Robust production and maintenance planning in stochasticmanufacturing systems

In this paper the authors consider a preventive maintenance and production model of a flexible manufacturing system with machines that are subject to breakdown and repair. The preventive maintenance can be used to reduce the machine failure rates and improve the productivity of the system. The control variables are the rate of maintenance and the rate of production; the objective is to choose a control process that optimizes a robust cost of inventory/shortage, production, and maintenance. The value function is shown to be locally Lipschitz and to satisfy a Hamilton-Jacobi-Isaacs equation. A sufficient condition for optimal control is obtained. Finally, an algorithm is given for solving the optimal control problem numerically     

Computational aspects of an extended EMQ model with variable production rate

The paper considers a generalized economic manufacturing quantity (EMQ) model with stochastic machine breakdown and repair in which the time to machine failure, corrective and preventive repair times are all assumed to be random variables. The model is formulated under general failure and general repair time distributions, treating the machine production rate (speed) as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate is assumed to be dependent on the production rate. The model is further extended to the case where certain safety stocks are hold in inventory to protect against possible stockout during machine repair. The solution procedure and computational algorithms of the associated constrained optimization problems are provided. Numerical examples are taken to determine the optimal production policies by the proposed algorithms and examine the sensitivity of the model parameters.Several economic manufacturing quantity (EMQ) models for unreliable manufacturing systems have been developed in the literature even for general failure and general repair (corrective) time distributions. In these studies, preventive repair has not been considered in a general way and efforts have been made to derive the production control and maintenance policy for inflexible manufacturing systems, where the machine capacity is pre-determined. The purpose of this article is to formulate a generalized EMQ model for a flexible unreliable manufacturing system in which (i) the time to machine failure and repair (corrective and preventive) times follow general probability distributions and (ii) the machine failure rate is dependent on the production rate. Consideration of a variable production rate makes the model hard to analyze completely. So, attempt has also been made to get into its computational aspects by developing solution algorithms.     

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.     

Hierarchical production and setup scheduling in stochasticmanufacturing systems

This paper is concerned with an asymptotic analysis of hierarchical production and setup scheduling in a stochastic manufacturing system consisting of a single failure-prone machine and facing constant demands for a number of products. At any given time the system can only produce one type of product, and the system requires a setup if production is to be switched from one type of product to another. A setup may involve setup time or setup cost or both. The objective of the problem is to minimize the total costs of setup, production, and surplus. The control variables are a sequence of setups and a production plan. An asymptotic analysis with respect to increasing rates of change in machine states gives rise to a deterministic limiting optimal control problem in which there is a control variable associated with each of the machine states and the production rate is obtained by weighting these controls with the stationary probabilities of the corresponding states. Asymptotic optimal controls for the original problem from optimal or near-optimal controls for the limiting problem are constructed     

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.     

Markov decision models for the optimal maintenance of a production unit with an upstream buffer

We consider a manufacturing system in which a buffer has been placed between the input generator and the production unit. The input generator supplies at a constant rate the buffer with the raw material, which is pulled by the production unit. The pull-rate is greater than the input rate when the buffer is not empty. The two rates become equal as soon as the buffer is evacuated. The production unit deteriorates stochastically over time and the problem of its optimal preventive maintenance is considered. Under a suitable cost structure it is proved that the optimal average-cost policy for fixed buffer size is of control-limit type, if the repair times are geometrically distributed. Efficient Markov decision process solution algorithms that operate on the class of control-limit policies are developed, when the repair times are geometrical or follow a continuous distribution. The optimality of a control-limit policy is also proved when the production unit after the end of a maintenance remains idle until the buffer is filled up. Furthermore, numerical results are given for the optimal policy if it is permissible to leave the production unit idle whenever it is in operative condition.     

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.     

Joint admission,production sequencing,and production rate control for a two-class make-to-order manufacturing system

Today's manufacturing industry faces a number of challenges related to the rapid delivery of products with a high degree of variety. Striking a balance between the effectiveness in capacity utilization and the rapidness in order-fulfillment is a substantial challenge for manufacturing companies. This work aims to provide a theoretical basis from which to address this practical question. To this end, we address the problem of coordinating the admission, production sequencing, and production rate controls for a two-class make-to-order manufacturing system. Formulating the problem as a Markov decision process model, we identify the structural properties of optimal control policies under both discounted and average profit criteria. We show that the cμ rule is optimal for production sequencing and the optimal admission and production rate control policies can be characterized by the state-dependent threshold levels, provided that the production times are not associated with customer class. We also show that the optimal production rates are monotone in the system state, as in the case of a single class queueing system, and that the lower priority class can be preferred to the higher priority class in order admission under a certain condition on the system parameters. Our numerical study demonstrates that a considerable economic benefit can be achieved if the production rate is dynamically controlled between the minimum and maximum rates rather than fixed to the mean rate of these values. Finally, we present a heuristic policy that is described by linear switching functions for the control of order admission and a selection rule for the control of production rate. We compare the performance of our heuristic to the optimal policy using a numerical experiment, revealing that the heuristic provides near optimal solutions to test example problems and is robust to the system parameters.     

An EMQ model in an imperfect production process

The intention of this article is to develop a framework of production policy (resumption and non-resumption) in order to find out optimal safety stock, optimal production rate and production lot size. It encompasses specific versions of the concept of quality and inventory model, stochastic machine breakdown and its correcting and regular repair paths with safety stocks. This framework hopefully serves to simplify answers to the important questions: How much safety stocks, production rate and production lot size are required to minimise the total expected system cost. The optimal production rate, production lot size, production run time and safety stocks are determined numerically and the joint effect of process deterioration, machine breakdown and its repair (correcting and preventive) on the optimal decision is investigated for a numerical example. Such an investigation should also yield logistics directions for the design of products and their manufacturing processes.     

Integrated production planning and preventive maintenance in deteriorating production systems

This paper discusses the issue of integrating production planning and preventive maintenance in manufacturing production systems. In particular, it tackles the problem of integrating production and preventive maintenance in a system composed of parallel failure-prone production lines. It is assumed that when a production line fails, a minimal repair is carried out to restore it to an ‘as-bad-as-old’ status. Preventive maintenance is carried out, periodically at the discretion of the decision maker, to restore the production line to an ‘as-good-as-new’ status. It is also assumed that any maintenance action, performed on a production line in a given period, reduces the available production capacity on the line during that period. The resulting integrated production and maintenance planning problem is modeled as a nonlinear mixed-integer program when each production line implements a cyclic preventive maintenance policy. When noncyclical preventive maintenance policies are allowed, the problem is modeled as a linear mixed-integer program. A Lagrangian-based heuristic procedure for the solution of the first planning model is proposed and discussed. Computational experiments are carried out to analyze the performance of the method for different failure rate distributions, and the obtained results are discussed in detail.     

Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns

This paper investigates the N-policy M/M/1 queueing system with working vacation and server breakdowns. As soon as the system becomes empty, the server begins a working vacation. The server works at a lower service rate rather than completely stopping service during a vacation period. The server may break down with different breakdown rates during the idle, working vacation, and normal busy periods. It is assumed that service times, vacation times, and repair times are all exponentially distributed. We analyze this queueing model as a quasi-birth–death process. Furthermore, the equilibrium condition of the system is derived for the steady state. Using the matrix-geometric method, we find the matrix-form expressions for the stationary probability distribution of the number of customers in the system and system performance measures. The expected cost function per unit time is constructed to determine the optimal values of the system decision variables, including the threshold N and mean service rates. We employ the particle swarm optimization algorithm to solve the optimization problem. Finally, numerical results are provided, and an application example is given to demonstrate the applicability of the queueing model.     

A volume flexible economic production lot-sizing problem with imperfect quality and random machine failure in fuzzy-stochastic environment

An “economic production lot size” (EPLS) model for an item with imperfect quality is developed by considering random machine failure. Breakdown of the manufacturing machines is taken into account by considering its failure rate to be random (continuous). The production rate is treated as a decision variable. It is assumed that some defective units are produced during the production process. Machine breakdown resulting in idle time of the respective machine which leads to additional cost for loss of manpower is taken into account. It is assumed that the production of the imperfect quality units is a random variable and all these units are treated as scrap items that are completely wasted. The models have been formulated as profit maximization problems in stochastic and fuzzy-stochastic environments by considering some inventory parameters as imprecise in nature. In a fuzzy-stochastic environment, using interval arithmetic technique, the interval objective function has been transformed into an equivalent deterministic multi-objective problem. Finally, multi-objective problem is solved by Global Criteria Method (GCM). Stochastic and fuzzy-stochastic problems and their significant features are illustrated by numerical examples. Using the result of the stochastic model, sensitivity of the nearer optimal solution due to changes of some key parameters are analysed.     

The economic production lot size model extended to include more than one production rate

We study an extension of the economic production lot size model, where more than one production rate can be used during a cycle. Moreover, the production rates, as well as their corresponding runtimes are decision variables. We decompose the problem into two subproblems. First, we show that all production rates should be chosen in the interval between the demand rate and the production rate which minimizes unit production costs, and should be used in an increasing order. Then, given the production rates, we derive closed‐form expressions for all optimal runtimes as well as the minimum average cost. This analysis reveals that it is the size of the setup cost that determines the need for being able to use several production rates. We also show how to derive a near‐optimal solution of the general problem.     

A two-stage hybrid manufacturing model with controllable make-to-order production rates

As an effective strategy to facilitate delivering customized products within short lead time, hybrid manufacturing via a two-stage process has received attention from academia and industry. In this paper, we study a two-stage hybrid manufacturing system in which semifinished products are manufactured in a make-to-stock fashion in the first stage and end-products are produced from semifinished goods in a make-to-order (MTO) mode in the second stage. The rate of MTO production can be controlled within given limits, depending on the status of the system. The primary goal of this paper is to study a policy for coordinating order admission, MTO production rate, and inventory replenishment controls. Formulating the problem as a Markov decision process model, we characterize the structure of optimal control policies to maximize the long-run average profit. Using a numerical experiment, we study how the flexibility in MTO production rate affects the optimal policy and the optimal profit. We also examine the effect of the number of alternative MTO production rates on the optimal profit. We propose three heuristic policies implementable for general cases. The first heuristic describes two linear switching functions for admission and production controls and a selection rule for MTO production rate control. The second heuristic specifies fixed thresholds for the control decisions using the local information. The third heuristic presents linear switching functions that approximate the optimal threshold curves. Unlike second and third heuristics, the first heuristic does not require a grid search to determine the control parameters. We implement numerical studies to examine the marginal impact of system parameters and the effect of the number of alternative MTO production rates on the performance of the heuristics. Compared to the optimal policy, the average percentage performance of the first and third heuristics is less than 1% for both numerical studies. On the other hand, the average percentage performance of the second heuristic is larger than 3%, and it exceeds 10% for a set of particular problem examples.     

An optimal replacement policy for repairable cold standby system with priority in use

In this article, a cold standby repairable system consisting of two nonidentical components and one repairman is studied. It is assumed that component 2 after a repair is “as good as new” while component 1 after a repair is not, but component 1 is given priority in use. Under these assumptions, by using the geometric process repair model, we consider a replacement policy N based on the number of failures of component 1 under which the system is replaced when the number of failures of component 1 reaches N. Our problem is to determine an optimal policy N* such that the long-run average cost per unit time (i.e. the average cost rate) of the system is minimized. The explicit expression of the average cost rate of the system is derived and the corresponding optimal replacement policy N* can be determined numerically. Finally, a special system with Weibull-distributed working time and repair time of component 1 is given to illustrate the theoretical results in this article.     

Optimal tracker for unreliable manufacturing systems

This paper deals with the inventory-production control problem where the produced items are assumed to deteriorate at a rate that depends on the demand rate of the production system. The state of this production system is assumed to be described by a continuous-time Markov process taking values in a finite discrete space. The inventory production control problem is formulated as a stochastic optimal control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost problem is also treated. A numerical example is provided to show the usefulness of the proposed model.     

Optimization analysis of an unreliable multi-server queue with a controllable repair policy

This article deals with an infinite-capacity multi-server queueing system, in which the servers are assumed unreliable and may fail at any time. To conserve energy while delivering reliable service, a controllable repair policy is introduced. With such a policy, the failed servers will be sent to the repair facility only when the number of failed machines in the system arrives at a preset threshold value. A quasi-birth-and-death process is used to model the complex system and the stability condition is examined. The rate matrix is calculated approximately and steady-state stationary distributions are obtained by a matrix-analytic approach. The closed-form expressions of important system characteristics are presented. A cost model is constructed to determine the optimal repair policy, the optimal value of service rate and the optimal value of repair rate. Three heuristic algorithms are employed to deal with the optimization problem. Some numerical results are provided to compare the efficiency of two methods.     

印染行业不可靠生产系统生产控制模型

基于印染行业自身特性,建立了适合于该行业特点的不可靠生产系统的生产控制模型。该模型不但考虑了生产设备时有故障和修复事件的发生,而且也把由于生产系统操作条件及生产原料属性的波动造成合格产品呈随机分布的情况纳入模型框架,其中当不同产品间生产切换时,所需切换时间及切换费用也被引入模型,并假设此时设备的故障过程为Markov过程。结合单设备单产品情况,给出了其最优生产控制策略。为实现印染行业生产的优化控制及建立完善的MES系统提供了理论支持。     

Decomposition program for allocating interstage storage along an automatic production line

A computer program called decomposition is presented for generating an approximate solution for the output rate of a serial, synchronized, automatic production line. Each pair of consecutive machines in the production line is separated by a storage buffer. Each machine is assumed to be subject to random failure if it is up or random repair if it is down each time that parts are transferred. The program can be used to allocate a fixed total storage capacity to the buffers between machines so as to maximize the steady state output rate. Decomposition is an iterative algorithm which requires only a small fraction of the computer time and memory needed by an exact solution. Although the accuracy of the approximate solution decreases as the line is lengthened, the accuracy increases as the total storage capacity of the production line increases. Approximate solutions can be obtained for lines which are too large to be treated by exact methods.