Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie Joint relocation and districting using a nested compliance model for EMS systems Kanchala Sudtachat a, ⁎ , Maria E. Mayorga b , Sunarin Chanta c , Laura A. Albert d a School of Manufacturing Engineering, Institute of Engineering, Suranaree University of Technology, 111 University Avenue, Muang, Nakhon Ratchasima 30000, Thailand b Department of Industrial and Systems Engineering, North Carolina State University, Campus Box 7906, Raleigh, NC, USA c Department of Industrial Management, King Mongkut’s University of Technology North Bangkok, Muang, Prachinburi 25230, Thailand d Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, USA ARTICLE INFO Keywords: Emergency medical service Relocation and districting problems Tabu search heuristic ABSTRACT Emergency medical service (EMS) systems provide medical care to pre-hospital patients who need rapid response and transport. This paper proposes a modeling approach for joint relocation and districting strategies in EMS systems. This combined approach aims to increase the efficiency of EMS systems. We extend the nested-com- pliance model (which provides a relocation policy) to consider an upper bound on relocation time by parti- tioning the whole region into smaller sub-areas (districts). We analyze the decision regarding how to partition the service area into smaller sub-areas in which each sub-area operates independently under separate relocation strategies. Once the district solution is determined, a Tabu search is used to allocate stations and zones to districts and the optimal nested-compliance model solution is applied to each sub-area. The objective is to maximize the overall realized expected coverage. The performance of the combined relocation and districting policies are compared to a static policy (non-relocation and non-district) based on the adjusted maximum ex- pected covering location problem (AMEXCLP) in a simulated system using real-world data. The numerical results show the benefits of our model over the AMEXCLP based on average realized coverage and the fraction of covered calls responded to by the first closest ambulance in the dispatching rank list. 1. Introduction The goal of emergency medical service (EMS) systems is to save the lives of out-of-hospital patients. The most common performance mea- sure used to evaluate the efficiency of EMS systems is coverage, which is the proportion of calls that can be responded to within a pre-specified time standard. Coverage is related to the allocation of ambulances to stations in the service areas of potential demand zones. Theoretically, a call is said to be covered if an ambulance is dispatched to respond to the call from a station that is within a pre-specified response time threshold (RTT). In reality, the results of realized coverage (whether the call is actually reached within the time standard, not whether it should have been reached) might be different. Relocation, which involves moving ambulances to replace ambulances that have become busy in order to prevent certain demand areas from being uncovered, is a well-known strategy to improve the performance of EMS systems. Sudtachat, Mayorga, and Mclay (2016) suggested that limiting relocation time was important for the implementation of a relocation model in real-world systems based on the average realized coverage measure. Long reloca- tion times could result in the loss of calls that arrive during the movement of an ambulance to a new station. Therefore, the decisions regarding relocation could be improved by imposing some limitation on relocation time. One possible way to impose a relocation time restric- tion is to partition the whole service area into districts. In this work, we incorporate the districting problem into our relocation model. The service area is partitioned into small sub-areas (districts). Each sub-area operates under a particular relocation strategy based on a compliance table policy. Another benefit of implementing a districting strategy is that it can be used to balance the efficiency of the EMS system among different regions. One such measure is the fraction of calls that are serviced (covered) by the frst closest ambulance in the dispatching rank list. A first closest ambulance refers to the ambulance that is closest to the demand zone among all of those stationed; this is different than the closest ambulance among those available. When a call arrives we as- sume that the closest available ambulance is dispatched, but if the first closest ambulance is not available, then the second closest or the third https://doi.org/10.1016/j.cie.2020.106327 Received 17 July 2019; Received in revised form 27 January 2020; Accepted 27 January 2020 ⁎ Corresponding author. E-mail addresses: kanchala@sut.ac.th (K. Sudtachat), memayorg@ncsu.edu (M.E. Mayorga), sunarin.c@fitm.kmutnb.ac.th (S. Chanta), laura@engr.wisc.edu (L.A. Albert). Computers & Industrial Engineering 142 (2020) 106327 0360-8352/ © 2020 Elsevier Ltd. All rights reserved. T