Optimal production control problem in stochastic multiple-product multiple-machine manufacturing systems

Abstract This paper deals with the issue of production control in a manufacturing system with multiple machines which are subject to breakdowns and repairs. The control variables considered are the production rates for different products on the machines. Our objective is to minimize the expected total discounted cost due to the finished good inventories and backlogs. Based on the structure of the hedging point policy, a parameterized near-optimal production policy for a multiple-product manufacturing system is proposed. The analytical formalism is combined with simulation-based statistical tools, such as experimental design and response surface methodology. The aim of such a combination is to provide an approximation of the optimal control policy. In the proposed approach, the parameterized near-optimal control policy is used as an input for the simulation model. For each entry consisting of a combination of parameters, the cost incurred is obtained. The significant effects of the control variables are determined by the experimental design. The relationship between the cost and these input factors is obtained through a response surface model. It is from the obtained relationship that the best values of control factors are determined. Extensive computational experience is reported for two-part-type and five-part-type production systems. Finally, simulation experiments on several examples are concentrated on the sensitivities of the control policy obtained.

[1]  W. Fleming,et al.  An Optimal Stochastic Production Planning Problem with Randomly Fluctuating Demand , 1987 .

[2]  Ali Gharbi,et al.  Production and preventive maintenance rates control for a manufacturing system: An experimental design approach , 2000 .

[3]  C. Berridge.  An Introduction to Reliability and Maintainability. , 1984 .

[4]  Ali Gharbi,et al.  Control policy simulation based on machine age in a failure prone one-machine, one-product manufacturing system , 1997 .

[5]  M. Caramanis,et al.  Numerical investigation of optimal policies for production flow control and set-up scheduling: Lessons from two-part-type failure-prone FMSs , 1997 .

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

[7]  A. Alan B. Pritsker,et al.  Simulation with Visual SLAM and AweSim , 1997 .

[8]  Ali Gharbi,et al.  Production planning problem in manufacturing systems with general failure and repair time distributions , 2000 .

[9]  Panganamala Ramana Kumar,et al.  Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems , 1988, Oper. Res..

[10]  G. Box,et al.  Empirical Model-Building and Response Surfaces. , 1990 .

[11]  J. Quadrat.  Numerical methods for stochastic control problems in continuous time , 1994 .

[12]  Charles E Ebeling,et al.  An Introduction to Reliability and Maintainability Engineering , 1996 .

[13]  Michael C. Caramanis,et al.  Near optimal manufacturing flow controller design , 1991 .

[14]  Bryan Dodson,et al.  Reliability Engineering Handbook , 1999 .

[15]  M. Caramanis,et al.  Infinitesimal perturbation analysis for second derivative estimation and design of manufacturing flow controllers , 1994 .

[16]  Dennis K. J. Lin,et al.  Small response-surface designs , 1990 .

[17]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[18]  Ali Gharbi,et al.  Experimental design in production and maintenance control problem of a single machine, single product manufacturing system , 1999 .

[19]  George Liberopoulos,et al.  Perturbation Analysis for the Design of Flexible Manufacturing System Flow Controllers , 1992, Oper. Res..

[20]  R. Rishel.  Dynamic Programming and Minimum Principles for Systems with Jump Markov Disturbances , 1975 .

[21]  Anthony B. Atkinson,et al.  How to Apply Response Surface Methodology , 1993 .

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

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

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

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

[26]  M. Caramanis,et al.  Production control of manufacturing systems with production rate-dependent failure rates , 1994, IEEE Trans. Autom. Control..

[27]  Don Edwards,et al.  How to Apply Response Surface Methodology , 1991 .

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

[29]  Richard P. Heydorn,et al.  Reliability Engineering Handbook , 2001, Technometrics.