برنامه ریزی نگهداری و کنترل تولید سیستم های تولید چند دستگاه

This paper deals with the production and preventive maintenance control problem for a multiple-machine manufacturing system. The objective of such a problem is to find the production and preventive maintenance rates for the machines so as to minimize the total cost of inventory/backlog, repair and preventive maintenance. A two-level hierarchical control model is presented, and the structure of the control policy for both identical and non-identical manufacturing systems is described using parameters, referred to here as input factors. By combining analytical formalism with simulation-based statistical tools such as experimental design and response surface methodology, an approximation of the optimal control policies and values of input factors are determined. The results obtained extend those available in existing literature to cover non-identical machine manufacturing systems. A numerical example and a sensitivity analysis are presented in order to illustrate the robustness of the proposed approach. The extension of the proposed production and preventive maintenance policies to cover large systems (multiple machines, multiple products) is discussed.

The problem of controlling manufacturing systems with unreliable machines was formulated as a stochastic control problem by Older and Suri (1980). Failure and repair processes were supposed to be described using homogeneous Markov processes. The related optimal control model falls under the category of problems studied previously by Rishel (1975). Similar investigations have resulted in the analytical solution of the one-machine one-product manufacturing system control problem obtained by Akella and Kumar (1986). In the case of non-homogeneous Markov processes involving states and control-dependent transition rates, the control problem becomes more complex. In this sphere, Boukas and Haurie (1990) considered the fact that the failure probabilities of a machine depend on its age, and they added the possibility of performing preventive maintenance to the existing models. The related age-dependent set of dynamic programming equations were solved numerically for a given manufacturing system. However, with the numerical scheme presented by Boukas and Haurie (1990), it remains difficult to obtain a general structure for the optimal control of a large class of manufacturing systems. A potential way of coping with such a difficulty is to develop heuristical methods based on the reduction of the size of the considered control problem. Hence, different approaches have been proposed in the existing literature with a view to deriving simple near-optimal control policies for manufacturing systems.

In this paper, we have extended the concept of hedging point policy to the production and preventive maintenance control problem of a multiple, non-identical machine manufacturing system. The proposed approach was based on the combination of the hierarchical control model, simulation experiments, experimental design and RSM. First, we investigated a near-optimal control policy of a machine age dependent Markov process through the construction of the stochastic control policy from one of the dependant deterministic models. We then associated to such a policy parameters called independent variables. A simulation model was developed to describe the dynamic of the production system under the proposed modified hedging point policy. An experimental design approach was then used to investigate the effects of specific factors on the cost incurred during the production horizon. The proposed approach combines the simulation method with the statistical method to provide the estimation of the cost function related to the control problem considered. A response surface methodology was used to perform this function in terms of significant main factors and interactions given by the experimental design approach. From the estimation of the cost function, the best values of control parameters were easily computed.