A minimum cost flow model for level of repair analysis R.J.I. Basten a,Ã , M.C. van der Heijden b , J.M.J. Schutten b a Eindhoven University of Technology, School of Industrial Engineering, Department of Operations, Planning, Accounting, and Control, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands b The University of Twente, School of Management and Governance, Department of Operational Methods for Production and Logistics, P.O. Box 217, 7500AE, Enschede, The Netherlands article info Available online 9 April 2010 Keywords: Maintenance Supply chain management Level of repair analysis Mixed integer programming Minimum cost flows abstract 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 flow 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 flexibility, 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. & 2010 Elsevier B.V. All rights reserved. 1. Problem setting and literature For capital goods, such as military naval equipment, MRI-scanners, or trains, customers increasingly take total life cycle costs (LCC) into account in their purchasing decisions (Ferrin and Plank, 2002). Also, we see a trend that customers outsource activities for system upkeep to the original equipment manufacturer (OEM) using service contracts that guarantee a certain service level against fixed yearly costs. For the OEM, this can be attractive, since selling services is generally more profitable than selling products (Deloitte, 2006; Murthy et al., 2004; Oliva and Kallenberg, 2003). This means that it becomes important for the OEM to take the costs of maintenance into account when designing new products. Costs of more reliable components can be earned back by lower maintenance costs during the product life cycle. Generally, capital goods are repaired by replacement, which means that a failed component is removed from the system and replaced by a functioning one. A defective component can either be discarded or repaired. If it is discarded, a new component needs to be purchased. If the component is repaired, this often means that a subcomponent failed and is replaced by a functioning one. The subcomponent should in turn be repaired or discarded itself. The system is thus seen as a multi-indenture system such as shown in Fig. 1. If a component should be repaired, it should also be decided where to do that. For example, if we consider military naval equipment, repairs can be performed on board the ship, at its marine base, a central depot, or even at the OEM. A network that connects all ships, bases, depots, and the OEM is called a multi- echelon repair network, see Fig. 2 for an example. In an early stage of the product life cycle, decisions upon discard or repair, and location of maintenance activities should be taken. These decisions are covered by a level of repair analysis (LORA). A LORA model should decide for a given product design and repair network:  which components to repair upon failure, and which to discard,  for each component that will be repaired, where in the repair network to do this, and,  for each required resource (e.g. test or repair equipment), where in the network to install it. such that the lowest possible life cycle costs are achieved. Those costs consist of both costs that are variable in the number of failures and fixed costs. Variable costs include costs of hiring service engineers and transportation of components; fixed costs include costs for resources such as test equipment and tools. The availability of the installed base is not considered in the LORA. Instead, the spare parts stocking problem is solved using the decisions that result from the LORA as an input (e.g., using METRIC- like methods, see Sherbrooke, 2004; Muckstadt, 2005). The goal in this problem is to allocate inventory in a repair network such that Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2010.03.025 Ã Corresponding author. Tel.: + 41 40 247 3947. E-mail addresses: r.j.i.basten@tue.nl (R.J.I. Basten), m.c.vanderheijden@utwente.nl (M.C. van der Heijden), j.m.j.schutten@utwente.nl (J.M.J. Schutten). Int. J. Production Economics 133 (2011) 233–242