A numerical method in optimal production and setup scheduling of stochastic manufacturing systems

In this paper, we consider optimal production and setup scheduling in a failure-prone manufacturing system consisting of a single machine. The system can produce several types-of products, but at any given time it can only produce one type of product. A setup is required if production is to be switched from one type of product to another. The decision variables are a sequence of setups and a production plan. The objective of the problem is to minimize the cost of setup, production, and surplus. An approximate optimality condition is given together with a computational algorithm for solving the optimal control problem.

[1]  Christian van Delft,et al.  Turnpike properties for a class of piecewise deterministic systems arising in manufacturing flow control , 1989, Ann. Oper. Res..

[2]  Stanley B. Gershwin,et al.  A real-time policy for performing setup changes in a manufacturing system , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  El-Kébir Boukas,et al.  Manufacturing flow control and preventing maintenance: a stochastic control approach , 1988 .

[4]  Stanley B. Gershwin,et al.  An algorithm for the computer control of a flexible manufacturing system , 1983 .

[5]  A. Sharifnia,et al.  Production control of a manufacturing system with multiple machine states , 1988 .

[6]  Jose-Luis Mendali.  Some estimates for finite difference approximations , 1989 .

[7]  Qing Zhang,et al.  Hierarchical Decision Making in Stochastic Manufacturing Systems , 1994 .

[8]  Stanley B. Gershwin,et al.  Selection of setup times in a hierarchically controlled manufacturing system , 1990, 29th IEEE Conference on Decision and Control.

[9]  R. Akella,et al.  Optimal control of production rate in a failure prone manufacturing system , 1985, 1985 24th IEEE Conference on Decision and Control.

[10]  Stanley B. Gershwin,et al.  Dynamic setup scheduling and flow control in manufacturing systems , 1991, Discret. Event Dyn. Syst..

[11]  Stanley B. Gershwin,et al.  Manufacturing Systems Engineering , 1993 .

[12]  Mark H. Davis.  Markov Models and Optimization , 1995 .

[13]  Michael C. Caramanis,et al.  Dynamic Set-Up Scheduling of Flexible Manufacturing Systems: Design and Stability of Near Optimal General Round Robin Policies , 1995 .

[14]  Dariusz Gatarek,et al.  Optimality conditions for impulsive control of piecewise-deterministic processes , 1992, Math. Control. Signals Syst..