On Optimality of Stochastic N-Machine Flowshop with Long-Run Average Cost
STOCHASTIC THEORY AND CONTROL: LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, B. Pasik-Duncan, ed., Vol. 280, pp. 399-417, Springer-Verlag, Berlin, 2002
17 Pages Posted: 29 May 2008 Last revised: 30 Mar 2014
This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled by a Markov chain. The objective is to choose the input rates at the various machines over time in order to meet the demand for the system's production at the minimum long-run average cost of production and surplus, while ensuring that the inventories in internal buffers between adjacent machines remain nonnegative. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the potential function.
Keywords: Production Planning, Optimal Controls, Stochastic Manufacturing System, Long-Run Average Cost, Dynamic Programming, Ergodic Problem, Feedback Controls, flowshop
JEL Classification: M11, C61
Suggested Citation: Suggested Citation