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

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.