考虑不完美检测的两阶段点检与备件订购策略联合优化

针对设备维修与备件管理相互影响与制约的问题, 在基于延迟时间理论的基础上, 提出了两阶段点检与备件订购策略联合优化。点检是不完美的, 当点检识别设备的缺陷状态时, 进行预防更新; 设备故障时, 进行故障更新。结合设备更新时备件的状态, 采用更新报酬理论建立了以第一阶段点检时间、第二阶段点检周期和备件订购时间为决策变量, 以最小化单位时间期望成本为目标的模型。最后, 通过人工蜂群算法对模型求解, 并在数值分析中将两阶段点检策略与定期点检策略进行比较, 结果表明:两阶段点检策略始终优于定期点检策略, 验证了所建模型的有效性。     

Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures

In this paper the joint maintenance and spare parts ordering problem for more than one identical operating items is studied. The operating items may suffer two types of silent failures: a minor failure, which results in item malfunctioning, and a major failure, which renders the item completely out-of-function. Inspections are periodically held to detect any failures and the inspected items are preventively maintained, repaired or replaced according to their condition. Two ordering policies are investigated to supply the necessary spare parts: a periodic review and a continuous review policy. The expected total maintenance and inventory cost per time unit is derived and the proposed models are optimized for real case data. In addition, the sensitivity of the proposed models is studied through numerical examples and the effect of some key problem characteristics on the optimal decisions is discussed.     

Optimal control of an inventory-production system with state-dependent random yield

In this paper we study a single stage, periodic-review inventory problem for a single item with stochastic demand. The inventory manager determines order sizes according to an order-up-to logic and observes a random yield due to quality problems in the production. We distinguish between two different states of the production process combined with different probabilities to produce a defective unit. In order to improve the production process, periodic inspections are conducted and in case of a failure the machine is repaired. Approximations are developed to evaluate the average cost for a given order-up-to level and a given inspection interval and we illustrate the existence of optimal policy parameters. The approximations are tested in a simulation study and reveal an excellent performance as they lead to near optimal policy parameters. Moreover, we decompose the problem and test different methods to compute the policy parameters either sequentially or separately. Our results show that a joint optimization of the inventory and maintenance policy leads to a better system performance and reduced costs.     

考虑非周期检测的视情维修与备件订购联合策略优化

针对单部件系统/关键部件提出视情维修与备件订购联合策略,其中系统退化服从两阶段延迟时间过程且采用非周期检测策略,退化初期以检测间隔T₁检查系统状态,而在第一次识别缺陷状态时,缩短检测周期为T₂、订购备件且进行不完美维修;若系统在随后的退化中被识别处于缺陷状态,执行不完美维修直至超过阈值次数N_max并采取预防性更换,但若在检测周期内发生故障则进行更换。根据系统状态和备件状态分析各种可能更新事件及相应的联合决策,利用更新报酬理论构建最小化单位时间内期望成本的目标函数,优化T₁,T₂, N_max。与对比模型策略相比,算例结果表明所提出的联合策略能有效降低单位时间内的期望成本。     

智能电表最优更换及备件库存联合决策

智能电表是智能电网运行的关键部件,提高其可靠性和可用度对保证电力的持续不间断供应和准确电能测量至关重要。充足的智能电表库存是其换装与维修的基本保障。本文基于智能电表的故障特性和换装需求分析,建立了智能电表的最优更换与备件库存联合决策模型,并给出了优化方法,以求得可以使系统长期平均运营成本最小的最优更换与备件库存策略。     

Machine reliability and preventive maintenance planning for cellular manufacturing systems

The paper proposes a preventive maintenance (PM) planning model for the performance improvement of cellular manufacturing systems (CMS) in terms of machine reliability, and resource utilization. In a CMS, parts are processed by a group of interdependent machines, where machine reliability plays an important role in the performance improvement of the cell. Assuming that machine failure times follow a Weibull distribution, the proposed model determines a PM interval and a schedule for performing PM actions on each machine in the cell by minimizing the total maintenance cost and the overall probability of machine failures. The model uses a combined cost and reliability based approach, and optimizes maintenance costs by administering a group maintenance policy subject to a desirable machine reliability threshold. The study also proposes a CMS design model that integrates the above PM concepts into the design process. Illustrative examples are presented to demonstrate the applicability of the proposed approach.     

Failure replacement and preventive maintenance spare parts ordering policy

This paper addresses inventory policy for spare parts, when demand for the spare parts arises due to regularly scheduled preventive maintenance, as well as random failure of units in service. A stochastic dynamic programming model is used to characterize an ordering policy which addresses both sources of demand in a unified manner. The optimal policy has the form (s(k),S(k)), where k is the number of periods until the next scheduled preventive maintenance operation. The nature of the (s(k),S(k)) policy is characterized through numeric evaluation. The efficiency of the optimal policy is evaluated, relative to a simpler policy which addresses the failure replacement and preventive maintenance demands with separate ordering policies.     

A number-dependent replacement policy for a system with continuous preventive maintenance and random lead times

This paper considers a number-dependent replacement policy for a system with two failure types that is replaced at the nth type I (minor) failure or the first type II (catastrophic) failure, whichever occurs first. Repair or replacement times are instantaneous but spare/replacement unit delivery lead times are random. Type I failures are repaired at zero cost since preventive maintenance is performed continuously. Type II failures, however, require costly system replacement. A model is developed for the average cost per unit time based on the stochastic behavior of the system and replacement, storage, and downtime costs. The cost-minimizing policy is derived and discussed. We show that the optimal number of type I failures triggering replacement is unique under certain conditions. A numerical example is presented and a sensitivity analysis is performed.     

提前期不确定条件下的预防性维修备件存储模型研究

在考虑预防性维修周期和提前期不确定的条件下,分别研究备件存储与其相关的维修费用、缺货费用、库存费用以及订购费用等四种费用之间的关系,明确了备件存储量对各项费用的影响.以各项费用总和最小化为目标,构建了提前期不确定条件下的预防性维修备件存储模型.通过备件存储模型的构建,对备件存储过程中的各项成本进行分析,以期对备件库存策略的确定给出一种解决方案.     

Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes

We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are expensive, ready–for–use spare parts are kept in stock to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival. Each stockpoint faces demands from multiple demand classes. We are interested in the optimal lateral transshipment policy. There are three ways in which a demand can by satisfied: from own stock, via a lateral transshipment, or via an emergency procedure. Using stochastic dynamic programming, we characterize and prove the structure of the optimal policy, that is, the policy for satisfying the demands which minimizes the average operating costs of the system. This optimal policy is a threshold type policy, with state-dependent thresholds at each stockpoint for every demand class. We show a partial ordering in these thresholds in the demand classes. In addition, we derive conditions under which the so-called hold back and complete pooling policies are optimal, two policies that are often assumed in the literature. Furthermore, we study several model extensions which fit in the same modeling framework.     

Optimization of component reliability in the design phase of capital goods

We introduce a quantitative model to support the decision on the reliability level of a critical component during its design. We consider an OEM who is responsible for the availability of its systems in the field through service contracts. Upon a failure of a critical part in a system during the exploitation phase, the failed part is replaced by a ready-for-use part from a spare parts inventory. In an out-of-stock situation, a costly emergency procedure is applied. The reliability levels and spare parts inventory levels of the critical components are the two main factors that determine the downtime and corresponding costs of the systems. These two levels are decision variables in our model. We formulate the portions of Life Cycle Costs (LCC) which are affected by a component’s reliability and its spare parts inventory level. These costs consist of design costs, production costs, and maintenance and downtime costs in the exploitation phase. We conduct exact analysis and provide an efficient optimization algorithm. We provide managerial insights through a numerical experiment which is based on real-life data.     

Multi-item spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of two-location inventory systems for repairable spare parts, used for expensive technical systems with high target availability levels. Lateral and emergency shipments occur in response to stockouts. A continuous review basestock policy is assumed for the inventory control of the spare parts. The objective is to minimize the total costs for inventory holding, lateral transshipments and emergency shipments subject to a target level for the average waiting time per demanded part at each of the two locations. A solution procedure based on Lagrangian relaxation is developed to obtain both a lower bound and an upper bound on the optimal total cost. The upper bound follows from a heuristic solution. An extensive numerical experiment shows an average gap of only 0.31% between the lower and upper bounds. The experiment also gives insights into the relative improvement achieved by applying lateral transshipments and or the system approach. We also apply the proposed model to actual data from an air carrier company.     

Intermediate buffer analysis for a production system

In this paper, a production system consisting of two serial machines and an intermediate buffer is studied. A shortage cost is incurred when the upstream machine is down and the buffer is exhausted. The practical example for this type of system can be an automated work center or an automobile general assembly.Researches on a similar two-machine system have been done in some articles where maintenance and an intermediate buffer are considered, but the spare parts are not involved. Nevertheless, spare parts are essential for maintenance implementation, and there is interaction between the buffer inventory and the spare parts due to maintenance activity. This paper is aimed to investigate three types of cost related to the intermediate buffer inventory, and obtain their expectations as functions of several decision parameters on maintenance, buffer, and spare parts during a renewal cycle, by using mathematical analysis. The proposed method can be an important basis for further study of system cost calculation and decision making optimization.     

A multi-objective approach for solving a replacement policy problem for equipment subject to imperfect repairs

This paper proposes a multi-objective approach to model a replacement policy problem applicable to equipment with a predetermined period of use (a planning horizon), which may undergo critical and non-critical failures. Corrective replacements and imperfect repairs are taken to restore the system to operation respectively when critical and non-critical failures occur. Generalized Renewal Process (GRP) is used to model imperfect repairs. The proposed model supports decisions on preventive replacement intervals and the number of spare parts purchased at the beginning of the planning horizon. A Multi-Objective Genetic Algorithm (MOGA) coupled with discrete event simulation (DES) is proposed to provide a set of solutions (Pareto-optimum set) committed to the different objectives of a maintenance manager in the face of a replacement policy problem, that is, maintenance cost, rate of occurrence of failures, unavailability, and investment on spare parts. The proposed MOGA is validated by an application example against the results obtained via the exhaustive approach. Moreover, examples are presented to evaluate the behavior of objective functions on Pareto set (trade-off analysis) and the impact of the repair effectiveness on the decision making.     

利用故障数据和估计的检查数据建立维修优化模型

利用时间延迟概念,根据故障记录数据和估计的检查数据建立了预防维修模型.通过对故障记录数据统计分析,提出了模型的假定条件.采用最大似然估计法,估计参数,包括缺陷发生率、不完全检查概率和时间延迟分布.建立了有关预防维修间隔期和总停机时间之间关系的检查模型,并根据估计参数和检查模型,计算最佳维修间隔期.     

Scheduling policies for a repair shop problem

In this paper, we analyze a repair shop serving several fleets of machines that fail from time to time. To reduce downtime costs, a continuous-review spare machine inventory is kept for each fleet. A spare machine, if available on stock, is installed instantaneously in place of a broken machine. When a repaired machine is returned from the repair shop, it is placed in inventory for future use if the fleet has the required number of machines operating. Since the repair shop is shared by different fleets, choosing which type of broken machine to repair is crucial to minimize downtime and holding costs. The optimal policy of this problem is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost and base-stock level for each spare machine inventory. As an alternative, we propose the dynamic Myopic(R) policy, which is easy to implement, yielding costs very close to the optimal. Most of the time it outperforms the static first-come-first-served, and preemptive-resume priority policies. Additionally, via our numerical study, we demonstrate that repair shop pooling is better than reserving a repair shop for each fleet.     

An improved stochastic programming model for supply chain planning of MRO spare parts

The maintenance, repair and operation (MRO) spare parts that are vital to machine operations are playing an increasingly important role in manufacturing enterprises. MRO spare parts supply chain management planning must be coordinated to ensure spare part availability while keeping the total cost to a minimum. Due to the specificity of MRO spare parts, randomness and uncertainties in production and storage should be quantified to formulate the problem in a mathematical model. Given these considerations, this paper proposes an improved stochastic programming model for the supply chain planning of MRO spare parts. In our stochastic programming model, the following improvements are made: First, we quantify the uncertain production time capacity as a random variable with a probability distribution. Second, the upper bound of the storage cost is modeled as a multi-choice variable in the constraint. To derive the equivalent deterministic model, the Lagrange interpolating polynomial approach is used. The results of the numerical examples validate the feasibility and efficiency of the proposed model. Finally, the model is tested in the supply chain planning of continuous caster (CC) bearings.     

Age-dependent production planning and maintenance strategies in unreliable manufacturing systems with lost sale

In this paper, we formulate an analytical model for the joint determination of an optimal age-dependent buffer inventory and preventive maintenance policy in a production environment that is subject to random machine breakdowns. Traditional preventive maintenance policies, such as age and periodic replacements, are usually studied based on simplified and non-realistic assumptions, as well as on the expected costs criterion. Finished goods inventories and the age-dependent likelihood of machine breakdowns are usually not considered. As a result, these policies could significantly extend beyond the anticipated financial incomes of the system, and lead to crises. In order to solve this problem, a more realistic analysis model is proposed in this paper to consider the effects of both preventive maintenance policies and machine age on optimal safety stock levels. Hence, a unified framework is developed, allowing production and preventive maintenance to be jointly considered. We use an age-dependent optimization model based on the minimization of an overall cost function, including inventory holdings, lost sales, preventive and corrective maintenance costs. We provide optimality conditions for the manufacturing systems considered, and use numerical methods to obtain an optimal preventive maintenance policy and the relevant age-dependent threshold level production policy. In this work, this policy is called the multiple threshold levels hedging point policy. We include numerical examples and sensitivity analyses to illustrate the importance and the effectiveness of the proposed methodology. Compared with other available optimal production and maintenance policies, the numerical solution obtained shows that the proposed age-dependent optimal production and maintenance policies significantly reduce the overall cost incurred.     

A dynamic joint replenishment policy with auto-correlated demand

We consider a joint replenishment problem where the product demands are auto-correlated but independent of each other. A dynamic periodic review policy is developed, and its parameters are determined by a heuristic which aims at minimizing the total inventory cost, which includes the holding cost, the set up cost and the shortage cost. The heuristic updates the review interval and the target inventory level of every product at each review point based on the current inventory status and the past demand data. A simulation model is developed to compare the performance of this proposed policy with an existing periodic review policy. The results show that the proposed policy has consistently achieved significant saving in all the different experimental scenarios.     

马尔科夫决策过程在R/M系统库存控制中的应用

给出了有限阶段R/M(再制造/制造)系统集成库存模式,利用马尔科夫决策理论对库存容量有限、具有随机再制造零部件的R/M系统集成库存进行研究,考虑再制造零部件单位成本、新零部件可变费用和固定费用、超过库存容量的那部分再制造零部件的附加费用及有缺货赔偿的情况,给出了马尔科夫决策过程模型,得到了随机最优控制策略.