A simulation optimization based control policy for failure prone one-machine,two-product manufacturing systems

This paper presents the optimal flow control for a one-machine, two-product manufacturing system subject to random failures and repairs. The machine capacity process is assumed to be a finite state Markov chain. 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 time distributions of the machine, the hedging point policy is optimal. Next, the hedging point policy is extended to non-exponential failure and repair time distributions models. The structure of the hedging point policy is parameterized by two factors representing the thresholds of involved products. With such a policy, simulation experiments are coupled with experimental design and response surface methodology to estimate the optimal control policy. Our results reveal that the hedging point policy is also applicable to a wide variety of complex problems (i.e. non-exponential failure and repair time distributions) where analytical solutions may not be easily obtained.     

Stohastic optimal production control problem with corrective maintenance

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 control of a pull system with production and demanduncertainty

We consider a continuous material-flow manufacturing system with an unreliable production system and a variable demand source which switches randomly between zero and a maximum level. The failure and repair times of the production system and the switching times of the demand source are assumed to be exponentially distributed random variables. The optimal production flow control policy that minimizes the expected average inventory carrying and backlog costs is characterized as a double-hedging policy. The optimal hedging levels are determined analytically by minimizing the closed-form expression of the cost function. We investigate two approximate single hedging policies. It is empirically shown that an approximate policy that uses a single hedging level which is the sum of a production uncertainty term and a demand uncertainty term gives accurate results for the expected average cost     

具有不确定需求的混杂系统的生产与维修控制

针对不可靠生产环境, 在需求不确定并且有可能存在需求大于生产的一般性情况下, 探讨了系统生产与维修的控制问题, 提出了一种考虑追加生产能力的具有较强即时动态特性的复合三阈值控制策略. 通过将有限时域上的问题分解到无限时域上的简化方法, 在给出了相应阈值求解方法的同时, 也建议了一种近似最优的复合单阈值控制策略. 仿真结果说明及验证了各控制策略及方法.     

Scheduling and control of failure prone systems with demand uncertainty and job overlaps

Given that the overlapping of jobs is permitted, the paper studies the scheduling and control of failure prone production systems,i, e.so-called settings with demand uncertainty and job overlaps. Because a variable demand resource is revolved in the production and corrective maintenance control problems of the system, which switched randomly between zero and a maximum level, it is difficult to obtain the analytical solutions of the optimal single hedging point policy. An asymptotic optimal scheduling policy is presented and a double hedging point policy is offered to control simultaneously the production rate and the corrective maintenance rate of the system. The corresponding analytical solutions and approximate solutions are obtained. Considering the relationship of production, corrective maintenance and demand variable, an approximate optimal single hedging point control policy is proposed. Numerical results are presented.     

Production control of a manufacturing system with multiple machinestates

The production control of a single-product manufacturing system with arbitrary number of machine states (failure modes) is discussed. The objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost. The optimal production policy has a special structure and is called a hedging-point policy. If the hedging points are known, the optimal production rate is readily specified. Assuming a set of tentative hedging points, the simple structure of the optimal policy is utilized to find the steady-state probability distribution of the surplus (inventory or backlog). Once this function is determined, the average surplus cost is easily calculated in terms of the values of the hedging points. The average cost is then minimized to find the optimum hedging points     

Optimality of hedging point policies in the production control offailure prone manufacturing systems

We study the necessary and sufficient conditions for the optimality of the hedging point policy for production systems in which the failure rate of machines depends on the rate of production. We focus on a one machine one part-type and infinite horizon discounted cost problem. It is shown that when the failure rate is independent of the rate of production and a constant, the hedging point policy is provably optimal. The main result of this paper is to show that the linearity of the failure rate function is both necessary and sufficient for the optimality of the hedging point policy     

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 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.     

Control of manufacturing systems with a two-value, production-dependent failure rate

In this paper we consider a failure prone, single machine, single part-type, limited inventory, manufacturing system subject to a non-homogeneous Markov failure/repair process with the failure rate depending on the production rate through a two-value function. The problem is to minimize a cost function which includes a penalty for waiting customers. We derive and prove the optimality of a policy which depends on a threshold but is not the so-called hedging point policy, optimal for the Markov homogeneous case.     

The queueing equivalence to a manufacturing system with failures

The authors consider optimal production rate control in a failure prone manufacturing system. It is well known that the hedging point policy is the optimum controller for such a system. They show that under the hedging point policy the system can be treated as an M/M/1 queue. Therefore, existing results in queuing theory can be readily applied to obtaining the steady-state probability density function of the production surplus, based on which the optimal hedging point policy can be computed. To a large extent, the approach is based on sample path analysis. It not only provides an alternative way to solve the problem but also reveals some interesting insights