ARTICLE IN PRESS JID: EOR [m5G;July 8, 2018;13:15] European Journal of Operational Research 000 (2018) 1–12 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Production, Manufacturing and Logistics An analysis of p-median location problem: Effects of backup service level and demand assignment policy ✩ Mumtaz Karatas a,b,∗ , Ertan Yakıcı a a Department of Industrial Engineering, Turkish Naval Academy, National Defense University, Tuzla, Istanbul 34940, Turkey b Bahcesehir University, Istanbul, 34353, Turkey a r t i c l e i n f o Article history: Received 18 May 2017 Accepted 9 June 2018 Available online xxx Keywords: Location p-median problem Backup service Discrete event simulation Emergency service systems a b s t r a c t Any solution to facility location problems will consider determining the best suitable locations with re- spect to certain criteria. Among different types of location problems, involving emergency service system (ESSs) are one of the most widely studied in the literature, and solutions to these problems will mostly aim to minimize the mean response time to demands. In practice, however, a demand may not be served from its nearest facility if that facility is engaged in serving other demands. This makes it a requirement to assign backup services so as to improve response time and service quality. The level of backup service is a key, strategic-level planning factor, and must be taken into consideration carefully. Moreover, in emer- gency service operations conducted in congested demand regions, demand assignment policy is another important factor that affects the system performance. Models failing to adopt sufficient levels of backup service and realistic demand assignment policies may significantly deteriorate the system performance. Considering the classic p-median problem (pMP) location model, this paper investigates the effects of backup service level, demand assignment policy, demand density, and number of facilities and their loca- tions on the solution performance in terms of multiple metrics. For this purpose, we adopt a combined optimization and simulation approach. We will first modify the classic pMP to account for distances to backup services. Next, we employ a discrete event simulation to evaluate the performance of location schemes obtained from the deterministic mathematical model. Our results provide insights for decision- makers while planning ESS operations. © 2018 Elsevier B.V. All rights reserved. 1. Introduction Planning of emergency service systems (ESSs) has been widely studied by many scholars and practitioners over the last 35 years. These systems refer to medical (e.g., hospitals, ambulances), secu- rity (e.g., police patrol, search and rescue, security guard opera- tions) and other services (e.g., repair services, firefighting) (Karatas & Yakıcı, 2018). The main objective of ESSs is to provide imme- diate response to emergency calls (Galvao & Morabito, 2008), and the models designed to solve ESS-related location problems are ex- pected to minimize the time required to serve a demand or the distance between a demand point and its nearest facility. The loca- tion problem which seeks to find p facility locations among multi- ✩ Disclaimer—The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or en- dorsements, either expressed or implied, of any affiliated organization or govern- ment. ∗ Corresponding author. E-mail addresses: mkaratas@dho.edu.tr (M. Karatas), eyakici@dho.edu.tr (E. Yakıcı). ple candidates to minimize the total (or average) distance between all demands and their nearest facilities is called the p-median problem (pMP) (Hakimi, 1964). The pMP has much been the ob- ject of both theoretical and applied research. In addition to ESSs, it has also been naturally used in many other public and private sector applications. In most real-life emergencies, a customer (demand) is likely not to receive immediate service if his designated nearest emer- gency service (facility) is engaged in serving other patients at the time of incident (Karatas, Razi, & Tozan, 2017). This is especially common in large-scale emergency location problems or in severely supply-restricted systems. Cases, where this is observed, include emergency ambulance operations, repair crews responding to criti- cal equipment failures, utilization of a limited number of expensive medical devices, etc. (Weaver & Church, 1985). Keeping in mind that the difference between life and death can be sometimes mea- sured in minutes (or even seconds), decision-makers should take into account the issue of congestions and queues and should con- sider providing backup supplies for demands. When a demand nearest (primary) facility is busy, a common approach is to serve the demand with an available backup facility. https://doi.org/10.1016/j.ejor.2018.06.017 0377-2217/© 2018 Elsevier B.V. All rights reserved. Please cite this article as: M. Karatas, E. Yakıcı, An analysis of p-median location problem: Effects of backup service level and demand assignment policy, European Journal of Operational Research (2018), https://doi.org/10.1016/j.ejor.2018.06.017