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.     

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.     

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.     

Quality issue in forecasting problem of production and maintenance policy for production unit

In this study, we consider an unreliable deteriorating production system that produces conforming and non-conforming products to satisfy a random demand under a given service level and during a finite horizon. The production system is subjected to a failure-prone machine. The quality of the produced products is affected by the machine deterioration since the rate of defectives increases as the deterioration increases. Preventive maintenance actions can be piloted on the production system to reduce the influence of deterioration and the defective rate. A joint control policy is based on a stochastic production and maintenance planning problem with goals to determine, firstly, the economic plan of production and secondly, the optimal maintenance strategy. The proposed jointly optimisation minimises the total cost of production, inventory, maintenance and defectives. A failure rate and quality relationship are defined to show the influence of the production rates variation on the failures rate as well as on the defective rate. A numerical example and an industrial case study are adopted to illustrate the proposed approach and a sensitivity analysis to validate the jointly optimisation.     

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.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

食品生产质量安全风险预警指标体系的构建

本文以每个食品加工企业为评价单元,从食品质量监管的角度出发,基于监管要素的实施,综合选取监管计划落实率、日常巡查整改项数、实物质量合格率、企业历史违规情况、许可审查整改项数、食品安全事件、企业规模、食品产业关联度8个风险因素构建了食品生产质量安全风险预警指标体系。     

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.     

Optimal investment and lot-sizing policies for improved productivity and quality

Productivity and quality are an integrated component of the operational strategy of any firm. An increase in productivity implicitly assumes an improvement in quality. The concept of dynamic process quality control and smaller lot-size production have been employed to eliminate defective items, to reduce the cycle time of a product and to improve quality and productivity. We present a mathematical model to establish the relationship between various parameters of productivity and quality. In addition, the proposed model is used to determine the optimal levels of productivity and quality parameters such as batch sizes, and investment in set-up and process control operations. The basic criterion considered for optimizing the level of such parameters is the minimization of total system cost. The proposed model relates productivity and quality to set-up reduction, queueing of batches, batch sizes, and drift rate reduction. We conclude with an example problem to illustrate the behaviour and application of the model.     

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.     

Optimal economic production quantity policy for a parallel system with repair,rework, free-repair warranty and maintenance

Hot standby redundancy maintains the working order of a system, repairs offer restoration in case of failure, and preventive maintenance (PM) prevents trouble. Warranties provide assurance to customers, and a superior warranty signifies higher product quality. The running costs of redundancy, maintenance and warranties influence decisions during product manufacture. Therefore, this paper presents an economic production quantity (EPQ) model for a parallel system with maintenance, production, and free-repair warranty (FRW) programmes. The production system begins with a basic unit and produces conforming items. PM is performed after the production run period and is classified as imperfect or perfect. If the basic unit fails, it is repaired and returned to operation after perfect PM; the spare unit is online only during the repair time of the basic unit. The spare will produce some number of defective goods, which are reworked in the same inventory cycle. The hot spare is minimally repaired if it fails in its standby or online mode. In this study, an inferior item is defined as one that satisfies specifications on inspection and is usable but is likely to incur postsale servicing costs when sold under an FRW. The total cost of this EPQ model includes setup, holding, PM, restoration, minimal repair, and warranty costs. The optimal production runtime is determined by minimising the total cost. Several cases are discussed in this paper, and the proposed model is illustrated using a numerical example and sensitivity.     

Optimum production lot size model for a system with deteriorating inventory

A production lot size model has been developed for an inventory system with deteriorating items. Both the varying and constant rate of deterioration have been included in the analysis. For the case of a varying rate, it seems impossible to obtain a simple expression for the production lot size, so a numerical method has been suggested. For the constant rate of deterioration case, an approximate expression has been derived for the production lot size. Finally, a numerical example is solved to show the impact of deterioration.     

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 optimisation of maintenance and production policies considering random demand and variable production rate

This paper deals with a randomly failing manufacturing system M1 which has to satisfy a random demand during a finite horizon given a required service level. To help meet this demand, subcontracting is used through another production system M2. M1 operates with a variable production rate and its failure rate depends on both time and the production rate. In these conditions, as a first step, we establish a preliminary production plan corresponding to a given service level. In a second stage, we integrate the effect of the machine degradation introducing a unitary degradation cost. The optimal production plan is then obtained by minimising the sum of the production, the inventory and the degradation costs. In the final stage, we propose another optimal plan combined with a preventive maintenance policy aiming at reducing the machine degradation while minimising the total cost including the production, inventory and maintenance costs.     

An efficient algorithm for maximizing the expected profit from a serial production line with inspection stations and rework

In this paper, an unreliable serial production line in which nonconforming items are sent back for rework is studied. The line consists of existing machines and optional quality control stations (QCSs). The designer of such a production line needs to decide where to install the QCSs along the line and to determine the production rate, so as to maximize the expected operational profit rate obtained at a steady state. An efficient algorithm for solving this problem is presented; several extensions of the problem are discussed. An extensive simulation study proves the applicability of the model in realistic settings and is used to derive some insights about the nature of optimal solutions.     

Integrated production maintenance and quality model for imperfect processes

In this paper, we develop an integrated model for the joint optimization of the economic production quantity, the economic design of x¯-control chart, and the optimal maintenance level. This is done for a deteriorating process where the in-control period follows a general probability distribution with increasing hazard rate. In the proposed model, Preventive Maintenance (PM) activities reduce the shift rate to the out-of-control state proportional to the PM level. Compared to the case with no PM, the extra cost of maintenance results in lower quality control cost which may lead to lower overall expected cost. These issues are illustrated using an example of a Weibull shock model with an increasing hazard rate.     

Production and quality control policies for deteriorating manufacturing system

In this paper, a novel model for a deteriorating manufacturing system is analysed, considering repairs and overhauls of random durations. The machine manufactures one product and the model is further complicated because the quality of the parts’ produced deteriorates according to the wear of the machine and human interventions. When a breakdown occurs, either a repair or an overhaul is performed. The machine is restored to as-good-as-new conditions if the overhaul is selected, and conversely, its condition deteriorates following repairs. Multiple operational states are considered to define an ageing process. The decision variables of the model are the production rate and the repair/overhaul switching strategy. This paper provides new insights to this research area by considering the simultaneous production and repair/overhaul control policy under the effect of deteriorations. The optimal decision policy minimises the total incurred cost comprising the inventory, backlog, repair and overhaul costs over an infinite planning horizon. Our paper differs from other research projects in its consideration of the machine’s history, defined by the number of repairs and multiple operational states. A numerical example is given to illustrate the proposed approach and a sensitivity analysis has been conducted to confirm the structure of the obtained control policies.     

Optimal locations of on-line and off-line rework stations in a serial production system

The production rate and product quality are two vital concerns for any manufacturing industry. Number of defective items reduces production rate and increases unit production cost. Moreover, if nonconforming items reach to the customers then manufacturer’s goodwill may drastically go down. Thus, quality inspection is treated as an inherent part of manufacturing. In this research, an N-stage serial production line with an inspection station at the end of it is considered to make decisions concerning this issue. On detecting a defective item at the end of the line it is scrapped or repaired at regular workstation or is sent to an off-line rework station for repair. Assuming each workstation produces a single type of defect a unit cost function is developed for alternative decisions on each type of defect. In order to minimise the unit cost of production and determine an appropriate decision for individual defect types, a fractional mixed integer nonlinear programming is formulated. After transformation to a mixed integer linear programming problem it is solved optimally. A small problem from garments industry is described in detail to show the solution procedure with a branch and bound method. Empirical tests with up to 40 workstations are permed to show the efficiency of the solution process.     

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.     

A consignment stock coordination scheme for the production,remanufacturing and waste disposal problem

This paper extends the model of a production, remanufacturing and waste disposal system by adding a buyer (retailer) to the vendor’s system to form a two-level forward/reverse supply chain. The vendor and the buyer are assumed to operate according to a consignment stock policy. A mathematical model is developed for the cases when the production and remanufacturing batches are of different and equal sizes. The model also accounts for transportation, inspection and sorting costs. Numerical examples are provided and results are discussed. The results show that the collection rate of used items and the repairable rate have a significant impact on the total cost of the system and the batch sizes. It was suggested that it may not be possible to operate a system like the one described in the paper at its maximum environmental edge without receiving some incentives or tax brackets. Another possibility is for the system to undergo a continuous improvement process to reduce its operational costs, which may require additional investment.