This paper deals with the optimal production control problem in a stochastic two-machine flow shop. Our aim is to develop approximation techniques for deriving close to optimal production policies within a suboptimal class of decentralized hedging policies, whereby each machine strives to maintain a fixed critical level of parts to be determined. For that purpose, using two approximate decoupling principles, a machines decoupling approximation and a so-called demand averaging principle, both upstream and downstream production costs required to maintain a given availability coefficient of the work-in-process (as well as the associated critical levels of parts) are derived analytically. The quality of the demand averaging principle as an approximation is theoretically assessed, and both approximations are numerically tested. Subsequently, one searches over all admissible availability coefficients for one that minimizes the overall production cost. The proposed optimization scheme appears to be very competitive for real-time use since it runs almost instantaneously when implemented using Matlab on a personal computer. In addition, it provides good performance when tested against Monte Carlo based optimization over the same class of control laws. Results emerging from a wide set of sample systems are presented, and the decoupling principles initiated appear to be generalizable for an N-machine flow shop, where N>2.
Paru en mars 1999 , 33 pages