Optimizing reliability and service parts logistics for a time-varying installed base

Performance based contracting (PBC) emerges as a new after-sales service practice to support the operation and maintenance of capital equipment or systems. Under the PBC framework, the goal of the study is to increase the system operational availability while minimizing the logistics footprint through the design for reliability. We consider the situation where the number of installed systems randomly increases over the planning horizon, resulting in a non-stationary maintenance and repair demand. Renewal equation and Poisson process are used to estimate the aggregate fleet failures. We propose a dynamic stocking policy that adaptively replenishes the inventory to meet the time-varying parts demand. An optimization model is formulated and solved under a multi-phase adaptive inventory control policy. The study provides theoretical insights into the performance-driven service operation in the context of changing system fleet size due to new installations. Trade-offs between reliability design and inventory level are examined and compared in various shipment scenarios. Numerical examples drawn from semiconductor equipment industry are used to demonstrate the applicability and the performance of the proposed method.     

The impact of fleet size on performance-based incentive management

Performance-based contracting (PBC) is envisioned to lower the asset ownership cost while ensuring desired system performance. System availability, widely used as a performance metric in such contracts, is affected by multiple factors such as equipment reliability, spares stock, fleet size, and service capacity. Prior studies have either focussed on ensuring parts availability or advocating the reliability allocation during design. This paper investigates a single echelon repairable inventory model in PBC. We focus on reliability improvement and its interaction with decisions affecting service time, taking into account the operating fleet size. The study shows that component reliability in a repairable inventory system is a function of the operating fleet size and service rate. A principal-agent model is further developed to evaluate the impact of the fleet size on the incentive mechanism design. The numerical study confirms that the fleet size plays a critical role in determining the penalty and cost sharing rates when the number of backorders is used as the negative incentive scheme.     

制造企业成品出入库两级排队协同服务模型

优化企业成品出入库协同服务水平、平衡工作负荷,从而提高企业仓储服务效率、降低物流成本,是现代制造企业亟待解决的一个重要的管理细节问题。针对这个问题,本研究以仓储入库和出库两个排队过程为研究对象,建立出入库等待时间溢出情景下的两级排队协同服务模型,分析了在排队等待时间控制目标下,出入库员工优化配置方案。该模型引入溢出和串联两个协同服务机制,分三种情景即前方与后方服务台都有空闲,前方繁忙与后方空闲,前方空闲(或繁忙)与后方繁忙,建立了各情景下的系统状态转移方程,求解系统状态的概率,并进而推算出反映系统表现的各项指标,如员工使用率,队列长度,等待时间,以及等待时间超过溢出界值的概率。用制造企业成品出入库管理案例进行验证分析,对企业目前采用的M/M/S出入库排队系统与两级排队协同服务系统进行了数值计算对比。结果表明后者能有效提升出入库服务效率,减少出入库排队系统平均等待时间,降低由于入库和出库两个服务过程效率不均衡而产生的企业内部物流成本,是提升企业内部物流协同管理水平的一个重要方法。其应用可以服务于仓储出入库协同管理的信息化与自动化水平的提高。     

Spares provisioning under performance-based logistics contract: profit-centric approach

Performance-based logistics (PBL) is emerging as a preferred logistic support strategy within the public sector, especially the Department of Defence. Under a PBL strategy, the customer buys performance, such as operational availability, mission readiness and operational reliability, instead of contracting for a specified collection of resources defining the underlying support infrastructure. The literature on PBL is still in its infancy and additional research is required to optimize logistic resources such as spare parts, equipment, facilities, labour etc within a PBL context. In this paper, an optimization model is developed for spares provisioning under a multi-item, multi-echelon scenario. The objective of the optimization model is to maximize the profit to the supplier under a PBL contract.     

基于绩效保障模式的可修备件保障系统运营管理策略

基于绩效保障模式,设计了一个由备件仓库和维修车间组成的装备可修部件闭环保障系统,推导了备件库存水平状态的稳态概率分布,计算了可用度等几个保障绩效度量指标,建立了基于可用度约束的保障系统运作优化模型,并通过仿真分析探讨了保障系统运营管理策略问题。     

A study of repairable parts inventory system operating under performance-based contract

Performance-Based Logistics (PBL) is becoming a dominant logistics support strategy, especially in the defense industry. PBL contracts are designed to serve the customer’s key performance measures, while the traditional contracts for after-sales services, such as Fixed-price (FP) and Cost-plus (C+), only provide insurance or incentive. In this research, we develop an inventory model for a repairable parts system operating under a PBL contract. We model the closed-loop inventory system as an M/M/m queue in which component failures are Poisson distributed and the repair times at the service facility are exponential. Our model provides the supplier and the customer increased flexibility in achieving target availability. Analysis of key parameters suggests that to improve the availability of the system with repairable spare parts, the supplier should work to improve the components reliability and efficiency of repair facility, rather than the base stock level, which has minimal impact on system availability.     

Multicriteria decision making on maintenance: Spares and contracts planning

The competitiveness of an industrial system is directly related to decision making in areas of product support logistics, such as the maintenance area. Multicriteria decision making takes into account various aspects associated with competitiveness of the system. This paper presents multicriteria decision models for two maintenance problems: repair contract selection and spares provisioning. In the repair contract problem the model incorporates consequences modelled through a multiattribute utility function. These consequences consist of contract cost and system performance, represented by the system interruption time. Two criteria (risk and cost) are combined through a multiattribute utility function in the spares provisioning decision model. This paper presents the formulation and derivations for both models and the numerical application illustrates the use of models including sensitivity analysis.     

Multicriteria modelling for a repair contract problem based on utility and the ELECTRE I method

Each alternative for a repair contract implies a specific responsetime and related cost. The response time is associated withthe commitment of repair time, based on the contract. A decisionmaker chooses the best alternative taking into account the systemperformance and the cost of the contract. This problem has beenanalysed through a multicriteria decision model. This decisionmodel supports decision makers in the determination of the bestcombination of contracting conditions. The decision model proposedallows the decision maker to quantify the consequences of anaction taking into account two basic criteria: the cost of thecontract and the system performance. Two different decisionmodels have been built to support decision makers. These decisionmodels are based on different multicriteria approaches. Thefirst, reported in a previous paper, is based on the multiattributeutility theory (MAUT). The model presented in this paper isbased on the ELECTRE I method combined with utility functions.The paper presents the main theoretical aspects related to bothapproaches and practical implications related to model building.A numerical application is presented in order to illustratethe use of the decision model.     

A Bayesian approach to service level performance monitoring in supplier,provider relationships

Techniques are presented for monitoring the performance of a delivery service. The techniques were developed from the practical need to support two parties: a virtual retailer that out-sources the home delivery of its goods and the logistics business that provides its courier service. The techniques are relevant to contractual negotiations and performance monitoring. A graphical tool for hypothesis testing is presented as an aid to contract negotiation and a dynamic model is developed to track performance over time for operational management. The approach is based upon the beta-binomial distribution, within a Bayesian decision context.     

Hub location–allocation in intermodal logistic networks

Within the context of intermodal logistics, the design of transportation networks becomes more complex than it is for single mode logistics. In an intermodal network, the respective modes are characterized by the transportation cost structure, modal connectivity, availability of transfer points and service time performance. These characteristics suggest the level of complexity involved in designing intermodal logistics networks. This research develops a mathematical model using the multiple-allocation p-hub median approach. The model encompasses the dynamics of individual modes of transportation through transportation costs, modal connectivity costs, and fixed location costs under service time requirements. A tabu search meta-heuristic is used to solve large size (100 node) problems. The solutions obtained using this meta-heuristic are compared with tight lower bounds developed using a Lagrangian relaxation approach. An experimental study evaluates the performance of the intermodal logistics networks and explores the effects and interactions of several factors on the design of intermodal hub networks subject to service time requirements.     

Designing multi-echelon service parts networks with finite repair capacity

We propose an approach to model and solve the joint problem of facility location, inventory allocation and capacity investment in a two echelon, single-item, service parts supply chain with stochastic demand. The objective of the decision problem is to minimize the total expected costs associated with (1) opening repair facilities, (2) assigning each field service location to an opened facility, (3) determining capacity levels of the opened repair facilities, and (4) optimizing inventory allocation among the locations. Due to the size of the problem, computational efficiency is essential. The accuracy of the approximations and effectiveness of the approach are analyzed with two numerical studies. The approach provides optimal results in 90% of scenarios tested and was within 2% of optimal when it did not.We explore the impact of capacity utilization, inventory availability, and lead times on the performance of the approach. We show that including tactical considerations jointly with strategic network design resulted in additional cost savings from 3% to 12%. Our contribution is the development of a practical model and approach to support the decision making process of joint facility location and multi-echelon inventory optimization.     

Joint optimization of fleet size and maintenance capacity in a fork-join cyclical transportation system

This article presents an asset management-oriented multi-criteria methodology for the joint estimation of a mobile equipment fleet size, and the maintenance capacity to be allocated in a productive system. Using a business-centred life-cycle perspective, we propose an integrated analytical model and evaluate it using global cost rate, availability and throughput as performance indicators. The global cost components include: (i) opportunity costs associated with lost production, (ii) vehicle idle time costs, and (iii) maintenance resources idle time costs. This multi-criteria approach allows a balanced scorecard to be built that identifies the main trade-offs in the system. The methodology uses an improved closed network queueing model approach to describe the production and maintenance areas. We test the proposed methodology using an underground mining operation case study. The decision variables are the size of a load-haul-dump fleet and specialized maintenance crew levels. Our model achieves savings of 20.6% in global cost terms with respect to a benchmark case. We also optimize the system to achieve desired targets of vehicle availability and system throughput (based on system utilization). The results show increments of 7.1% in vehicle availability and 13.5% in system throughput with respect to baseline case. For the case studied, these criteria also have a maximum, which allows for further improvement if desired. The results also show the importance of using balanced performance measures in the decision process. A multi-criteria optimization was also performed, showing the Pareto front of considered indicators. We discuss the trade-offs among different criteria, and the implications in finding balanced solutions. The proposed analytical approach is easy to implement and requires low computational effort. It also allows for an easy re-evaluation of resources when the business cycle changes and relevant exogenous factors vary.     

Improving the computational efficiency of metric-based spares algorithms

We propose a new heuristic algorithm to improve the computational efficiency of the general class of Multi-Echelon Technique for Recoverable Item Control (METRIC) problems. The objective of a METRIC-based decision problem is to systematically determine the location and quantity of spares that either maximizes the operational availability of a system subject to a budget constraint or minimizes its cost subject to an operational availability target. This type of sparing analysis has proven essential when analyzing the sustainment policies of large-scale, complex repairable systems such as those prevalent in the defense and aerospace industries. Additionally, the frequency of these sparing studies has recently increased as the adoption of performance-based logistics (PBL) has increased. PBL represents a class of business strategies that converts the recurring cost associated with maintenance, repair, and overhaul (MRO) into cost avoidance streams. Central to a PBL contract is a requirement to perform a business case analysis (BCA) and central to a BCA is the frequent need to use METRIC-based approaches to evaluate how a supplier and customer will engage in a performance based logistics arrangement where spares decisions are critical. Due to the size and frequency of the problem there exists a need to improve the efficiency of the computationally intensive METRIC-based solutions. We develop and validate a practical algorithm for improving the computational efficiency of a METRIC-based approach. The accuracy and effectiveness of the proposed algorithm are analyzed through a numerical study. The algorithm shows a 94% improvement in computational efficiency while maintaining 99.9% accuracy.     

A methodology for integrated critical spare parts and insurance management

Critical spare‐parts stock optimization has become a relevant topic for academy and industry. In most articles, the problem has been stated as a trade‐off between economic risks of shortages and financial costs. Risk optimization in this context has been mainly studied from a logistics point of view. The most common decision variables have been stock levels, stock location, and reorder points. In this context, buying insurance to cover shortage cost can be a complementary (or exclusive) measure for risk mitigation. Insurance optimization traditionally has been studied from a microeconomic and financial perspective. The main decision variable has been the indemnity function, and occasionally, the insurance premium. Its use in the context of physical asset management has not been observed to the best of our knowledge. This creates an opportunity to link inventory optimization techniques with insurance optimization for shortage losses. In this work, we present a novel approach to jointly manage the shortage risk of a critical non‐repairable component in a unique critical system. We develop an original model to integrate critical spare‐parts stock optimization with insurance optimization techniques. The result is a decision model to select the optimal stock and insurance policy that maximizes the decision maker's expected utility. This allows for a business‐centered integrated perspective in critical parts decisions. We present a case study representative of the mining industry, illustrating the complementary nature of selecting optimal stock levels and contracting an optimal insurance. Our results show that contracting an insurance can lead to policies preferred by a risk‐averse decision maker. The case study shows that this may even occur lowering stock levels and increasing profits. Copyright © 2015 John Wiley & Sons, Ltd.     

TPL介入的产运销供应链联盟决策及运作效率评价

在生产商批发价格为内生变量且TPL物流服务水平影响零售商市场需求的情形下,研究了整体联盟、分散决策、产运联盟和运销联盟四种模式下产运销供应链系统内各决策主体的决策行为以及系统的运作效率。分别构建了各决策模式下的数学模型,并证明了系统最优解或博弈均衡解的存在性和唯一性。通过对上述四种模式下的运算结果进行两两比较,发现:较之整体联盟,其他三种决策模式下系统利润均出现损失;其他三种模式下的最优订购量、物流服务水平和二者的比值大小均取决于某些特定的条件,这导致TPL介入的供应链内部联盟并非一定能使系统整体运作效率获得提高。进一步通过数值算例对零售价格和可变物流服务成本进行了灵敏度分析,发现在大多数情形下,运销联盟模式下的系统运作效率是上述三种决策模式中最高的。     

Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers

We consider an infinite capacity M/M/c queueing system with c unreliable servers, in which the customers may balk (do not enter) and renege (leave the queue after entering). The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. System performance measures are explicitly derived in terms of computable forms. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is derived to determine the optimal values of the number of servers, service rate and repair rate simultaneously at the minimal total expected cost per unit time. The parameter optimization is illustrated numerically by the Quasi-Newton method.     

Optimal corrective maintenance contract planning for aging multi‐state system

This paper considers an aging multi‐state system, where the system failure rate varies with time. After any failure, maintenance is performed by an external repair team. Repair rate and cost of each repair are determined by a corresponding corrective maintenance contract with a repair team. The service market can provide different kinds of maintenance contracts to the system owner, which also can be changed after each specified time period. The owner of the system would like to determine a series of repair contracts during the system life cycle in order to minimize the total expected cost while satisfying the system availability. Operating cost, repair cost and penalty cost for system failures should be taken into account. The paper proposes a method for determining such optimal series of maintenance contracts. The method is based on the piecewise constant approximation for an increasing failure rate function in order to assess lower and upper bounds of the total expected cost and system availability by using Markov models. The genetic algorithm is used as the optimization technique. Numerical example is presented to illustrate the approach. Copyright © 2009 John Wiley & Sons, Ltd.     

带时间窗的三维装载物流配送优化方法研究

针对城市物流配送优化研究在客户服务时间窗和货物装载方式合理结合方面存在的不足,考虑物流配送车厢货物装载方式与客户访问序列相关的特征对车厢空间进行合理的区域划分。首先,构建了包含配送中心的固定成本、配送车辆的运输成本、维修成本、租赁成本和违反时间窗惩罚成本的物流运营成本最小化和配送车辆空间利用率最大化的双目标优化模型;然后,提出一种结合遗传算法(GA)全局搜索能力和禁忌搜索算法(TS)局部搜索能力的GA-TS混合算法求解模型;最后,结合重庆市某配送中心的三维装载物流配送实例数据进行了优化计算,实验结果给出了带时间窗的三维装载物流配送路径优化方案,并进行了不同车厢空间分区模式下平均装载率、物流运营成本和车辆使用数的比较分析。研究表明,当客户需求货物种类数与车辆的空间区域划分数相等且按货物类型进行区域划分时,物流运营成本最小,配送车辆使用数最少和车辆平均装载率最高。     

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.     

Freight railway operator timetabling and engine scheduling

In this paper we consider timetable design at a European freight railway operator. The timetable is designed by choosing the time of service for customer unit train demands among a set of discrete points. These discrete points are all found within the a time-window. The objective of the model is to minimize cost while adhering to constraints regarding infrastructure usage, demand coverage, and engine availability. The model is solved by a column generation scheme where feasible engine schedules are designed in a label setting algorithm with time-dependent cost and service times.