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.     

备件品种选择的rough方法

分析了影响备件储备品种选择的重要性、可更换性、消耗性、获得难度和经济性等五个因素,利用粗集方法,按条件属性的不同顺序对备件储备品种的选择规则进行了约简,根据工程实践,从中选择一个更加合理的约简结果作为最终的备件储备品种的选择规则,并得到了相应的决策算法.该方法能够克服各影响因素在备件品种选择过程中的影响不足或影响过强等弱点,具有简单、操作方便等特点,为导弹武器装备备件保障部门选择导弹备件品种提供了一种新的理论依据.     

On the Robustness of ‘Insurance Type’ Spares Provisioning Strategies

‘Insurance type’ spares are spares for unique parts which are essential to the operation of the equipment in which they serve, and which have an appreciable probability of not needing replacement during the lifetime of the equipment. They require a stocking strategy which is dependent on time and the actual occurrence of failures. The values of parameters in even the simplest of models of the dynamic spares stocking decision problem are usually known with great uncertainty, if at all. For one such model the sensitivity of (near-)optimal strategies to variations in the parameter values is investigated.     

Modeling sourcing strategies to mitigate part obsolescence

Part obsolescence is a common problem across industries, from avionics and military sectors to most original equipment manufacturers serving industrial markets. When a part supplier announces that a part will become obsolete, the OEM can choose from a number of sourcing options. In practice, the three most commonly adopted mitigation strategies are: (1) a lifetime, or life-of-type (LOT), buy from the original supplier; (2) part substitution, which finds a suitable alternative; and (3) line redesign, which modifies the production line to accommodate a new part. We first develop a framework incorporating fixed cost, variable cost, leadtime, demand uncertainty and the discount rate to directly compare and characterize these three sourcing strategies in a static context. We next formulate an integrated sourcing approach that starts with a bridge buy and may continue with part substitution or line redesign when the originals parts are depleted. Through numerical studies, we identify the joint impact of the problem parameters on the static and integrated sourcing strategies and the optimal choice among them. While the integrated sourcing approach outperforms the static ones in many cases it is not a dominant strategy.     

Optimization models for critical spare parts inventories—a reliability approach

In industries characterized by heavy utilization of equipment and machinery, such as mining, oil & gas, utilities, transportation, adequate stockholding of critical spare parts becomes essential. Insufficient stocks affect overall performance of physical assets, as lack of spares may result in gross penalties, lower availability or increased operational risks. On the other hand, oversized inventories lead to inefficient use of capital and may imply severe expenditures. This paper presents various approaches for the determination of the optimal stock size, when the stock is composed of (i) non-repairable or (ii) repairable parts. The paper is focused on spares for relatively expensive, highly reliable components, rather than on fast-moving spare parts. Optimization criteria considered are minimization of costs, maximization of equipment availability, and the achievement of a desired stock reliability (probability that a spare part request will not be rejected because of the lack of spares in stock). For stock reliability, instantaneous and interval reliability calculations are considered. In addition, models directed to the estimation of the remaining life of a given stock of spare parts (at a certain stock reliability level) are introduced. The paper describes several models subject to practical industrial application, and presents case studies from utilities and mining to illustrate their use.     

Consolidating Maintenance Spares

The inventory of spare parts that a firm holds depends on the number of working parts and age of the equipment to be serviced, the expected failure rate associated with each working part, and the acceptable level of service. We model the problem of consolidation of spare parts to reduce overall inventory as an integer program with a nonlinear objective function. A linear reformulation of this model is obtained that helps solve some practical instances. A more compact implicit formulation is developed and solved using a specialized branch-and-price technique. We also demonstrate how this specialized branch-and-price technique is modified to devise a very effective heuristic procedure with a prespecifiable guarantee of quality of solution produced. This provides a practical and efficient methodology for maintenance spare consolidation.     

A multi-objective approach to simultaneous determination of spare part numbers and preventive replacement times

Different models have been proposed in the field of preventive maintenance planning for finding optimal age replacement policies. While previous studies have focused mainly on classical cost objectives, this paper presents a novel multi-objective model for preventive replacement of a part over a planning horizon. The proposed model considers different objectives and practical issues, such as corrective replacement and its consequences, residual lifetime objective, and kind of productivity index. Also, the model determines number of spare parts, required for replacement with the defected part, to be provided at the beginning of the planning horizon. The multi-objective model is applicable for machines or equipments which are repaired through replacing their defected part with new spare part.For solving the multi-objective model, regarding to ability of ε-constraint method to generate different pareto-optimal solutions, a procedure is developed based on this method. The procedure shows how the ε-constraint method can be used for finding preferred solution in situations where there is no access to decision maker. The model and solution procedure are illustrated by a numerical example.     

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.     

Speed-up Benders decomposition using maximum density cut (MDC) generation

The classical implementation of Benders decomposition in some cases results in low density Benders cuts. Covering Cut Bundle (CCB) generation addresses this issue with a novel way generating a bundle of cuts which could cover more decision variables of the Benders master problem than the classical Benders cut. Our motivation to improve further CCB generation led to a new cut generation strategy. This strategy is referred to as the Maximum Density Cut (MDC) generation strategy. MDC is based on the observation that in some cases CCB generation is computational expensive to cover all decision variables of the master problem than to cover part of them. Thus MDC strategy addresses this issue by generating the cut that involves the rest of the decision variables of the master problem which are not covered in the Benders cut and/or in the CCB. MDC strategy can be applied as a complimentary step to the CCB generation as well as a standalone strategy. In this work the approach is applied to two case studies: the scheduling of crude oil and the scheduling of multi-product, multi-purpose batch plants. In both cases, MDC strategy significant decreases the number of iterations of the Benders decomposition algorithm, leading to improved CPU solution times.     

A new partial pooling structure for spare parts networks

Motivated by real-life spare parts networks, we introduce a new spare parts inventory model with lateral transshipment. We consider a multi-item, multi-location, single-echelon system with base stock control and aggregate mean waiting time constraints. The local warehouses are divided into two types: main and regular local warehouses. Lateral transshipment is allowed from main local warehouses only. A practical advantage of this structure is that only a limited number of local warehouses has to be equipped to provide lateral transshipment. This structure represents a new form of partial pooling, with no pooling (zero main locals) and full pooling (zero regular locals) as special cases. We develop an accurate and fast approximate evaluation method, and exploit this method in a heuristic procedure for the base stock level determination. We show that only a small number of main locals is sufficient to obtain most of the full pooling benefits. We also apply our methods to case data of ASML, an original equipment manufacturer in the semiconductor supplier industry. As a result of our work ASML was able to improve spare parts planning.     

A stochastic model for joint spare parts inventory and planned maintenance optimisation

Spare parts demands are usually generated by the need of maintenance either preventively or at failures. These demands are difficult to predict based on historical data of past spare parts usages, and therefore, the optimal inventory control policy may be also difficult to obtain. However, it is well known that maintenance costs are related to the availability of spare parts and the penalty cost of unavailable spare parts consists of usually the cost of, for example, extended downtime for waiting the spare parts and the emergency expedition cost for acquiring the spare parts. On the other hand, proper planned maintenance intervention can reduce the number of failures and associated costs but its performance also depends on the availability of spare parts. This paper presents the joint optimisation for both the inventory control of the spare parts and the Preventive Maintenance (PM) inspection interval. The decision variables are the order interval, PM interval and order quantity. Because of the random nature of plant failures, stochastic cost models for spare parts inventory and maintenance are derived and an enumeration algorithm with stochastic dynamic programming is employed for finding the joint optimal solutions over a finite time horizon. The delay-time concept developed for inspection modelling is used to construct the probabilities of the number of failures and the number of the defective items identified at a PM epoch, which has not been used in this type of problems before. The inventory model follows a periodic review policy but with the demand governed by the need for spare parts due to maintenance. We demonstrate the developed model using a numerical example.     

The final order problem for repairable spare parts under condemnation

We consider a manufacturer of complex machines that offers service contracts to her customers, committing herself to repair failed spare parts throughout a fixed service period. The suppliers of spare parts often discontinue the production of some parts as technology advances and ask the manufacturer to place a final order. We address the problem of determining final orders for such spare parts. The parts that we consider are repairable, but they are subject to the risk of condemnation. We build a transient Markovian model to represent the problem for a repairable spare part with a certain repair probability and repair lead time and we present some approximations that allow for further real-life characteristics to be included. Furthermore, an approximate model that can be computed more efficiently is presented, and the sensitivity of the results obtained with respect to the problem parameters is discussed, helping us develop several managerial insights.     

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.     

Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.     

基于设备状态监控的单级备件库存系统补货策略研究

本文研究一个周期性订货的多设备同备件库存系统,将备件库存策略与设备状态监控相结合,讨论了存在设备状态监控情形下的备件库存策略。针对设备状态自然腐蚀过程和人 为修复过程的复合过程,运用一个新的马尔科夫概率转移矩阵对设备需求概率进行刻画,并在此基础上给出静态订货模型和状态监控下的动态订货模型的最优订货策略。通过对比以上两种订货策略优缺点,本文提出一种新的启发式订货策略: 基于关键状态的订货策略模型。该策略可以有效降低对全部设备实行动态监控的信息成本,且成本节省优于静态订货策略,对于企业的现实问题有着较好的指导意义。     

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。     

Using commonality as backup safety stock

It is well known that replacing several parts by a single common part can reduce required safety stock levels due to the benefits of risk pooling. It is not clear, however, if this reduces cost when the common part is more expensive than the parts it would replace. Recent analysis has shown that even when the common part is more expensive, it is often still worthwhile to employ in the single-period case. However, this is usually not true in the multiple-period case. This paper will consider the possibility of using both cheaper unique parts and a more expensive common part. Initial demand is met with the unique parts. The common part is used only as backup, when one or more of the unique parts stocks out. A multiple-period (or infinite-horizon) model is developed that considers purchasing, holding, and shortage costs. Results will show that the strategy of using commonality as backup (CAB) dominates the strategies of no commonality (NC) or pure commonality (PC), and may still be worthwhile even if the common part is significantly more expensive than the unique parts.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

一种基于随机森林的备件预测模型研究

对舰船零部件发生故障问题进行故障诊断,并对故障诊断结果进行分析,建立舰船零部件备件需求模型,给出零部件之间的发生故障概率的关系与备件需求特征;将随机森林回归原理应用到了舰船零部件的备件需求预测领域,构建了基于随机森林的预测模型,以及预测结果准确率的评价。用诊断结果数据对算法进行验证,结果表明,将随机森林算法运用到舰船的备件预测领域可以为舰船装备在一次海上任务期内备件配置问题提供参考价值。     

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.