Journal of the Operational Research Society (2007) 58, 1178--1184  2007 Operational Research Society Ltd. All rights reserved. 0160-5682/07 $30.00 www.palgrave-journals.com/jors Centralized decision of internal transfer-prices with congestion externalities for two modes of repair with limited repair capacity Y Perlman 1∗ and M Kaspi 2 1 Bar-llan University, Ramat Gan, Israel; and 2 Ben-Gurion University of the Negev, Beer-Sheva, Israel The internal transfer-prices set by an organization are what an organization’s bases ‘pay’ its service centre, the depot, for its services. Since each base has a limited budget, these transfer-prices control and motivate the base’s usage of two types of repair services: normal and expedited. In this paper, we implement a unique approach—transfer-prices with congestion externalities—to determine the optimal transfer-price for the expedited repair service. Inventory systems with limited repair capacity are affected by congestion externalities, which reflect the negative externalities caused by the use of a shared service. We also describe different models that develop transfer prices schemas, and which differ in the way they consider congestion externalities. Numerical illustrations based on data from an air force display the incompatibility between two optimization models. One model ignores congestion externalities, while another considers congestion externalities. In the case of congestion externalities, the base must pay extra for the expedited repair service. The increased costs are due to expanded usage of the limited repair capacity which a particular base is imposing on the rest of the system in the form of longer queues that degrade service quality. Journal of the Operational Research Society (2007) 58, 1178 – 1184. doi:10.1057/palgrave.jors.2602290 Published online 16 August 2006 Keywords: limited repair capacity; transfer pricing; congestion externalities 1. Introduction Organizations that offer different kinds of services can maxi- mize their (system) utility by using their transfer prices to con- trol the user’s (individual) utilization of each service. When users of the services offered by the organization are all inter- nal, we call the pricing approach (internal) transfer pricing; that is, the service centre sets a ‘price’ for its services that users have to pay for. Each user has only a limited budget it may spend on these services. In this paper, we evaluate a multi-echelon, repairable-item inventory system by setting prices for the repair services of- fered by the service centre. In repairable-item inventory sys- tems, faulty units are repaired at the service centre, rather than discarded. A multi-echelon inventory system implies the exis- tence of a hierarchy of stocking locations and the dependence and interactions between these inventories. This study focuses on an air force environment, where the inventory system is dedicated to serving a number of aircraft stationed at several geographically distributed operating locations or bases. Each base supports its aircraft with an inventory of spare repairable- items. The depots are repair facilities. When a failure occurs ∗ Correspondence: Y Perlman, The interdisciplinary Department of Social Sciences-Logistics Studies, Faculty of Social Sciences, Bar llan University, Ramat Gan 52900, Israel. E-mail: perlmay@mail.biu.ac.il on an aircraft, the failed item is then removed from the aircraft and replaced with a serviceable spare from the base stock as soon as one is available. The failed item is then sent to the depot to be repaired, and a requisition is placed upon the depot for a serviceable unit to be sent to the base. An inventory system of this type is called a multi-echelon system. Multi-echelon and multi-indenture models are considered in- depth in Sherbrooke (1992). For simplicity, we assumed a two- echelon system, with the first echelon being the bases (users) and the second echelon being the service centre (depot). The depot analysed in this paper has a limited repair capac- ity, which means that a queue can build up at the depot leading to delays in its repair services. Thus, the bases, which share a common limited service, may impose costs that are known as congestion externalities. When an individual user expands his utilization of this limited capacity, he imposes costs on the overall system in the form of degraded service quality. See, for example, Dewan and Mendelson (1990), Mendelson and Whang (1990), Westland (1992), Bradford (1996) and Ha (1998). Transfer prices with congestion externalities ac- knowledge these costs. When externalities are present, an in- compatibility between individual and system optimization is apt to arise, as discussed in Knudsen (1972), Lippman and Stidham (1977) and Bell and Stidham (1983). This incom- patibility derives from the need to account for the costs that individual actions impose on the overall society.