Optimization of spare parts for hierarchicall decomposable systems

Complex technical systems are often hierarchically composed of exchangeable modules, which themselves may be composed of exchangeable submodules. The hierarchy of modules of such systems can be represented by trees. Defective systems are repaired in a supply depot system by exchanging the defective modules from a stock of spare parts. The exchanged defective modules are repaired for resupply. In this paper, a dynamic programming algorithm for optimizing the stocks of spare parts, under a budget constraint, is presented. The optimization criterion is the minimization of the backlog of entire systems at the supply depot system. An implementation of the algorithm is described and some illustrative examples are given.     

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.     

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.     

Service differentiation in spare parts inventory management

The contemporary after-sales market is of increasing importance. One of the features required by the market is to provide differentiated service levels to different groups of customers. We use critical levels as a means to offer differentiation. Critical level policies aim to exploit the differences in target service levels by inventory rationing. In our multi-item single-location spare parts inventory model, we aim to minimize the spare parts provisioning cost, that is inventory holding and transportation cost, under the condition that aggregate mean waiting time constraints for all customer groups are met. In a computational experiment and a case study with data from a company in the semiconductor supplier industry, we show that significant cost reductions can be obtained when critical level policies are used instead of base stock policies (ie policies without critical levels).     

Supply rationing in multi-echelon divergent systems

In this paper we determine a simple inventory control rule for multi-echelon distribution systems under periodic review without lot sizing. The primary focus is the two-echelon model with a stockless central depot, but several extensions (>2 echelons, central stock allowed) are discussed as well. The, control rule consists of two parameter sets: a set of rationing fractions at the central depot with the purpose to minimize inventory imbalance, and a set of order-up-to levels for the local stockpoints with the purpose to achieve a target service level (fill rate) per local stockpoint. The problem to calculate these control parameters is solved by decomposition in two subproblems. First the rationing fractions are determined such that the (approximate) expected system imbalance is minimized. Next the order-up-to levels are calculated such that the target fill rates are achieved. Numerical results show that this control rule, called Balanced Stock (BS) rationing, is accurate and more robust than the Consistent Appropriate Share (CAS) rationing polocy.     

Stability of time-varying switched systems with time-varying delay

In this paper, we investigate the stability of time-varying switched systems with time-varying delay. We first give a generalization of Halanay’s inequality and then use this inequality to obtain sufficient conditions for the stability of switched systems.     

Dynamic demand fulfillment in spare parts networks with multiple customer classes

We study real-time demand fulfillment for networks consisting of multiple local warehouses, where spare parts of expensive technical systems are kept on stock for customers with different service contracts. Each service contract specifies a maximum response time in case of a failure and hourly penalty costs for contract violations. Part requests can be fulfilled from multiple local warehouses via a regular delivery, or from an external source with ample capacity via an expensive emergency delivery. The objective is to minimize delivery cost and penalty cost by smartly allocating items from the available network stock to arriving part requests. We propose a dynamic allocation rule that belongs to the class of one-step lookahead policies. To approximate the optimal relative cost, we develop an iterative calculation scheme that estimates the expected total cost over an infinite time horizon, assuming that future demands are fulfilled according to a simple static allocation rule. In a series of numerical experiments, we compare our dynamic allocation rule with the optimal allocation rule, and a simple but widely used static allocation rule. We show that the dynamic allocation rule has a small optimality gap and that it achieves an average cost reduction of 7.9% compared to the static allocation rule on a large test bed containing problem instances of real-life size.     

Simple,efficient heuristics for multi-item multi-location spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of a multi-location inventory system of repairable spare parts, in which lateral and emergency shipments occur in response of stock-outs. The objective is to determine close-to-optimal stocking policies minimizing the total cost for inventory holding, lateral transshipments, and emergency shipments subject to a target level for the average waiting times at all locations. We structure the optimization problem as a combinatorial problem and four different heuristics are developed and evaluated in terms of their total costs and computation times. It is shown that the greedy-type heuristic has the best performance. A numerical study is carried out to look at the relative cost savings obtained from the use of multi-item approach and lateral transshipments.     

Inventory management of spare parts in an energy company

We address the problem of how to determine control parameters for the inventory of spare parts of an energy company. The prevailing policy is based on an (s, S) system subject to a fill rate constraint. The parameters are decided based mainly on the expert judgment of the planners at different plants. The company is pursuing to conform all planners to the same approach, and to be more cost efficient. Our work focuses on supporting these goals. We test seven demand models using real-world data for about 21?000 items. We find that significant differences in cost and service level may appear from using one or another model. We propose a decision rule to select an appropriate model. Our approach allows us to recommend control parameters for 97.9% of the items. We also explore the impact of pooling inventory for different demand sources and the inaccuracy arising from duplicate item codes.     

Forecasting for the ordering and stock-holding of spare parts

A modern military organization like the UK's Royal Air Force is dependent on readily available spare parts for in-service aircraft in order to maximize operational capability. A large proportion of spare parts are known to have an intermittent or slow-moving demand pattern, presenting particular problems as far as forecasting and inventory control are concerned. In this paper, we use extensive demand and replenishment lead-time data to assess the practical value of forecasting models put forward in the literature for addressing these problems. We use an analytical method for classifying the consumable inventory into smooth, irregular, slow-moving and intermittent demand patterns. Recent forecasting developments are compared against more commonly used methods across the identified demand patterns. One recently developed method, a modification to Croston's method referred to as the approximation method, is observed to provide significant reductions in the value of the stock-holdings required to attain a specified service level for all demand patterns.     

Optimal provisioning strategies for slow moving spare parts with small lead times

When an expensive piece of equipment is bought, spare parts can often be bought at a reduced price. A decision must be made about the initial provisioning of spare parts. Furthermore, if at a certain time the stock drops to zero, because a number of failures have occurred, a decision must be made about the number of parts to be ordered. We focus on one specific expensive slow-moving part that is essential for the functioning of the equipment. The lead time of that part is small compared to its lifetime. We seek an ordering strategy for this part that covers the entire lifetime. Such a strategy should also be applicable to cases where there is uncertainty about the lifetime of the machine, the reliability of the components and the cost of failure. The main result is the development of a simple strategy that performs well in almost all cases. Furthermore, this strategy can easily deal with uncertainty and changes in the parameters.     

Models for multi-echelon repairable item inventory systems with limited repair capacity

The dominant models for inventory control of repairable items, both in the literature and in practical applications, are based on the assumption of ample repair capacity. This assumption can introduce a serious underestimation of the spare parts requirements in systems with high repair facility utilization, as is typical in industry. In this paper, we introduce approximations that can deal with limited repair facilities, under the scenarios of single-class exponentially distributed repair distributions, single-class general repair distribution, and multi-class general repair distributions. We provide numerical experiments that demonstrate how these models significantly outperform traditional models in the case of high repair facility utilization. Their ease of implementation is illustrated in a case study of the spare parts requirements at the Caracas subway system     

Decision support for spare parts acquisition in post product life cycle

A major task in service management is the timely and cost efficient provision of spare parts for durable products. This especially holds good, when the regular production of the product, its components and parts has been discontinued, but customer service still has to be guaranteed for quite a long time. In such post product life cycle period, three options are available to organize the spare parts acquisition, namely (i) setting up a single large order within the final lot of regular production, (ii) performing extra production runs until the end of service and (iii) using remanufacturing to gain spare parts from used products. These three options are characterized by different cost and flexibility properties. Due to the time-variability and uncertainty of demands for spare parts and also that of the returns of used products, it is a challenging task to find out the optimal combination of these three options. In this paper we show how this problem can be modeled and solved by Decision Tree and stochastic Dynamic Programming procedure. Based on the Dynamic Programming approach a heuristic method is proposed, which can be employed to come up with a simple solution procedure for real-world spare parts acquisition problems during the post product life cycle. A numerical example is presented to demonstrate the application of the solution methods described in the paper.     

Optimization of multi-echelon repairable item inventory systems with simultaneous location of repair facilities

We study a support system for a fleet of technical systems. Our tasks are to determine the amount of spares and test equipment necessary for the support system to operate satisfactorily and to determine where repair should take place. Our decisions are made on an economical basis, or more precisely, we seek the optimal support system configuration that meets a specified life-cycle cost constraint. A mathematical framework is presented which allows for these three tasks to be solved simultaneously.     

Joint optimization of level of repair analysis and spare parts stocks

In the field of after sales service logistics for capital goods, generally, METRIC type methods are used to decide where to stock spare parts in a multi-echelon repair network such that a target availability of the capital goods is achieved. These methods generate a trade-off curve of spares investment costs versus backorders. Backorders of spare parts lead to unavailability of the capital goods. Inputs in the spare parts stocking problem are decisions on (1) which components to repair upon failure and which to discard, and (2) at which locations in the repair network to perform the repairs and discards. The level of repair analysis (LORA) can be used to make such decisions in conjunction with the decisions (3) at which locations to deploy resources, such as test equipment that are required to repair, discard, or move components. Since these decisions significantly impact the spare parts investment costs, we propose to solve the LORA and spare parts stocking problems jointly. We design an algorithm that finds efficient solutions. In order for the algorithm to be exact and because of its computational complexity, we restrict ourselves to two-echelon, single-indenture problems. In a computational experiment, we show that solving the joint problem is worthwhile, since we achieve a cost reduction of over 43% at maximum (5.1% on average) compared with using a sequential approach of first solving a LORA and then the spare parts stocking problem.     

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     

Optimal control of parabolic systems with time-varying lags

Various optimal control problems for linear parabolic systemswith time-varying lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwart's, the representation of the optimalfeedback control is given.     

Inventory pooling of repairable spare parts with non-zero lateral transshipment time and delayed lateral transshipments

In this paper, we develop an analytical model to estimate several performance measures in a single-item, multi-company, repairable inventory system where complete pooling of stock is permitted among the companies. Compared to previous research, this paper is different in that both non-zero lateral transshipment time and delayed lateral transshipments are considered in the model. We model the system as a multi-dimensional Markovian problem and solve it using a two-stage solution method. The proposed method is very accurate and computationally efficient.     

Dissipativity analysis for singular systems with time-varying delays

This paper is concerned with the dissipativity analysis problem for singular systems with time-varying delays. A delay-dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique. All the results given in this paper are not only dependent upon the time delay, but also dependent upon the number of delay partitions. The effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples.