A Minimum Cost Flow model for Level of Repair Analysis

Given a product design and a repair network for capital goods, a level of repair analysis determines for each component in the product (1) whether it should be discarded or repaired upon failure and (2) at which location in the repair network to do this. In this paper, we show how the problem can be modelled as a minimum cost ow problem with side constraints. Advantages are that (1) solving our model requires less computational effort than solving existing models and (2) we achieve a high model exibility, i.e., many practical extensions can be added. Furthermore, we analyse the added value of modelling the exact structure of the repair network, instead of aggregating all data per echelon as is common in the literature. We show that in some cases, cost savings of over 7% can be achieved. We also show when it is sufficient to model the repair network by echelons only, which requires less input data

Level of Repair Analysis: A Generic Model

Given a product design and a repair network, a level of repair analysis (lora) determines for each component in the product (1) whether it should be discarded or repaired upon failure and (2) at which echelon in the repair network to do this. The objective of the lora is to minimize the total (variable and fixed) costs. We propose an ip model that generalizes the existing models, based on cases that we have seen in practice. Analysis of our model reveals that the integrality constraints on a large number of binary variables can be relaxed without yielding a fractional solution. As a result, we are able to solve problem instances of a realistic size in a couple of seconds on average. Furthermore, we suggest some improvements to the lora analysis in the current literature

An efficient model formulation for level of repair analysis \ud

Given a product design and a repair network, a level of repair analysis (LORA)\ud determines for each component in the product (1) whether it should be discarded or repaired\ud upon failure and (2) at which echelon in the repair network to do this. The objective of\ud the LORA is to minimize the total (variable and fixed) costs. We propose an IP model that\ud generalizes the existing models, based on cases that we have seen in practice. Analysis of\ud our model reveals that the integrality constraints on a large number of binary variables can\ud be relaxed without yielding a fractional solution. As a result, we are able to solve problem\ud instances of a realistic size in a couple of seconds on average. Furthermore, we suggest some\ud improvements to the LORA analysis in the current literatur

Practical extensions to the level of repair analysis

The level of repair analysis (lora) gives answers to three questions that are posed when deciding on how to maintain capital goods: 1) which components to repair upon failure and which to discard, 2) at which locations in the repair network to perform each type of repairs, and 3) at which locations in the network to deploy resources, such as test equipment. The goal is to achieve the lowest possible life cycle costs. Various models exist for the lora problem. However, these models tend to be restrictive in that specic business situations cannot be incorporated, for example, having repair equipment with a capacity restriction or the occurrence of unsuccessful repairs.We discuss and model various practically relevant extensions to an existing minimum cost \ud ow formulation for the lora problem. We show the added value of these model renements in an extensive numerical experiment

An optimal approach for the joint problem of level of repair analysis and spare parts stocking

We propose a method that can be used when deciding on how to maintain capital goods, given a product design and the layout of a repair network. Capital goods are physical systems that are used to produce products or services. They are expensive and technically complex and have high downtime costs. Examples are manufacturing equipment, defense systems, and medical devices

An iterative method for the simultaneous optimization of repair decisions and spare parts stocks

In the development process of a capital good, it should be decided how to maintain it once it is in the field. The level of repair analysis (LORA) is used to answer the questions: 1) which components to repair upon failure, and which to discard, 2) at which locations in the repair network to perform the repairs, and 3) at which locations to deploy resources, such as repair equipment. Next, it should be decided what amount of spare parts to store at each location in the network in order to guarantee a certain availability of the product. Usually, the LORA and the spare parts stocking problem are solved sequentially. However, solving the LORA first can lead to high spare parts costs. Therefore, we propose an iterative approach to solve the two problems jointly. We find that the total costs are lowered with 3.2% on average and almost 35% at maximum in our experiments. A cost reduction of a few percent may be worth hundreds of thousands of euros over the life cycle of a capital good

An approximate approach for the joint problem of level of repair analysis and spare parts stocking

For the spare parts stocking problem, generally METRIC type methods are used in the context of capital goods. A decision is assumed on which components to discard and which to repair upon failure, and where to perform repairs. In the military world, this decision is taken explicitly using the level of repair analysis (LORA). Since the LORA does not consider the availability of the capital goods, solving the LORA and spare parts stocking problems sequentially may lead to suboptimal solutions. Therefore, we propose an iterative algorithm. We compare its performance with that of the sequential approach and a recently proposed, so-called integrated algorithm that finds optimal solutions for twoechelon, single-indenture problems. On a set of such problems, the iterative algorithm turns out to be close to optimal. On a set of multi-echelon, multi-indenture problems, the iterative approach achieves a cost reduction of 3%on average (35%at maximum) as compared to the sequential approach. Its costs are only 0.6 % more than those of the integrated algorithm on average (5 % at maximum). Considering that the integrated algorithm may take a long time without guaranteeing optimality, we believe that the iterative algorithm is a good approach. This result is further strengthened in a case study, which has convinced Thales Nederland to start using the principles behind our algorithm

Motrusca : interactive model transformation use case repository

Modeling and model transformations tools are maturing and are being used in larger and more complex projects. The advantage of a modeling environment and its transformation tools cannot be easily exploited by non-expert users as many subtle intricacies determine the efficiency of transformation languages and their tools. We introduce transformation use case examples that highlight such language/tooling properties. These simple, non-trivial examples have been extracted from an experiment with transformations of Design Space Exploration models. These examples show some typical modeling patterns and we give some insight how to address the examples. We make a case for initiating an interactive, on-line repository for model transformation use cases. This repository is aimed to be example-centric and should facilitate the interaction between end-users and tooling developers, while providing a means for comparing the applicability, expressivity, and efficiency of transformation tools

Near-optimal heuristics to set base stock levels in a two-echelon distribution network

We consider a continuous-review two-echelon distribution network with one central warehouse and multiple local stock points, each facing independent Poisson demand for one item. Demands are fulfilled from stock if possible and backordered otherwise. We assume base stock control with one-for-one replenishments and the goal is to minimize the inventory holding and backordering costs. Although this problem is widely studied, only enumerative procedures are known for the exact optimization. A number of heuristics exist, but they ??nd solutions that are far from optimal in some cases (over 20% error on realistic problem instances). We propose a heuristic that is computationally e??cient and ??nds solutions that are close to optimal: 0.1% error on average and less than 3.0% error at maximum on realistic problem instances in our computational experiment