A numerical method in optimal production and setup scheduling of stochastic manufacturing systems

Yan, Hua; Zhang, Q.

doi:10.1109/9.633837

Cited by 74 publications

(44 citation statements)

References 14 publications

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“…Stochastic manufacturing systems with setup costs and/or times have been considered by Sethi and Zhang (1994), Yan and Zhang (1997) and Boukas and Kenné (1997). The proposed models lead to the optimality conditions described by the Hamilton Jacobi Bellman equations (HJB).…”

Section: Introductionmentioning

confidence: 99%

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

Gharbi¹,

Kenné

Hajji³

2006

International Journal of Production Research

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This paper deals with the control of the production rates and setup actions of an unreliable multiple-machine, multiple-product manufacturing system. Each part type can be processed for a specified length of time on one of the involved machine. When switching the production from one type to another, each machine requires both setup time and setup cost. Our objective is to determine the production rates and a sequence of setups in order to minimize the total setup and surplus cost. Aiming the fact that 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. We will prove experimentally that an extended version of the hedging corridor policy is more realistic and guarantees better performance for two cases of study. The first one consists on the unreliable one machine case facing exponential failure and repair time distribution. The second one, which is more complex and where the optimal control theory may not be easily used to obtain the optimal control policy, consists on 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.

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Section: Introductionmentioning

confidence: 99%

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

Gharbi¹,

Kenné

Hajji³

2006

International Journal of Production Research

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“…In the case of complex manufacturing systems, no analytical solution to HJB equations is currently possible. To find the optimal solution to the stochastic control optimization problem, Yan and Zhang [18] used a numerical method based on the Kushner approach [10] to manufacturing systems producing several parts. Addressing realistic manufacturing systems, Kenné and Nkeungoue [19] modeled machine failure and repair using non-homogenous Markov processes, showing that machine failure probability increases with machinery age.…”

Section: Introductionmentioning

confidence: 99%

Considering human error in optimizing production and corrective and preventive maintenance policies for manufacturing systems

Emami-Mehrgani

Neumann

Nadeau

et al. 2016

Applied Mathematical Modelling

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This article extends previous work on co-optimization of production and corrective and preventive maintenance including lockout/tagout. We study the impact of human error on repairable manufacturing systems subject to random failure over an infinite planning horizon and its implications for system capacity and inventory policies, and we derive an optimal policy for minimizing production cost based on machinery maintenance and inventory management while meeting market demand over an infinite horizon. A numerical example is provided to demonstrate the usefulness of the proposed approach and a sensitivity analysis is presented to confirm the efficiency of the control policy.

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“…This numerical method is based on the finite difference approximations and policy improvement technique, and is described in Kushner and Dupuis 13 as well as also in Yan and Zhang. 24 It consists in using an approximation for the gradient of the value function based on the numerical scheme of finite differences. Let ℎ and ℎ denote the length of the finite difference intervals of the state variables and .…”

Section: Optimality Conditions and Numerical Approachmentioning

confidence: 99%

Age-dependent production and replacement strategies in failure-prone manufacturing systems

Ouaret

Kenné

Gharbi

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part B:

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IntroductionIn the manufacturing environment, the availability of the machine often decreases due to its age and also to imperfect maintenance activities. In general, corrective or preventive maintenance brings the state of the machine to a level which is not new, and it may not be able to meet the demand rate for the commodity produced. For this reason, the machine has to be replaced. We consider a machine that is subject to random breakdowns and repairs. It undergoes deterioration while in operation, and the failure rate increases with its age. The aging of the machine is an increasing function of its production rate. The corrective maintenance activities performed are imperfect and restore the machine to as-bad-as-old conditions. Replacement activities for their part renew the machine, which is similar to restoring the machine to as-good-as-new conditions (resetting its age to zero).The first objective of this paper is to simultaneously determine production and replacement policies in a manufacturing environment under deterioration and imperfect repairs. We enhance existing mathematical models by including the production cost in the objective function. Given that the dynamics of the machine aging process depends on the production rate, penalizing the latter helps to amplify the impact of aging and push the system (optimal control policies) towards an appropriate solution. The proposed model appears to be better at addressing industrial reality, and is yet to be used in the literature in analyzing age-dependent production and replacement strategies. The obtained solution provides the simultaneous optimal control of production and replacement of the machine (assuming that one replacement is performed). The decision variables are the production rate and the replacement policy. The dynamics of the machine is described by a semi-Markov decision model due to the machine's deterioration and imperfect repairs (as-bad-as-old). The optimal control policies are determined in order to satisfy a deterministic customer demand and minimize inventory, backlog, production, repair and replacement costs over an infinite planning horizon. AbstractA failure-prone manufacturing system that consists of one machine producing one type of product is studied. The random phenomena examined are machine breakdowns and repairs. We assume that the machine undergoes a progressive deterioration while in operation and that the machine failure rate is a function of its age. The aging of the machine (the dynamics of the machine age) is assumed to be an increasing function of its production rate. Corrective maintenance activities are imperfect and restore the age of the machine to as-bad-as-old conditions (ABAO). When a failure occurs, the machine can be repaired, and during production, the machine can be replaced, depending on its age. When the replacement action is selected, the machine is replaced by a new and identical one. The decision variables are the production rate and the replacement policy. The objective of this paper is to address th...

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A numerical method in optimal production and setup scheduling of stochastic manufacturing systems

Cited by 74 publications

References 14 publications

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

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

Considering human error in optimizing production and corrective and preventive maintenance policies for manufacturing systems

Age-dependent production and replacement strategies in failure-prone manufacturing systems

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