Modeling and analysis of a kit management problem

Abstract

In this study, we consider a multi-item inventory system in which customers may order different but possibly overlapping kits. Customer demand for a kit follows a Poisson process where there is a fixed probability for each kit to be demanded. When the kit is formed, it is sent to the demand location for a common time and one item from the kit is consumed. The unused items in the kit are returned to stock while an order is placed for the consumed item. We consider two supply processes for the consumed item. In the first supply system, replenishment lead times for each component are independent and identically distributed random variables as in an M/G/1 queue. Second supply system is a load dependent system where items are processed through an M/M/1 queue. Firstly, we derive the joint probability distribution of outstanding orders to evaluate the availability of a kit to be formed when a demand arrives. Secondly, we develop an efficient heuristic to optimize the base-stock levels of each item subject to a service level constraint. We have conducted many numerical computations to prove the effectiveness of our heuristic approach. For computations, we develop a code in MATLAB computing program and a simulation model in Arena simulation package.