Optimal integrated maintenance/production policy for randomly failing systems with variable failure rate

This article deals with the combined production and maintenance plans for a manufacturing system satisfying a random demand. We first establish an optimal production plan which minimises the average total inventory and production cost. Second, using this optimal production plan, and taking into account the deterioration of the machine according to its production rate, we derive an optimal maintenance schedule which minimises the maintenance cost. A numerical example illustrates the proposed approach, this analytical approach, based on a stochastic optimisation model and using the operational age concept, reveals the significant influence of the production rate on the deterioration of the manufacturing system and consequently on the integrated production/maintenance policy.     

A cost minimisation model for joint production and maintenance planning under quality constraints

In this paper, integrated planning of production, imperfect maintenance and process inspections in a multi-machine system is investigated. This system consists of parallel machines which deteriorate with time and they may shift from a primarily in-control state to a degraded state with a higher defective rate or to a failed state. Maintenance scheduling corresponds to a discrete time age-based imperfect maintenance with a large number of maintenance alternatives. Process inspections are considered to detect the current state of the system. Detecting a deteriorated condition initiates the quality check of the related sub-lots, rework of defective items and a process adjustment that brings the machine in its normal conditions. Production planning includes a capacitated lot-sizing problem with multiple products. We propose a joint approach that coordinates the decisions of the three functions, where the objective function minimises the total cost. Evaluation of costs and interacting factors is presented and two heuristic methods are proposed to solve the problem. The results of the joint model are compared to a non-integrated method and a sensitivity analysis is conducted.     

Joint optimisation of production,maintenance and quality for batch production system subject to varying operational conditions

This paper considers the integration problem of production, maintenance and quality for a capacitated lot-sizing production system subject to deterioration. The effects of varying operational conditions from batch to batch on system reliability and product quality are modelled by proportional hazards models, resulting in non-monotonic failure rate and defect rate. After each batch production, imperfect preventive maintenance (PM) is determined to mitigate the system deterioration, and inspection is taken to sort nonconforming items in the finished goods. Once the cumulative number of nonconforming items exceeds a predetermined threshold, an overhaul is performed to renew the system. An integrated model for optimising production plan, PM plan and overhaul strategy is developed to minimise the total cost while satisfying all product demands. A genetic algorithm is proposed to solve the integrated model efficiently. Numerical results validate the rationality of the model with varying operational conditions consideration and its applicability in economic benefits.     

Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items

For an imperfect production system, to reduce quality-related costs, a manager may consider investing capital in quality improvement. In general, the investment expense in reducing the defective rate of items is often paid by the vendor. On the other hand, the buyer may inspect the product quality as the order is received which implies it incurs an inspection cost. In a supply chain integrated system, to accomplish global optimisation, the vendor and buyer can agree to jointly invest capital to improve the imperfect production processes, and the buyer can remove the inspection programme as the defective rate reaches a certain low-level. Hence, this paper investigates the impacts of collaborative investment and inspection policies on an integrated inventory model with defective items. The objective of this study is to seek the optimal order quantity, shipping times from the vendor to the buyer per production run, and the defective rate that minimise the joint total cost per unit time. An algorithm is developed to find the optimal solution. Several numerical examples are presented to demonstrate the proposed model and solution procedure, and then several management insights are obtained from the numerical examples.     

A genetic algorithm approach for production scheduling with mould maintenance consideration

The traditional approach for maintenance scheduling concerns single-resource (machine) maintenance during production which may not be sufficient to improve production system reliability as a whole. Besides, in the literature many researchers schedule maintenance activities periodically with fixed maintenance duration. However, in a real manufacturing system maintenance activities can be executed earlier and the maintenance duration will become shorter since less time and effort are required. A practical example is that in a plastic production system, the proportion of machine-related downtime is even lower than mould-related downtime. The planned production operations are usually interrupted seriously because of the mismatch among the maintenance periods between injection machine and mould. In this connection, this paper proposes to jointly schedule production and maintenance tasks of multi-resources in order to improve production system reliability by reducing the mismatch among various processes. To integrate machine and mould maintenance tasks in production, this paper attempts to model the production scheduling with mould scheduling (PS-MS) problem with time-dependent deteriorating maintenance schemes. The objective of this paper is to propose a genetic algorithm approach to schedule maintenance tasks jointly with production jobs for the PS-MS problem, so as to minimise the makespan of production jobs.     

Effects of maintenance policy on an imperfect production system under trade credit

The traditional production model development assumed that all products are perfect quality and did not consider maintenance, which is far from reality. In practice, the production process may shift randomly from an in-control state to an out-of-control state during a production run, i.e. process deterioration. This paper considers both preventive maintenance and corrective maintenance which are used to increase the system reliability. The objective of this paper is to determine the optimal production run time and maintenance frequency while minimising the total cost under process deterioration and trade credit. This paper develops a theorem and an algorithm to solve the problem described, provides numerical analysis to illustrate the proposed solution procedure, and discusses the impact of various system parameters. A real case of hi-tech manufacturer is used to verify the model. It predicts a 10.36% decrease in total cost if the preventive maintenance decision is considered.     

Quality control in a single state production system: open and closed loop policies

The output quality in a single state production system depends on the input quality and the machine state. The machine state deteriorates with production and affects output quality. The deterioration, and hence output quality can be controlled through proper maintenance actions. This paper formulates a model and examines optimal open and closed loop policies for carrying out such maintenance actions.     

Modelling and analysis for sequentially optimising production,maintenance and delivery activities taking into account product returns

This paper develops and analyses a stochastic optimisation problem with a service level constraint for generating a sequentially optimal plan of production, maintenance and delivery activities in a deteriorating manufacturing system. Stochastic demand along with product returns are both assumed the latter of which allows for restocking products returned by the customer which are still new and thus in saleable condition. A constrained production/maintenance/delivery problem with service level, stochastic demand, delivery time, failure rate and product returned is formulated based on quadratic model. This quadratic formulation is adapted to provide an inventory, delivery, production and maintenance policies. The objective of this paper is to study the delivery time influence on the planning of the production, maintenance and delivery activities. Finally, we present simulation results to illustrate the exploitation of the proposed approach.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

Integrated production,statistical process control,and maintenance policy for unreliable manufacturing systems

The objective of this paper is to develop an integrated approach for the joint control of production, maintenance and quality for batch manufacturing systems. We consider such systems that are subject to degradation which is at the origin of the production of defective units. The quality control of lots produced is performed using an ‘x-bar’ control chart. This graphical tool will allow estimating the quality of the batch being produced and possibly undertake perfect preventive or corrective maintenance actions on the production system. A buffer stock is built to maintain continuity of supply during maintenance actions. The incurred total cost includes setup cost, inventory costs, the cost of unused products, maintenance costs and quality costs. Decision variables include the buffer stock size, the sample size, the sampling interval, the surveillance and the control limits of the control chart. Numerical experiments and sensitivity analyses are provided to evaluate the effectiveness of the proposed control policy and the robustness of the solving approach.     

Integrating quality and maintenance decisions in a production-inventory model for deteriorating items

In typical production-inventory models of deteriorating items, deterioration of the production process has not been considered. In this paper, a model is proposed in which both the produced items and the production equipment deteriorate. When the production system deteriorates, it shifts to an out-of-control state and begins to produce a proportion of defective items, necessitating corrective maintenance action. A model is formulated to integrate several realistic aspects, including item and process deterioration, varying demand and production rates, quality, inspection, and maintenance. A heuristic solution algorithm is developed to determine the production and inspection schedules, and a numerical example is solved.     

Joint production and quality control of unreliable batch manufacturing systems with rectifying inspection

Production control policy and economic sampling plan design problems have been studied separately in previous research. This paper considers a joint production control policy and economic single sampling plan design for an unreliable batch manufacturing system. The production is controlled by a modified hedging point policy which consists of building and maintaining a safety stock of finished product to avoid shortages during corrective maintenance. The main objective of this paper is to determine simultaneously the economic production quantity, the optimal safety stock level and the economic sampling plan design which minimise the expected overall cost. A stochastic mathematical model is developed and solved using a simulation optimisation approach based on the response surface methodology. Simulation is used to imitate the complex dynamic and stochastic behaviour of processes as in the real-life industrial systems. The obtained results show clearly strong interactions between production quantity, inventory state and sampling plan design which confirm the necessity of jointly considering production and quality control parameters in an integrated model. Moreover, it is shown a significant impact of production system reliability on the economic sampling plan design and therefore on the quality of finished product delivered to consumers. Numerical example and sensitivity analyses are presented for illustrative purposes.     

Preventive maintenance of a batch production system under time-varying operational condition

This paper proposes a dynamic opportunistic preventive maintenance (PM) strategy for a production system with a time-varying batch production pattern. The operation of such a system is generic in that the operational condition (OC) varies from batch to batch and the information about the next batch can be confirmed only upon the completion of the current batch. To accommodate time-varying OC, a modified imperfect maintenance model is developed to optimise the performance of maintenance actions that can only be performed at batch-shift points. The first study presents a PM policy for a single machine with short-term production plans. Then, a multi-machine system is studied with a goal of developing an optimum dynamic opportunistic PM strategy for a group of machines at batch-shift points. Numerical examples are proceeded to illustrate the proposed maintenance strategy in practice. The result reveals that more cost will be incurred if OC is ignored. Moreover, the proposed opportunistic PM strategy achieves the lowest total cost comparing with other strategies as the system downtime cost and maintenance cost has been jointly minimised.     

Manufacturing quality density,control and maintenance

The purpose of this paper is to define conceptually and operationally, a measure of quality density in manufacturing. This is expressed in terms of a manufacturing process propensity to ‘output’ units which are defectives, as a function of the manufactured production output, the manufacturing deterioration process, maintenance, quality control, and generally the risks a manufacturing process is subjugated to. Particularly, we assume that the production process induces ‘shocks’ which lead to poorer manufactured quality, while maintenance efforts are continually being employed to restore the process propensity to produce units of better quality. Quality control is used then to monitor the output quality of units produced. Using a methodology of level crossing in stochastic point processes, the stationary probability distribution of a manufactured output quality is defined. Applications to production quality management, combined quality and maintenance management, as well as quality control are considered. Finally, an exponential shock model is resolved analytically.     

Coordination of pricing,inventory, and production reliability decisions in deteriorating product supply chains

In this article, we study a two-level supply chain model for deteriorating items, in which the supplier’s production system is unreliable and the retailer’s demand is price-sensitive. The supplier’s production line may randomly shift from the in-control state to the out-of-control state. When the production line is in the out-of-control state, a proportion of the produced products will have bad quality. To mitigate the out-of-control risks, the supplier can improve the production line reliability by investing in high-quality machines, highly skilled workers, or advanced maintenance technologies. We start with the study of pricing and inventory problems concerning endogenous reliability in the integrated and decentralised scenario. To better illustrate the proposed models, two applicable algorithms are designed to determine the optimal production reliability, ordering quantity, and prices. Then, a cooperative reliability investment and revenue-sharing contract is proposed to coordinate the supply chain. Numerical examples and sensitivity analysis of the equilibrium strategies and coordinating results on key system parameters (e.g. deterioration rate, production rate, etc.) are given to verify the effectiveness of the contract, and meanwhile get some managerial insights.     

Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.     

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach.     

Determining the optimal lot size for the finite production model with random defective rate,the rework process,and backlogging

This paper considers the effects of the reworking of defective items on the economic production quantity (EPQ) model with backlogging allowed. The classic EPQ model assumes that manufacturing facility functions perfectly during a production run. However, due to process deterioration or other factors, the production process may shift and produce imperfect quality items. In this study, a random defective rate is considered, and when regular production ends, the reworking of defective items starts immediately. Not all of the defective items are reworked, a portion of them are scrap and are discarded. Repairing and holding cost per reworked item and disposal cost per scrap item are included in the proposed mathematical modelling and analysis. The renewal reward theorem is utilized to deal with the variable cycle length, and the optimal lot size that minimizes the overall costs for the imperfect quality EPQ model is derived where backorders are permitted.     

Joint optimization of preventive maintenance and inventory control in a production line using simulation

This paper proposes an integrated method for preventive maintenance and inventory control of a production line, composed of n machines (n?≥?1) without intermediate buffers. The machines are subject to failures and an age-dependent preventive maintenance policy is used. Approximate analytical results are proposed for the one machine case. Simulation software is used to model and simulate the behaviour of the production line of n machines under various maintenance and inventory control strategies. A methodology combining the simulation and genetic algorithms is proposed jointly to optimize maintenance and inventory control policies. Results are compared with the analytical solutions.     

Production policies under deteriorating process conditions

This paper examines a single-stage production system that manufactures multiple products under deteriorating equipment conditions. The machine condition worsens with production, and improves with maintenance. The condition of the process can be in any one of several discrete states, and transitions from state to state follow a semi-Markov process. In many production environments, the quality or yield of output depends heavily on the condition of the production process. The problem considers the trade-offs between manufacturing products that have a higher profit, a longer processing time, and therefore, a higher deterioration probability versus products that have a smaller profit, shorter processing time with a lower process deterioration probability. The firm needs to determine the optimal production choice in each state in a way that maximizes the long-run expected average reward per unit time.

The paper makes three sets of contributions. First, it introduces the concept of critical ratios for the firm's manufacturing decision at each state regarding whether to switch from one product to another. Second, through the use of critical ratios, the main result shows that the optimal production choice for each state can be determined independently of the actions taken in other states, despite the complex interconnections between the production decisions and state transitions. Third, the paper provides generalizations that illustrate the depth, scope and richness of the proposed solution technique by extending the model in the number of machine states, to settings where maintenance is performed in intermediate states, and to settings where transition probabilities are influenced by both mean and variance of processing times.