The replacement of machines in a serially dependent multi-machine production system

In this paper a heuristic procedure is developed for solving the problem of planning machine replacements for a serially dependent production system. Given a finite planning horizon, the decision-maker wishes to decide (1) which periods, if any, that the entire production system must be shut down in order to make replacements, and (2) what specific machine or machines in the system should be scheduled for replacement during each of these downtime periods. The problem involves a balancing of costs. If the production system is brought down to make one or more replacements a fixed downtime cost is incurred; this cost is independent of the machines replaced during the downtime. In addition, other fixed coats are incurred for each of the machines replaced. Our motivation for scheduling these replacements is to realize lower variable costs for operating the machines. The variable operating costs are assumed to increase as the age or vintage of the machines increases. An optimal replacement policy is one in which the total of the present-value fixed and operating costs are minimized for the entire planning horizon. The paper also presents computational results using the heuristic to solve a large number of randomly generated test problems of varying numbers of machines and periods. These heuristic solutions are compared to known optimal solutions for a number of the problems. One of the important advantages of the heuristic procedure is that it is capable of producing several solutions to a given problem, all rank ordered by increasing cost. Thus, the decision-maker is afforded alternative choices from which he or she may select a replacement policy.     

An optimal replacement policy for a repairable system based on its repairman having vacations

This paper studies a cold standby repairable system with two different components and one repairman who can take multiple vacations. If there is a component which fails and the repairman is on vacation, the failed component will wait for repair until the repairman is available. In the system, assume that component 1 has priority in use. After repair, component 1 follows a geometric process repair, while component 2 can be repaired as good as new after failures. Under these assumptions, a replacement policy N based on the failed times of component 1 is studied. The system will be replaced if the failure times of component 1 reach N. The explicit expression of the expected cost rate is given, so that the optimal replacement time N^? is determined. Finally, a numerical example is given to illustrate the theoretical results of the model.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.     

An optimal replacement policy for complex multi-component systems

Given a reward structure, this paper addresses an optimal replacement problem for complex multi-component systems. To maintain revenue stream resulting from system, the system is inspected according to a homogeneous Poisson process and certain actions are carried out in response to the system state. Decisions are based on a performance measure described by a Squared Bessel process. Given some assumption, we explore the inherent relation between the Squared Bessel process and an extended Gamma (EG) process. Since there are some flow of income and increasing costs due to inspections, the problem is to optimally stop processing the system and carrying out a renewal to maximize the reward functional. To this end, using the local characteristics of the EG process as a stopping criterion and the expected total discounted reward as a measure of policy, this paper aims at determining an optimal operating (stopping) time which truly balances both income and cost and so maximizes the expected discounted reward over a cycle. In support of the model a numerical example is provided to show feasibility of this programme in real application. Attention is restricted to perfect repair and inspection, but the paper provides the structure so that different scenarios can be explored.     

An economic model for determining the optimal quality and process control policy in a queue-like production system

This paper interrelates and synthesizes the economic design of quality and process control policy and the management of a production system described in terms of an M/G/X queue. A mathematical model is developed to determine the optimal quality and process control policy when both the quality and quantity issues in the production system are considered. The optimal control policy is defined as the one that maximizes the expected profit per unit time over an infinite horizon. Hypothetical data is used to illustrate the impact of on-line control policies on the operating characteristics of the production process.

For a given control policy, it is shown that the expected profit per unit time of the production system can be increased by either improving the reliability of the production system, increasing the arrival rate of incoming jobs, increasing the system's processing rate, or shortening the system's shutdown time. The results also indicate that the larger the performance difference between the in-control and the out-of-control states, the greater the amount of effort should be involved in quality and process control. Finally, it is important for the capacity design of a production system to take into account the requirrments for both quality control and process adjustment.     

An optimal cart moving policy for a flexible manufacturing system

A flexible manufacturing system is composed of many stations such as a load/unload station, a set of workstations, and a common buffer, that are linked together with a material handling system. Each workstation consists of a limited input buffer, a single machine and a limited output buffer. The material handling system consists of a single cart moving parts in the system according to the process paths required by the parts. A part is blocked when it is moved to a workstation but cannot enter the workstation. The function of the common buffer is to temporarily store blocked parts. A blocked part is treated in accordance with a flexible manufacturing system blocking mechanism. We model the flexible manufacturing system by a closed queueing network with the flexible manufacturing system blocking mechanism and a block-dependent static Markov part routing. An optimal cart moving policy that maximizes the expected system throughput is formulated as an undiscounted semi-Markov decision process. Several properties of the optimization problem are characterized. A loop approach is developed for finding an optimal policy. An example is given to illustrate the methodology, and investigate its convergence.     

An optimal inspection and diagnosis policy for a multi-mode system

This paper considers a multi-mode system that is inspected periodically, and the period of inspection is a random variable. The system has three modes: normal (N), abnormal (A) and failure (F), where F is a self-announcing mode whereas, N and A are non-self-announcing and operating modes. When the system is operating, it is inspected once every random time T to make sure whether it is in N or A until it attains F, or until it is detected to be in A. Each inspection consists in measuring a value taken by a diagnostic parameter. The diagnostic parameter, which is a random variable, has a close relation with the operating modes. If it is found to have exceeded a certain critical value, a preventive maintenance (or repair) is performed. By using the supplementary variable technique, the reliability indices and an optimal inspection and diagnosis policy for the system are obtained.     

An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon

It is difficult to find the optimal solution of the sequential age replacement policy for a finite-time horizon. This paper presents an accurate approximation to find an approximate optimal solution of the sequential replacement policy. The proposed approximation is computationally simple and suitable for any failure distribution. Their accuracy is illustrated by two examples. Based on the approximate solution, an approximate estimate for the total cost is derived.     

An age-based replacement policy with non-zero repair times for a continuous production process

In this paper a case study for maintenance optimization is presented. The theoretical features of the model, an age-based replacement model taking into account non-zero repair times, are briefly discussed. The main part of the paper focuses on the application aspects of such problems like data gathering and finding the appropriate solution method. An extensive discussion of the results concludes the paper.     

Optimal replacement policy for a redundant system

Summary This paper considers the reliability of a system which consists ofn components connected in series, the i^thcomponent being supported by (m _i – 1) units in parallel and obtains the optimal policy of replacement by dynamic programming. In the case of a system consisting of identical pairs, the decision depends on the number of operable pairs. For this case sample calculations are presented.

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Zusammenfassung Wir untersuchen die Zuverlässigkeit eines Seriensystems ausn Komponenten, bei dem für diei-te Komponentem _i – 1 Reserveelemente zur Verfügung stehen. Mit Hilfe der dynamischen Optimierung bestimmen wir die optimale Ersetzungspolitik. Besteht das System aus identischen Paaren, hängt die Entscheidung von der Zahl der intakten Paare ab. Für diesen Fall geben wir beispielhaft einige numerische Ergebnisse.

     

An optimal production and shipment policy for a single-vendor single-buyer integrated system with both learning effect and deteriorating items

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a collaborative system is to propose an integrated replenishment plan aimed at maintaining a win-win partnership for both vendor and buyer. The objective of this study is to develop a production and shipment model for a system that incorporates learning effect and deteriorating items and to derive an optimal joint total cost from the integrated perspective of both vendor and buyer. A simple solution procedure is presented to determine the optimal production time and number of deliveries. A numerical example is provided to illustrate the proposed model. A sensitivity analysis is conducted to study the effect of changes in the related parameters on the optimal solution. This paper shows that the proposed integrated model can result in a significant cost reduction as compared with the independent decisions made by either vendor or buyer.     

An optimal consignment stock production and replenishment policy with controllable lead time

This paper considers a single-vendor and single-buyer production system in which the lead-time is controllable with an extra investment under a long-term agreement between the two trading partners. The vendor produces at a finite rate, ships the outputs in lots of equal size within a production cycle, and delays those shipments for a certain period when the buyer’s inventory approaches the capacity limits. Therefore, the arrival of these shipments does not lead to an increase in the buyer’s inventory. Meanwhile, the buyer holds the payment until the complete consumption of the products. The holding cost consists of a storage component and a financial component. A joint EOQ/EPQ model is then established under cases where the buyer’s unit storage holding cost might be greater or less than that of the vendor to jointly determine the number of shipments, the size of each shipment, the number of delayed shipments, and the lead time that minimise the yearly joint total expected cost (JTEC) of the system. An efficient solution procedure is provided to solve the non-linear integer optimisation model that defined the system under consideration. A method to determine the integer global optima from the real global optima is also presented. Two numerical experiments are conducted to illustrate the procedure and the results show that considering the combined effect of adopting a consignment stock policy and lead time crashing opportunities may lead to a better result than any of these two policies considered separately.     

The optimal production and quality policy for the vendor in a trade

Arranging an inspection schedule for the production process and taking inspection and burn-in tests to screen out defective items in a production lot before items are shipped to the buyer are widely used by the vendor, such that the defective percentage in an outgoing batch satisfies the quality requirement specified in the contract between them. For an inspection schedule, the number of inspections and the length of time intervals between two inspections are influential to both the precision of detecting the manufacturing process and the inspection cost. As to the inspection test, it is not perfect, so there are two types of errors (Types I and II). Nevertheless, compared with inspection test, burn-in is usually costly. Hence, how to make a suitable trade-off between these three treatments (i.e., inspection schedule, inspection test, and burn-in test) such that the outgoing batch satisfies the purchaser's quality requirement with low cost is an important issue. The main purpose of this paper is to deal with the problem of determining the optimal inspection schedule and the optimal mixed policy of inspection and burn-in, where the average outgoing quality is used as the measure of quality. More specifically, by using the criterion of maximizing the expected profit that the vendor makes in a trade, a nonlinear programming problem is built to determine (a) the number of inspections undertaken in the production process, (b) the times at which the production process is inspected, (c) the total number of items that the vendor should produce (or the production run time), (d) the number of items for inspection, the number of items for burn-in, and the number of items that need neither inspection or burn-in, and (e) the optimal burn-in time for those needing burn-in testing. An example is provided to illustrate the proposed method.     

Lifetime replacement policy in discrete time for a single unit system

We consider, in discrete time, a single unit system which operates for a period of time represented by a general distribution. This unit is subjected to failures during operations. Some of these failures are repairable and the unit is repaired in the repair facility. When the unit experiences a non-repairable failure then it has to be replaced with a new one. We consider a replacement policy based on the lifetime of the unit. This policy can be studied from two different approaches. The first approach, named Model I, is to replace the unit by a new one when the unit attains a predetermined lifetime. The other approach, named Model II, is to close repair facility when the lifetime of the unit attains a predetermined quantity. For each model, we obtain the stationary distribution and some performance measures of interest.     

A study of replacement policy for components in a mechanical system

The degradation of system performance during operation can be improved by different considerations. One of the methods is to take the preventive replacement for the key components. In this paper we propose a methodology of the replacement scheduling of key components in a system. A hierarchical structure for the assessment is built based on the intrinsic and extrinsic characteristics of the system. In the first stage the key components are identified through the consideration of replaceability, failure consequence and life. After that, the priority of replacement is decided by the evaluation of reliability and economics of the selected components. As to the replacement time it is determined according to maximizing the operation profit. The procedures for deciding the priority and replacement time are repeated for the next action, until the replacement profit is less than that without replacement. The suggested approach can be applied to maintain the performance of some profitoriented mechanical system in a better way, e.g. vehicle, machine tool system, etc. Finally, the replacement scheduling of a hydraulic system is used to demonstrate the proposed methodology.     

Optimisation-based control coordination of PSSs and FACTS devices for optimal oscillations damping in multi-machine power system

An optimal procedure for designing co-ordinated controllers of power system stabiliser and flexible ac transmission system devices is developed for achieving and enhancing small-disturbance stability in multi-machine power systems. A constrained optimisation approach is applied for minimising an objective function formed from selected eigenvalues of the power systems state matrix. The eigenvalue-eigenvector equations associated with the selected modes form a set of equality constraints in the optimisation. There is no need for any standard eigenvalue calculation routines, and the use of sparse Jacobian matrix in the case of large system for forming the eigenvalue-eigenvector equations leads to the sparsity formulation. Inequality constraints include those for imposing bounds on the controller parameters. Constraints which guarantee that the modes are distinct ones are derived and incorporated in the control coordination formulation using the property that eigenvectors associated with distinct modes are linearly independent. The robustness of the controllers is achieved very directly through extending the sets of equality constraints and inequality constraints in relation to selected eigenvalues and eigenvectors associated with the state matrices of power systems with loading conditions and/or network configurations different from that of the base case. Simulation results of a multi-machine power system confirm that the procedure is effective in designing controllers that guarantee and enhance the power system small-disturbance stability.     

Scheduling of the optimal tool replacement times in a flexible manufacturing system

In Flexible Manufacturing Systems (FMSs). a cutting tool is frequently used for different operations and on different part types to minimize tool change-overs and the number of tools required, and to increase part-routing flexibility. In such situations, the tools become shared resources and work in job-dependent, changeable and nonhomogeneous conditions. It is well known that the tool failure rate depends on both age and machining conditions and that tool reliability is a function of the duration, machining conditions, and the sequence of the operations in FMS. The objective of this paper is to obtain a schedule of the optimal preventive replacement times for the cutting tools over a finite time horizon in a flexible manufacturing system. We assume that the tool will be replaced either upon failure during an operation or preventively after the completion of each operation, incurring different replacement costs. A standard stochastic dynamic programming approach is taken to obtain the optimal tool replacement times. The optimal schedule is obtained by minimizing the total expected cost over a finite time horizon for a given sequence of operations. A computational algorithm is developed and a numerical example is given to demonstrate the procedure.     

Optimising lot sizing with nonlinear production rates in a multi-product multi-machine environment

In a variety of discrete manufacturing environments, it is common to experience a nonlinear production rate. In particular, our interest is in the case of an increasing production rate, where learning creates efficiencies. This leads to greater output per unit time as the process continues. However, the advantages of an increasing production rate may be offset by other factors. For examples, JIT policies typically lead to smaller lot sizes, where the value of an increasing production rate is largely lost. We develop a general model that balances the impact of various competing effects. Our research focuses on determining lot sizes that satisfy demand requirements while minimising production and holding costs. We extend our prior work by developing a multi-product, multi-machine method for modelling and solving this class of production problems. The solution method is demonstrated using the production function from the PR#2 grinding process for a production plant in Carlisle, PA. The solution heuristic provides solution times that are on average only 0.22 to 0.55% above optimum as the solution parameters are varied and the ratio of heuristic solution times to optimal solution times varies from 18.16 to 14.15%.     

Optimal production plan for a multi-products manufacturing system with production rate dependent failure rate

This study deals with the problem of dependence between production and failure rates in the context of a multi-product manufacturing system. It provides an answer about how to produce (i.e. the production rates) and what to produce (i.e. which product) over a finite horizon of H periods of equal length. We consider a single randomly failing and repairable manufacturing system producing two products P_a and P_b . The product P_a is produced to supply the strategic demand d(k) of the principal customer via a buffer stock S over k periods (k?=?1,?2,?…?,?H). The second product P_b is produced to meet a secondary but very profitable demand. It is produced during a given interval at the end of each period k. We develop a genetic algorithm to determine simultaneously the optimal production rate of the first product during each period k and the optimal duration of the production interval of the second product, maximising the total expected profit.