Stochastic inventory management at a service facility with a set of reorder levels

Abstract

We consider a continuous review perishable inventory system at a service facility with
a finite waiting capacity. The maximum inventory level is fixed and the customers
arrive according to a Markov arrival process. The life time of each item and the
service time are assumed to have independent exponential distributions. Unlike the
conventional method of placing an order at a prefixed level, we consider a set of
reorder levels with a specified probability for placing an order at a particular reorder
level. This allows the modelling of a situation in which the decision maker may
advance or postpone the placement of reorder as a result of his/her memory on the
past supply behaviour. The reordering quantity depends upon the reorder level at
which an order was triggered and the lead time is distributed as negative exponential.
The joint probability distribution of the number of customers in the system and the
inventory level is obtained in the steady state. We also derive some stationary system
performance measures and compute the total expected cost rate under a cost structure.
We also present a numerical illustration.

Keywords: Stochastic inventory, Markov arrival process, set of reorder levels, service facility.

ORiON Vol. 23 (2) 2007: pp. 137-149