Multi-echelon Repairable Item Inventory Systems Research Articles

Multi-echelon repairable item inventory system with limited repair capacity under nonstationary demands

Classical multi-echelon repairable item inventory models are based either on steady-state analysis or infinite repair capacity, which may not work well in situations when the demand is nonstationary, or repair capacity is limited. In this paper, we propose an analytical model for evaluating system performance that works well under limited repair capacity and nonstationary demands. Following the METRIC methodology, we then develop an optimisation algorithm to solve the corrective maintenance problem in military logistics. Experimental results show that our approach yields good solutions efficiently. This work has also resulted in a software that has been field-tested by a military organisation.

Evaluation of time-varying availability in multi-echelon spare parts systems with passivation

The popular models for repairable item inventory, both in the literature as well as practical applications, assume that the demands for items are independent of the number of working systems. However this assumption can introduce a serious underestimation of availability when the number of working systems is small, the failure rate is high or the repair time is long. In this paper, we study a multi-echelon repairable item inventory system under the phenomenon of passivation, i.e. serviceable items are passivated (“switched off”) upon system failure. This work is motivated by corrective maintenance of high-cost technical equipment in the miltary. We propose an efficient approximation model to compute time-varying availability. Experiments show that our analytical model agrees well with Monte Carlo simulation.

An algorithm for repairable item inventory system with depot spares and general repair time distribution

We consider the problem of determining the initial spare inventory level for a multi-echelon repairable item inventory system. We extend the previous results to the system, which has an inventory at the central depot as well as at bases and with a general repair time distribution. We propose an algorithm which finds spare inventory level to minimize the total expected cost and simultaneously to satisfy a specified minimum service rate. Extensive computational experiments show that the algorithm is accurate and efficient.

A Multiechelon Repairable Item Inventory System with Lateral Transshipment and a General Repair Time Distribution

This paper discusses the determination of the spare inventory level for a multiechelon repairable item inventory system, which has several bases and a central depot with emergency lateral transshipment capability. Previous research is extended by removing a restrictive assumption on the repair time distribution. A mathematical model that allows a general repair time distribution, as well as an algorithm to find a solution of the model, is developed. Thus, the main focus of this study is to improve the accuracy of previous models and to estimate the gain in accuracy from use of the current methodology. Computational experiments are performed to estimate the accuracy improvement and to determine the managerial implications of the results.

Modeling lateral transshipments in multiechelon repairable-item inventory systems with finite repair channels

This article concerns the problem of determining the optimal spare inventory level for a multiechelon repairable-item inventory system, which has several bases and a central depot. When an item fails, the failed item is replaced immediately if a spare is available at the base. If there is no spare item available at the base, it is requested as a lateral transshipment to another base that has a spare in stock. If an item is not available from any of the bases, the item is backordered until a spare becomes available. We propose a model to describe the behavior of the system and develop an algorithm to find the spare inventory level at each base, which minimizes the total expected cost of the system. The algorithm is illustrated using examples of various sizes. Scope and purpose Repairable-items refer to components that are very expensive, critically important, and subject to infrequent failure. The navigational computer of a plane or subway cars are typical examples of the repairable-items. In multiechelon repairable-item inventory systems that cover extensive geographical regions, lateral transshipment between bases is often used for improved service levels. However, previous research of the lateral transshipments assumes infinite repair capacity and is less appropriate for most industrial systems, where it is resource constrained. In this paper, we propose a model and an algorithm to find the optimal spare level for the system with finite repair channels.

Setting expediting repair policy in a multi-echelon repairable-item inventory system with limited repair capacity

Inventory systems with limited repair capacity are affected by congestion externalities, caused by use of a shared service. There is incompatibility between individual and system optimisation in considering congestion externalities. Three models are described that investigate the congestion effect in a multi-echelon inventory system which has two modes of repair, each with a limited repair capacity. An expanding repair policy employed by the bases in order to choose which repair mode to use is described and compared with different expediting policies related to congestion externalities. The expanding repair policy that considers congestion externalities was found to lead to better system performance measurement than an expanding policy with no congestion. The results of the numerical experiment indicate that the model that ignores congestion externalities—that is, the model that measures each base as an individual—leads to poorer performance measurement for every expediting repair policy, and particularly for the optimal expediting repair policy.

An optimal algorithm for repairable-item inventory system with depot spares

We consider the problem of determining the spare inventory level for a multiechelon repairable-item inventory system. Our model extends the previous results to the system, which has an inventory at the central depot, as well as at the bases. We have developed an algorithm to find the optimal spare inventory levels, which minimise the total expected cost and simultaneously satisfy a specified minimum service rate. The algorithm is illustrated using examples of various sizes.

Optimizing discrete stochastic systems using simulated annealing and simulation

The objective of this paper is to present an integrated approach of two models: simulation and optimization. This approach is used to determine the design parameters of stochastically constrained systems where the measure of performance is available only via simulation. The optimization model is solved using simulated annealing (SA) for parameter selection followed by the use of Monte Carlo simulation to evaluate the measure of performance. Based on the expected simulation output, the parameter set is either accepted or rejected. A modified rejection/acceptance criterion is presented for the proposed SA algorithm taking into consideration the stochastic system constraints. Moreover, a control variate is employed as a variance reduction technique in order to obtain an efficient estimate of performance measure. The proposed approach is tested using three real cases of the multi-echelon repairable item inventory systems (MERIIS). The results show that the proposed method is efficient in determining an optimal choice of spares and repair channels in these systems.

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.

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

Optimal algorithm to determine the spare inventory level for a repairable-item inventory system

This article concerns the problem of determining the optimal spare inventory level for a multiechelon repairable-item inventory system, which has several bases and a central depot. When an item fails, it is dispatched to a repair facility, and a spare, if available, is plugged in immediately. We develop an optimal algorithm to find the spare inventory level which minimizes the total expected cost and simultaneously satisfies a specified minimum service rate. The algorithm is applied to examples with good results.

Iterative solution methods for obtaining the steady-state probability distributions of Markovian multi-echelon repairable item inventory systems

The Jacobi, Gauss-Seidel and bi-conjugate gradient methods are used to compute the steady-state probability distributions for finite state-space continuous time Markov processes (closed queueing networks) that arise in the modeling of two- and three-echelon repairable item inventory systems. Alternative systems of linear equations that express the steady-state conditions are examined, generation and storage of the transition rate matrix are discussed briefly and various initializations and stopping criteria are tested. Numerical results are given for problems with up to one million states. Good results are obtained with a two-phase algorithm that uses the Gauss-Seidel method first and the bi-conjugate gradient method subsequently.

An approximation to the stationary distribution of a multiechelon repairable-item inventory system with finite sources and repair channels

We consider a multiechelon repairable-item inventory system where several bases are supported by a central depot. Unlike METRIC-based models, there are only a finite number of repairmen at each base and the depot, and the failure rates at the bases depend on the current number of items online. The principal objective of this article is to develop a quick and accurate approximation to the steady-state distribution of this system. A secondary objective is to compare the solution of this system with a comparable METRIC solution.

Transient behavior of large Markovian multiechelon repairable item inventory systems using a truncated state space approach

Abstract : Calculations for large Markovian finite source, finite repair capacity two echelon repairable item inventory models are shown to be feasible using the randomization technique and a truncated state space approach. More complex models (involving transportation pipelines, multiple item types and additional echelon levels) are also considered.

On Some Common Interests Among Reliability, Inventory, and Queuing

Queuing networks can be used to model maintained systems. Under many conditions, closed-network queuing theory can be applied to ascertain the availability of such systems. Multi-echelon repairable-item inventory systems are one such class. Problems of common interest to the reliability, queuing, and inventory communities are highlighted, and solution techniques for these problems are presented.