An Analytical Model of a Two-Product, One-Machine, Production-Inventory System

This paper is concerned with the modeling and analysis of a one-machine two-product, integrated production-inventory system. A semi-Markovian model is developed which incorporates a state dependent control system heretofore not used in integrated production-inventory models. Control optimization is achieved through the use of Markov-renewal programming. The model is exercised over a range of parameters in order to determine the characteristics of the system. An analysis of the experimental results leads to the following conjectures about the production-inventory system:

1. For the production-inventory system, the economic manufacturing quantity is greater than that seen in the deterministically derived EMQ. The increase results primarily from increases in expected overtime costs and expected setup costs rather than increases in stockout costs. This is important for applications, since overtime and setup costs are a good deal easier to quantify than stockout costs in a real system.

2. Under some conditions, deterministically derived rules for the application of overtime have merit in a stochastic system.