Pooling of repairable spare parts: A study on inventory policies

This is a summary of the most important results presented in the author's PhD thesis (Wong 2004). This thesis, written in English, was defended on 14 June 2004 at the Katholieke Universiteit Leuven (Belgium) and supervised by Dirk Cattrysse and Dirk Van Oudheusden. A copy is available from the author upon request. It presents a number of modeling and solution approaches for investigating how the use of pooling contributes to the goal of increased service performance and reduced cost in the context of repairable spare parts inventory management. MSC classification: 47N10, 90B05, 91A80     

串并联可修系统的可靠性

本文通过密度演化法讨论了部件的寿命和修理时间都服从一般分布的由n个不同子系统串并联组成的可修系统的可靠性,为串并联系统的可靠性研究提供了理论依据.     

A solution approach to the inventory routing problem in a three-level distribution system

We consider the infinite horizon inventory routing problem in a three-level distribution system with a vendor, a warehouse and multiple geographically dispersed retailers. In this problem, each retailer faces a demand at a deterministic, retailer-specific rate for a single product. The demand of each retailer is replenished either from the vendor through the warehouse or directly from the vendor. Inventories are kept at both the retailers and the warehouse. The objective is to determine a combined transportation (routing) and inventory strategy minimizing a long-run average system-wide cost while meeting the demand of each retailer without shortage. We present a decomposition solution approach based on a fixed partition policy where the retailers are partitioned into disjoint and collectively exhaustive sets and each set of retailers is served on a separate route. Given a fixed partition, the original problem is decomposed into three sub-problems. Efficient algorithms are developed for the sub-problems by exploring important properties of their optimal solutions. A genetic algorithm is proposed to find a near-optimal fixed partition for the problem. Computational results show the performance of the solution approach.     

Revisiting the model of servicing machines with repairable service facility-a new analyzing idea and some new results

In this paper the model of servicing machines with repairable facility is further studied.By standard conditioning decomposition argument,two reliability indices-the probability that the service facility fails at time t and the expected number of failure occurring during（0,t] are discussed.Some important relations of them are given.Furthermore,some new reliability problems are presented and discussed as follows：1） The numbers of the service facility failures during the generalized service time and the generalized busy period;2） The asymptotic expansion of the expected failure number of the service facility during（0,t].A series of new reliability results of the service facility are obtained.     

Periodic review lost-sales inventory models with compound Poisson demand and constant lead times of any length

In almost all literature on inventory models with lost sales and periodic reviews the lead time is assumed to be either an integer multiple of or less than the review period. In a lot of practical settings such restrictions are not satisfied. We develop new models allowing constant lead times of any length when demand is compound Poisson. Besides an optimal policy, we consider pure and restricted base-stock policies under new lead time and cost circumstances. Based on our numerical results we conclude that the latter policy, which imposes a restriction on the maximum order size, performs almost as well as the optimal policy. We also propose an approximation procedure to determine the base-stock levels for both policies with closed-form expressions.     

Ergodic and light traffic properties of a complex repairable system

A repairable system is composed of components ofI types. A component can be loaded, put on standby, queued or repaired. The repair facility is here assumed to be a queueing system of a rather general structure though interruption of repairs is not allowed. Typei components possess a lifetime distributionA _i (t) and repair time distributionB _t (t). The lifetime of componentj is exhausted with a state-dependent rate _j (t). A Markov process Z(t) with supplementary variables is built to investigate the system behaviour. An ergodic result, Theorem 1, is established under a set of conditions convenient for light traffic analysis. In Theorems 2 to 6, a light traffic limit is derived for the joint steady state distribution of supplementary variables. Applying these results, Theorems 7 to 10 derive light traffic properties of a busy period-measured random variable. Essentially, the concepts of light traffic equivalence due to Daley and Rolski (1992) and Asmussen (1992) are used. The asymptotic (light traffic) insensitivity of busy period and steady state parameters to the form ofA _i(t) [given their means and (in some cases) values of density functions for smallt], is observed under some analytic conditions.Some abbreviations & notations LHS, RHS lefthand side, righthand side - w.r.t. with respect to - (i.i.d.) r.v. (independent identically distributed) random variables - A ^c complement event - d.f., p.d.f. distribution function, probability density function - m.g.f. moment generating function - I _A indicator function of eventA - (t) =1–A(t)     

Inventory management of multiple items with irregular demand: A case study

We present the case of a Greek commercial enterprise facing the problem of managing the inventories of thousands of different items, supplied by more than 20 European and Asian manufacturers and sold to a large number of different-type customers. A key feature of the problem is that the demand for the vast majority of items is intermittent and lumpy, thus not allowing the use of the usual normal or Poisson distributions. The paper describes the solutions given to several practical problems in the course of developing an easy-to-use yet effective and all-encompassing inventory control system. Emphasis is placed on the accurate modeling of demand by means of a gamma distribution with a probability mass at zero or a package Poisson distribution for very-slow-moving items. Using those models and simple quantitative tools we develop an efficient procedure for approximate but quite accurate determination of the base stock levels that achieve the desired fill rates in the proposed periodic review system. We briefly describe the computerized implementation of the new system and the very encouraging results.     

A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization

The joint economic lot sizing problem (JELP) model provides a global view to facilitate the development of a production-inventory policy for an integrated system. However, when a deteriorating item is involved, previous studies have neglected the following two important issues: (1) the deterioration quantity increases the demand for the supplier's capacity, which consequently requires the supplier to recalculate the corresponding average cost and reevaluate the capacity utilization, and (2) given the supplier's production rate, in-transit deterioration imposes restrictions on the delivery distance or in-transit time. Therefore, the existing integrated policies may lead to infeasible solutions for the distribution channel when a deterioration item is included. In view of these two issues, a generalized JELP model under delay in payments is formulated to investigate the integrated production-inventory policy for an item with two-stage deterioration (in-transit and retail deterioration) while incorporating both transportation time and capacity utilization. By developing the average cost functions of the supply chain members and employing several new definitions (e.g., variable capacity utilization), this paper provides a mechanism for measuring the influence of two-stage deterioration on the supplier's capacity utilization for the JELP. Three algorithms are proposed to obtain optimal decisions based on the theoretical results. This paper demonstrates that the supplier's variable capacity utilization is relevant to transportation time and two-stage deterioration, which can be applied to evaluate the feasibility of the integrated production-inventory policy for the deteriorating item. Furthermore, there is a maximum allowable value for the retailer's order cycle.     

A fractional algorithm for optimal cutting of lumber into dimension parts

A fractional algorithm is described which optimizes the cutting of boards or lumber into dimension parts. The model is an extension of previously developed models and is purposely designed for cutting scenarios where the customer order for the dimension parts can be satisfied within a given range, i.e., flexible rather than exact demand. An illustrative example is presented simply to describe the model and compare results between the standard procedure and the modified procedure proposed in this paper.     

Exponential asymptotic property of a parallel repairable system with warm standby under common-cause failure

We discuss exponential asymptotic property of the solution of a parallel repairable system with warm standby under common-cause failure. This system can be described by a group of partial differential equations with integral boundary. First we show that the positive contraction C₀-semigroup T(t) [Weiwei Hu, Asymptotic stability analysis of a parallel repairable system with warm standby under common-cause failure, Acta Anal. Funct. Appl. 8 (1) (2006) 5-20] which is generated by the operator corresponding to these equations is a quasi-compact operator. Then by using [Weiwei Hu, Asymptotic stability analysis of a parallel repairable system with warm standby under common-cause failure, Acta Anal. Funct. Appl. 8 (1) (2006) 5-20] that 0 is an eigenvalue of the operator with algebraic index one and the C₀-semigroup T(t) is contraction, we conclude that the spectral bound of the operator is zero. By using the above results the exponential asymptotical stability of the time-dependent solution of the system follows easily.     

自然灾害风险下区域应急储备设施选址可靠性研究

自然灾害发生时,为了保证区域应急储备系统的服务不被中断,考虑设施被破坏数目的发生概率并提供备份库存,以加强应急储备系统的可靠性。模型采用非支配排序遗传算法(NSGA-II)进行求解,产生一组选址决策方案。以四川省八大城市的人口及运输距离为输入数据的仿真结果表明,与一般模型比较,本文考虑可靠性的选址模型能更好抵御自然灾害造成的中断影响,并且能获得更优的应急响应满意度、多重覆盖或总成本的单目标值。因此,在地震等灾害的破坏风险下,该模型可成为应急储备设施可靠选址的有效工具。     

Stability and optimization of a production inventory system under prioritized base-stock control

Email: dongping.song{at}plymouth.ac.uk Received on 19 July 2007. Accepted on 1 May 2008. A make-to-stock system producing two part-types with stochasticprocessing times and random demands is considered. A prioritizedbase-stock policy is used to control the production to meetexogenous Poisson demands, where the unmet high-priority demandsare partially backordered due to their limited patience andthe unmet low-priority demands are fully backordered. Basedon the matrix analytical method, a necessary and sufficientcondition for the stability of the system is provided. The explicitstationary distribution is derived using the spectral expansionapproach. Interesting steady-state performance measures suchas stock-out probabilities and lost-sale fraction are then calculated.By investigating the structural properties of the objectivefunctions, simple procedures are presented to find the optimalbase-stock levels either to minimize the expected cost or tosatisfy the stock-out probability and the lost-sale fractionconstraints. In addition, the optimization problem with respectto the maximum backlog level for part-type one and two base-stocklevels is addressed and a solution procedure is presented. Numericalexamples are given to demonstrate the results.     

A measure of bullwhip effect in supply chains with a mixed autoregressive-moving average demand process

In this paper, we quantify the impact of the bullwhip effect – the phenomenon in which information on demand is distorted as moving up a supply chain – for a simple two-stage supply chain with one supplier and one retailer. Assuming that the retailer employs a base stock inventory policy, and that the demand forecast is performed via a mixed autoregressive-moving average model, ARMA(1, 1), we investigate the effects of the autoregressive coefficient, the moving average parameter, and the lead time on the bullwhip effect.     

An inventory control system for spare parts at a refinery: An empirical comparison of different re-order point methods

Inventory control of spare parts is essential to many organizations, since excess inventory leads to high holding costs and stock outs can have a great impact on operations performance. This paper compares different re-order point methods for effective spare parts inventory control, motivated by a case study at a large oil refinery. Different demand modeling techniques and inventory policies are evaluated using real data.     

A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K

A reliability system subject to shocks producing damage and failure is considered. The source of shocks producing failures is governed by a Markovian arrival process. All the shocks produce deterioration and some of them failures, which can be repairable or non-repairable. Repair times are governed by a phase-type distribution. The number of deteriorating shocks that the system can stand is fixed. After a fatal failure the system is replaced by another identical one. For this model the availability, the reliability, and the rate of occurrence of the different types of failures are calculated. It is shown that this model extends other previously published in the literature.     

油田A类物资采购决策支持系统研究

结合大庆油田物资公司在重要供应链管理环节,即采购、需求和库存中所面临的实际问题(物资需求增加、仓储压力增大、采购成本增多)及三者之间的相互作用,基于预测和优化理论,构建了针对油田A类物资的采购优化和库存管理决策支持系统原型,包括：预测模块、优化模块和方案调整评估模块,为相关部门制定合理物资采购方案提供决策支持.进一步,以银浪仓库中的4种A类物资为例,运用该原型系统进行数值模拟. 结果表明,2009年和2010年4种物资的总成本节省率分别为10.35%和8.07%,效益可观. 考虑到油田物资数据结构不完备及优化模型的复杂性,该原型系统在大庆油田大规模推广方面仍需进一步完善.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money

In this paper, a production-repairing inventory model in fuzzy rough environment is proposed incorporating inflationary effects where a part of the produced defective units are repaired and sold as fresh units. Here, production and repairing rates are assumed as dynamic control variables. Due to complexity of environment, different costs and coefficients are considered as fuzzy rough type and these are reduced to crisp ones using fuzzy rough expectation. Here production cost is production rate dependent, repairing cost is repairing rate dependent and demand of the item is stock-dependent. Goal of the research work is to find decisions for the decision maker (DM) who likes to maximize the total profit from the above system for a finite time horizon. The model is formulated as an optimal control problem and solved using a gradient based non-linear optimization method. Some particular cases of the general model are derived. The results of the models are illustrated with some numerical examples.     

专职修理工多重休假且修理设备可更换的k/n(G)表决系统研究

讨论专职修理工多重休假,修理设备可发生失效且可更换的k/n（G）表决可修系统.当系统中没有故障部件时,专职修理工开始一次休假,在此期间,若有工作部件发生故障,则立即指派普通修理工修理故障部件,一直持续到系统中无故障部件或专职修理工休假回来.利用马尔可夫过程理论和矩阵解法,给出了系统瞬态和稳态下的可用度和故障频度、可靠度、系统首次故障前的平均时间、修理设备处于更换状态的概率等指标的表达式.在此基础上,基于不同的初始条件研究了相关指标随时间的变化情况.最后,特殊情形的讨论验证了所得结果的正确性.