Average Cost Optimal Policy for a Stochastic Two-Machine Flowshop with Limited Work-in-Process

Abstract

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.

Keywords: Production Planning, Optimal Controls, Stochastic Manufacturing System, Long-Run Average Cost, Dynamic Programming, Ergodic Problem, Feedback Controls, flowshop, average cost optimality

JEL Classification: M11, C61