution. The quantity demanded at a demand epoch is arbitrarily distributed which depends only on the time elapsed since the last demand epoch. Transient and steady state probabilities of the inventory levels are derived by identifying suitable semi-regenerative process. In the case when the demand is for unit item and the disaster affects only an exhibiting item, the steady state probability distribution is obtained as uniform. An optimization problem is discussed and numerical examples are provided.

Key Words:

• Inventory
• Disaster
• Perishability
• Markov renewal process
• Semi-regenerative process
• Optimization

AMS Subject Classification:

• 90B05
• 90C90
• 60K99

Acknowledgment

The second author acknowledges the U. G. C. research award 30-97/98(SA III).