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

On two-echelon inventory systems with Poisson demand and lost sales

We derive approximations for the service levels of two-echelon inventory systems with lost sales and Poisson demand. Our method is simple and accurate for a very broad range of problem instances, including cases with both high and low service levels. In contrast, existing methods only perform well for limited problem settings, or under restrictive assumptions.\u

Joint optimization of level of repair analysis and spare parts stocks

In the field of 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 may be 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 points, i.e., lower backorder levels cannot be achieved against the same (or lower) costs. In a computational experiment, we show that solving the joint problem is worthwhile, since we achieve a cost reduction of 5.1% on average and over 43% at maximum compared with using a sequential approach of first solving a lora and then the spare parts stocking problem

Fleet readiness : stocking spare parts and high-tech assets

We consider a maintenance shop that is responsible for the availability of a eet of assets, e.g., trains. Unavailability of assets may be due to active maintenance time or unavailability of spare parts. Both spare assets and spare components may be stocked in order to ensure a certain percentage of eet readiness (e.g., 95%), i.e., having sucient assets available for the primary process (e.g., running a train schedule). This is dierent from guaranteeing a certain average availability, as is typically done in the literature on spare parts inventories. We analyse the corresponding system, assuming continuous review and base stock control. We propose an algorithm, based on a marginal analysis approach, to solve the optimization problem of minimizing holding costs for spare assets and spare parts. Since the problem is not item separable, even marginal analysis is time consuming, but we show how to eciently solve this. Using a numerical experiment, we show that our algorithm generally leads to a solution that is close to optimal, and we show that our algorithm is much faster than an existing algorithm for a closely related problem

Optimal and heuristic repairable stocking and expediting in a fluctuating demand environment

We consider a single stock point for a repairable item. The repairable item is a critical component that is used in a fleet of technical systems such as trains, planes or manufacturing equipment. A number of spare repairables is purchased at the same time as the technical systems they support. Demand for those items is a Markov modulated Poisson process of which the underlying Markov process can be observed. Backorders occur when demand for a ready-for-use item cannot be fulfilled immediately. Since backorders render a system unavailable for use, there is a penalty per backorder per unit time. Upon failure, defective items are sent to a repair shop that offers the possibility of expediting repair. Expedited repairs have shorter lead times than regular repairs but are also more costly. For this system, two important decisions have to be taken: How many spare repairables to purchase initially and when to expedite repairs. We formulate the decision to use regular or expedited repair as a Markov decision process and characterize the optimal repair expediting policy for the infinite horizon average and discounted cost criteria. We find that the optimal policy may take two forms. The first form is to never expedite repair. The second form is a type of threshold policy. We provide necessary and sufficient closed-form conditions that determine what form is optimal. We also propose a heuristic repair expediting policy which we call the world driven threshold (WDT) policy. This policy is optimal in special cases and shares essential characteristics with the optimal policy otherwise. Because of its simpler structure, the WDT policy is fit for use in practice. We show how to compute optimal repairable stocking decisions in combination with either the optimal or a good WDT expediting policy. In a numerical study, we show that the WDT heuristic performs very close to optimal with an optimality gap below 0.76% for all instances in our test bed. We also compare it to more naive heuristics that do not explicitly use information regarding demand fluctuations and find that the WDT heuristic outperforms these naive heuristics by 11.85% on average and as much as 63.67% in some cases. This shows there is great value in leveraging knowledge about demand fluctuations in making repair expediting decisions

A New Multi Echelon Repair Network Model with Multiple Upstream Locations for Level of Repair Analysis Problem

Level of repair analysis (LORA) determines (1) the best decision during a malfunction of each product component; (2) the location in the repair network to perform the decision and (3) the quantity of required resources in each facility. Capital goods have long life cycles and their total life cycle costs are extremely high. LORA, which can be done repeatedly during the life cycle of the product, both at design and product support phase, plays an important role in minimising the total life cycle costs of capital goods. It is mostly applied to systems that operate in different geographical areas and deployed in different regions, which include different subsystems with special technology and expertise, and have a complex product structure. In this study, we propose a new mathematical model to the LORA problem, which is more comprehensive and flexible than the other pure LORA models in the literature. The proposed model uses the multiple upstream approach that allows the transfer of the components from a location in the lower echelon to the predefined locations in the upper echelon and determines the material movement paths between each facility, defining the facilities’ locations in the repair network. The performance of the proposed model is tested on benchmark instances and the results are compared with the single upstream model. Computational experiments show that the proposed model is more effective than the single upstream model and reduces the total life cycle costs by 4.85% on average, which is an enormous cost saving when total life cycle costs of capital goods are considered