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.     

Designing a supply chain network for deteriorating inventory under preservation effort and trade credits

When designing a perishable goods supply chain network under trade credit arrangements, distribution companies must contend with deteriorating inventory and product preservation efforts to maximise profits. Key decisions include locating distribution centres (DCs), assigning retail stores to DCs, joint replenishment cycle time and investing in preservation technology. This paper addresses these factors from the position that as preservation effort increases, preservation technology cost increases and deterioration rate decreases. An algorithm based on piecewise nonlinear optimisation is provided for solving supply chain network design problems efficiently. In contrast to other studies that have used the approximation approach, the proposed approach solves the original problem accurately and efficiently. Numerical studies are conducted to demonstrate the solutions procedures and determine the effects of the parameters on decisions and profits. The results of this study and the proposed modelling approach are useful references for managerial decisions in designing a supply chain network the context of trade credit and inventory deterioration.     

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.     

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.     

Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.     

Preventive maintenance and optimal buffer inventory for products sold with warranty in an imperfect production system

This paper deals with an imperfect production system with allowable shortages due to regular preventive maintenance for products sold with free minimal repair warranty. Preventive maintenance is an essential factor of the just-in-time structure that results in a shutdown of the production process for a certain period of time. During such an interruption, a buffer stock is needed to adjust the market demand. The study includes the possibility of imperfect production and determines the optimum buffer level and production run time by trading off the holding cost, shortage cost, rework cost, repair cost for warranty, labour/energy costs, material cost and cost for maintenance so that the cost per unit product is minimised.     

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,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.     

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.     

Optimal process mean and quality improvement in a supply chain model with two-part trade credit based on Taguchi loss function

The two-part trade credit policy is developed to accelerate cash inflow that can avoid bad debt risk in the earlier economic order quantity (EOQ) models allowing only one period of time for delay in payment. Taguchi loss function has proved to be a more realistic function for fitting the actual quality loss cost in economic product quantity (EPQ) model. To minimise quality loss, optimal process mean setting shifts process mean to balance the cost outside the specification limits, quality improvement applies investment to reduce process variation. Supply chain integration has been proved that it can be used to minimise the entire cost more effectively than independent EOQ or EPQ models. This paper improves the earlier studies by incorporating the above research topics that have not been simultaneously discussed before, develops a supply chain model based on the Taguchi loss function, which combines the trade strategy from the retailer’s perspective and the quality adjustments from the supplier’s perspective to maximise total supply chain profit. We find that the trade credit terms definitely affect suppliers and retailers’ optimal decisions, and numerical examples can provide decision references for supply chain managers to set a trade credit policy and control quality.     

Optimized production planning model for a multi-plant cultivation system under uncertainty

An inexact multi-constraint programming model under uncertainty was developed by incorporating a production plan algorithm into the crop production optimization framework under the multi-plant collaborative cultivation system. In the production plan, orders from the customers are assigned to a suitable plant under the constraints of plant capabilities and uncertainty parameters to maximize profit and achieve customer satisfaction. The developed model and solution method were applied to a case study of a multi-plant collaborative cultivation system to verify its applicability. As determined in the case analysis involving different orders from customers, the period of plant production planning and the interval between orders can significantly affect system benefits. Through the analysis of uncertain parameters, reliable and practical decisions can be generated using the suggested model of a multi-plant collaborative cultivation system.     

A production quantity model for imperfect quality items with shortage and screening constraint

This study develops an economic production quantity (EPQ) model and solution procedure for imperfect items with shortage and screening constraint. The Renewal Reward Theorem (RRT) is applied to formulate the exact expected total profit per unit time. We have shown the robustness of our model using time interval as decision variable rather than the traditional order size and backorder quantity. A solution procedure is provided to derive the optimal policy. Special cases of the EOQ/EPQ models can be obtained by taking the parameter limiting values. Numerical examples and sensitivity analysis are presented to verify our results.     

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.     

A spread-sheet model for efficient production and scheduling of a manufacturing line/cell

In this paper we develop an efficient spread-sheet production planning/scheduling model for a resource-constraint production line or a manufacturing cell that produces several products but one at a time with significant changeover time and changeover cost. There are also management and physical constraints related to the operating hours, production capacity and amount of inventory allowed. The production line/cell supplies several products to customers who pull the products according to their own operating policy (working hours) that may be different from manufacture's operating hours. We also show several real-world applications and highlight the benefits and merits of the model.     

A sensitivity analysis of an integrated model for joint determination of economic design of $\overline{x}$‐control charts,economic production quantity and production run length for a deteriorating production system

This study presents an integrated model for the joint economic design of ‐control charts and maintenance schedules and, simultaneously, determines the economic production quantity and production run length for a deteriorating production system. The operating state of the production process is classified as either in control or out of control. In the latter state, the process produces some defective items. An ‐control chart is used to monitor the process mean. Both uniform and non‐uniform inspection schemes are adopted. Inspection and maintenance are performed simultaneously. Replacement cost is assumed to be very high. The process failure mechanism is assumed to follow a general probability distribution with an increasing failure rate. The concept of a truncated production cycle is introduced. The production cycle begins when a new component is installed and ends with a repair after the detection of a failure or after a specified number of inspection intervals, , whichever occurs first. The effects of preventive maintenance on quality control are discussed. Numerical examples are provided to evaluate the performance of the model. Sensitivity analyses are conducted to study the effects of various model parameters. Copyright © 2002 John Wiley & Sons, Ltd.     

A variable neighbourhood search for integrated production and preventive maintenance planning in multi-state systems

This paper presents a variable neighbourhood search (VNS) to the integrated production and maintenance planning problem in multi-state systems. VNS is one of the most recent meta-heuristics used for problem solving in which a systematic change of neighbourhood within a local search is carried out. In the studied problem, production and maintenance decisions are co-ordinated, so that the total expected cost is minimised. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimise the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-state components. The formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. The proposed VNS deals with the preventive maintenance selection task. Results on test instances show that the VNS method provides a competitive solution quality at economically computational expense in comparison with genetic algorithms.     

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.     

Robust production control policy for a multiple machines and multiple product-types manufacturing system with inventory inaccuracy

Inventory inaccuracy often exists in manufacturing systems, which has great negative impact on the performance of production control, e.g. very high work-in-process holding cost or backlog penalty. To hedge against inventory inaccuracy, the robust production control problems will be investigated for a multiple machines and multiple product-types manufacturing system with uncertain production capacity. The objective of our problem is to minimise the average production cost. To solve this problem, a robust production control policy is developed, which is insensitive to the inventory record errors, and whose robustness is better than the traditional hedging point policy for optimal production control. Finally, numerical experiments are conducted to examine the performance of the proposed robust production control policy against inventory inaccuracy. Based on the experimental results, the conditions of applying the proposed policy are also obtained.     

空间绳系系统自由展开建模与仿真

运用Hamilton原理建立了空间绳系展开动力学模型,研究绳系展开过程中绕线盘出线、系绳振动以及末端质量的运动规律,并利用中心差分法、四阶Runge-Kutta和预估校正法等数值方法对绳系的自由展开过程进行仿真,仿真结果显示该模型可以较精确描述绳系系统在展开过程中的复杂非线性动力学行为,绳系自由展开不能满足稳定展开的要求,仿真数据可以为后续的绳系展开控制提供参考依据.     

A trade-off between productivity and cost for the integrated part quality inspection and preventive maintenance planning under uncertainty

This paper proposes a robust possibilistic and multi-objective mixed-integer linear programming mathematical model to concurrently plan part quality inspection and Preventive Maintenance (PM) activities for a serial multi-stage production system. This system contains the deteriorating stages and faces the uncertainty about estimated cost components and demand amount. The integrated model reaches two significant decisions which are the right time and place for performing the part quality inspection and PM. These decisions are made while the model is to simultaneously optimise the implied system productivity and total cost. To measure the implied system productivity, a new piecewise utility function for the ratio of produced conforming products to input workpieces is developed. A real case study and a numerical example are explored to validate and verify the developed model. The results prove the significance and effectiveness of considering the uncertainty and conflicting practical objectives for the problem.