Analysis of Average Cost Optimality for an Unreliable Two-Machine Flowshop

This paper is concerned with a production planning problem in a two-machine flowshop subject to breakdown and repair of machines subject to nonnegativity constraints on work-in-process. The objective is to choose machine production rates over time to meet the demand facing the flowshop at a minimum long-run average cost. It si shown that the dynamic programming equation for the problem has a solution consisting of the minimal average cost and the so-called potentila function. The result helps in establishing the verification theroem and partial characterization of the optimal control policy if it exists