Hierarchical Production Controls in a Stochastic Two-Machine Flowshop with a Finite Internal Buffer

This paper presents an asymptotic analysis of hierarchical production planning in a manufacturing system with two tandem machines that are subject to breakdown and repair. The system produces a single product, whose rate of demand over time is given to be constant. The problem is formulated as a continuous-time dynamic programming problem in which the objective is to minimize the cost of production, inventories, and backlogs. The size of the buffer between the two machines is assumed to be finite. As the rates of change in machines' states approach infinity, the analysis results in a limiting problem in which the stochastic machine capacity is replaced by the average capacity. The value function for the original problem is shown to converge to the value function of the limiting problem. Both open-loop and feedback controls for the original problem are constructed from near-optimal controls of the limiting problem in a way which guarantees their asymptotic optimality as the rates of changes in machines' states become large in comparison to the discount rate. The convergence rate of the value function for the original problem to that of the limiting problem together with the error estimate for the constructed asymptotic optimal controls are obtained. In addition, the constructed feedback control is compared to the Kanban control policy for the stochastic two-machine flowshop.

[1]  Suresh P. Sethi,et al.  Optimal feedback production planning in a stochastic N-machine flowshop , 1995, Autom..

[2]  Stanley Gershwin,et al.  An algorithm for the computer control of production in a flexible manufacturing system , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[3]  Suresh P. Sethi,et al.  Hierarchical controls in stochastic manufacturing systems with convex costs , 1994 .

[4]  Suresh P. Sethi,et al.  Computational Evaluation of Hierarchical Production Control Policies for Stochastic Manufacturing Systems , 1997, Oper. Res..

[5]  S. Gershwin,et al.  PRODUCTION CONTROL FOR A TANDEM TWO-MACHINE SYSTEM , 1993 .

[6]  Stanley B. Gershwin,et al.  Hierarchical real-time scheduling of a semiconductor fabrication facility , 1990, Ninth IEEE/CHMT International Symposium on Electronic Manufacturing Technology,Competitive Manufacturing for the Next Decade.

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

[8]  Suresh P. Sethi,et al.  An Asymptotic Analysis of Hierarchical Control of Manufacturing Systems Under Uncertainty , 1991, Math. Oper. Res..

[9]  Suresh P. Sethi,et al.  Hierarchical Production Planning in Dynamic Stochastic Manufacturing Systems: Asymptotic Optimality and Error Bounds , 1994 .

[10]  Ram Akella,et al.  Optimal control of production rate in a failure prone manufacturing system , 1985 .

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

[12]  Suresh P. Sethi,et al.  Optimal Feedback Production Planning in a Stochastic N-Machine Flowshop , 1993 .

[13]  Suresh P. Sethi,et al.  Optimal feedback production planning in a stochastic two-machine flowshop , 1994 .

[14]  Stanley B. Gershwin,et al.  Scheduling manufacturing systems with work-in-process inventory control: multiple-part-type systems , 1994 .

[15]  Suresh P. Sethi,et al.  Hierarchical controls in stochastic manufacturing systems with machines in tandem , 1992 .

[16]  Stanley B. Gershwin,et al.  Scheduling manufacturing systems with work-in-process inventory , 1990, 29th IEEE Conference on Decision and Control.

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