Ali Gharbi

Production and preventive maintenance rates control for a manufacturing system: An experimental design approach

In this paper, a multiple-identical-machine manufacturing system with random breakdowns, repairs and preventive maintenance activities is considered. The objective of the control problem is to find the production and the preventive maintenance rates of the machines so as to minimize the total cost of inventory/backlog. By combining analytical formalism and simulation based statistical tools such as experimental design and response surface methodology (RSM), an approximation of the optimal control policy is obtained. A numerical example is presented to illustrate the usefulness of the proposed approach. It is found that the complexity of the experimental design problem remains constant (33 factorial design) when the number of machines increases. Based on the obtained results, the extension of the proposed approach to more complex manufacturing systems is discussed.

Maintenance scheduling and production control of multiple-machine manufacturing systems

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 nonidentical 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.

Control of production and corrective maintenance rates in a multiple-machine, multiple-product manufacturing system

This paper presents the analysis of the optimal production control and corrective maintenance planning problem for a failure prone manufacturing system consisting of several identical machines. Machines are subject to breakdowns and repairs and can produce several parts of products. At any given time, each machine can only produce one type of product. The introduction of the corrective maintenance will increase the availability of the production system which guarantees the improvement of the systems productivity if the production planning is well done. The decision variables are the production and the machine repair rates which influence the inventory levels and the system capacity, respectively. The objective of the work is to minimize the cost of surplus and repair activities. A computational algorithm, based on numerical methods, is given for solving the optimal control problem. Finally, a numerical example is presented to illustrate the usefulness of the proposed approach and extensions to more complex manufacturing systems are discussed.

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.

Experimental design in production and maintenance control problem of a single machine, single product manufacturing system

This paper describes an approach to control the production and preventive maintenance rates of a manufacturing system using a computer simulation experiment. The system consists of one machine producing one part type which is subject to failures, repairs and preventive maintenance activities. The production and maintenance planning problem in such a system is a highly complex control problem. It has been shown that, when the transition rates are constant, the hedging point policy is optimal. Owing to the machine age dependent failure distribution, a practical conjecture is made on the dependence of the control variables on the machine age. The hedging point policy is then age dependent. In this paper, we determine the optimal parameters of a modified hedging point policy. The experimental design is used to prove the significance of the control variables compared with the dependent variable or incurred cost. A second-order response surface is fitted in the presence of a random block effect to estimate the ...

A simulation optimization approach in production planning of failure prone manufacturing systems

In this paper, the implementation of a new method to control the production rate of manufacturing systems, based on the combination of stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology is outlined. The system under study consists of several parallel machines, multiple-product manufacturing system. Machines are subject to failures and repairs and their capacity process is assumed to be a finite state Markov chain throughout the analytical control model. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. The structure of the hedging point policy is then parameterized by factors representing the thresholds of involved products. With such a policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal control policy. We obtain that the hedging point policy is also applicable to a wide variety of complex problems including non-exponential failure and repair times distributions and random demand rates. Analytical solutions may not be easily obtained for such complex situations.

Stohastic optimal production control problem with corrective maintenance

Abstract We consider a production control problem in a manufacturing system with failure-prone machines and a constant demand rate. The objective is to minimise a discounted inventory holding and backlog cost over an infinite planning horizon. The availability of the machines is improved through a corrective maintenance strategy. The decision variables are the production and the machine repair rates, which influence the inventory levels and the system capacity, respectively. It is shown that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. Such a policy is modified herein and parameterised by factors representing the thresholds of involved products and switching inventory levels for corrective maintenance. With the obtained policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal production and corrective maintenance policies, respectively. The usefulness of the proposed approach is illustrated through a numerical example.

Production planning problem in manufacturing systems with general failure and repair time distributions

We study the optimal flow control for a manufacturing system subject to random failures and repairs. In most previous work, it has been proved that, for constant demand rates and exponential failure and repair times distributions of machines, the hedging point policy is optimal. The aim of this study is to extend the hedging point policy to non-exponential failure and repair times distributions and random demand rates models. The performance measure is the cost related to the inventory and back order penalties. We find that the structure of the hedging point policy can be parametrized by a single factor representing the critical stock level or threshold. With the corresponding hedging point policy, simulation experiments are used to construct input-output data from which an estimation of the incurred cost function is obtained through a regression analysis. The best parameter value of the related hedging point policy is derived from a minimum search of the obtained cost function. The extended hedging point policy is validated and shown to be quite effective. We find that the hedging point policy is also applicable to a wide variety of complex problems (i.e. non-exponential failure and repair times distributions and random demand rates), where analytical solutions may not be easily obtained.

Production control and replenishment strategy with multiple suppliers

This paper considers the joint supplier selection, replenishment and manufacturing control problem in a dynamic stochastic context. This problem is characterized by conflicting interests between suppliers, the manufacturer, and clients, which raise the need for coordination and information sharing. This paper contributes to the discourse mainly by developing and resolving an integrated mathematical model leading to information sharing strategies for supplier selection, replenishments and production activities. This is an optimal control problem with state constraints and hybrid dynamics. A dynamic stochastic model is thus proposed, and the optimality conditions obtained are then solved numerically. It is shown that the problem considered leads to a modified state-dependent multi-level (s, S) policy for the supplier selection and replenishment strategy and a base-stock policy for the production activities. The fact that these control policies are coupled confirms the necessity of considering the interactions present in the system in an integrated model. The obtained results show clearly that it is always profitable to consider multiple suppliers to make replenishment and production decisions. Moreover, it is shown that the availability rates of the supply chain actors and the replenishment lead time are important parameters to consider when choosing the best supplier.

Operational level-based policies in production rate control of unreliable manufacturing systems with setups

This paper deals with the control of the production rates and set-up actions of an unreliable multiple-machine, multiple-product manufacturing system. Each part type can be processed for a specified period on one of the involved machines. When switching the production from one type to another, each machine requires both set-up time and set-up cost. Our objective is to determine the production rates and a sequence of set-ups in order to minimize the total set-up and surplus cost. As an analytical or even a numerical solution of the problem is very difficult to find, a combined approach is presented. The proposed approach is based on stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology. It is proved experimentally that an extended version of the Hedging Corridor Policy is more realistic and guarantees better performance for two study cases. The first consists of the unreliable one-machine case facing exponential failure and repair time distribution. The second, which is more complex and where the optimal control theory may not be easily used to obtain the optimal control policy, consists of five machines facing non-exponential failure and repair time distributions. To illustrate the contribution of the paper and the robustness of the obtained control policy, numerical examples and sensitivity analysis are presented.