The Compensation Method Applied to a One-Product Production Inventory Problem

Abstract

This paper considers a one-product, one-machine production/inventory probelm. Demand requests for the product are governed by a Poisson process with demand size being an exponential random variable. The production facility may be in production or idle; while in production, the facility produces continuously at a constant rate. The objective is to minimize system costs consisting of setup costs, inventory holding costs, and backorder costs. Given a two-critical-number policy, the problem is analyzed as a constrained Markov process using the compensation method. The policy space may then be searched to find the optimal policy.