UNIVERSITY OF CALIFORNIA Santa Barbara Emergency Medical Service Ambulance System Planning: History and Models A Thesis submitted in partial satisfaction of the requirements for the degree Master of Arts in Geography by Carlos Alain Baez Tapia Committee in charge: Professor Richard L. Church, Chair Professor Stuart H. Sweeney Professor Alan T. Murray December 2017 The thesis of Carlos Alain Baez Tapia is approved. _____________________________________________ Alan T. Murray _____________________________________________ Stuart H. Sweeney _____________________________________________ Richard L. Church, Committee Chair December 2017 Emergency Medical Service Ambulance System Planning: History and Models Copyright © 2017 by Carlos Alain Baez Tapia iii ACKNOWLEDGEMENTS First, I would like to dedicate this thesis to my grandpa Carlos Baez who is unfortunately not here to see me finish this thesis. Que en paz descanse. Second, I want to thank my parents Carlos and Elva Baez for the incredible sacrifices they had to make beginning with our journey from Michoacán, Mexico all the way through UCSB and today. Third, I want to thank my family: my grandmas, uncles (including Gordo), aunts, my brother Erwin and even my sister Amber. In one way or another I would not be here without your help. Fourth, I want to thank my colleagues at UCSB and elsewhere that helped in more way or another. I especially want to thank Grant Brokenzie, Dan Ervin, Mike Alonzo, Kevin Mwenda, Olaf Mezner, Lumari Pardo, Jacky Banks(!), Matt and Tim Niblett, Yiting Ju, Dylan Parenti, the fifth floor, and everyone else (not that I mean to exclude anyone but I have a filing deadline!). I also want to thank Jose Saleta who was invaluable to every graduate student at UCSB Geography and just a wonderful person who is dearly missed. Fifth, I want to thank all my friends (not mentioned above) that helped me get here in one way or another. I don’t think I could’ve done it without your support (that includes letting me crash on your couch). So thank you Jesse Vasquez, Erin Corrigan, Sonya, Michelle Himden, Saba Dowlatshahi, Ryan Darby, Svetlin “Foolio” Bostandjiev, Don “I love Mayo” Buyers, Maciek Baranski, Atif Khan, Taylor Horgan, Laurel Patterson, all my friends from the Merton, Fernando Castorena, Sergio Herrera and Lenny, Yuri N., Andrew “Ding Dong” Johnson (unfortunately), and that’s again just at the top of my head. Sixth, shout out to my bros/the gang Nick, Yasin, Cody, Gaykers, Rel (I guess), Colleen, Vicky, Debi, Andrew, Quade, JeBee, Arman Bro, Jen and Dorian, and also, Elaine and Joe, who unfortunately can’t be here with us. For lack of better words, your friendship means so much to me. Seventh, I really want to thank my adviser Rick “The Doc” Church. I don’t know how I’m still here or where I would be it wasn’t for his brilliance, compassion, and patience. We’re still not done but thanks keeping me along! Lastly, I would like to say, THANKS OBAMA. In 2012, I didn’t know if I was going to be able to stay at UCSB but out of nowhere DACA came out. So thank you, President Barrack Obama. #RESIST iv ABSTRACT Emergency Medical Service Ambulance System Planning: History and Models by Carlos Alain Baez Tapia Integer linear programming models that incorporate probabilistic and stochastic components represent one approach for capturing the stochastic nature of emergency medical service ambulance systems. This includes modeling non-deterministic call arrival and servicing rates and congestion in the ambulance network (i.e., ambulance unavailability). These models focus on maximizing the total population that can find an available ambulance within a set service time standard (s) with a probability of at least α%. In MALP the concept of local vehicle busyness estimates is introduced to estimate the availability of service in a neighborhood given the neighborhood’s level of demand and the number of ambulance vehicles located in the neighborhood. QMALP is an extension of MALP where queue-theory derived parameters are implemented in the MALP model framework in order to relax the assumption that the probability of different ambulances being busy are independent. Despite this considerable development, several concerns remained about MALP and QMALP, namely the districting assumption where its assumed that a neighborhood’s calls for service are served only by an ambulance in the area, that ambulances in a neighborhood only serve calls for service originating within the neighborhood, or that at least the flow of ambulance service to and from external v neighborhoods was roughly equal. Questions have been raised about the validity of MALP and QMALP’s reliability estimates, that is, whether a neighborhood actually received α- reliable service. To address these issues, we developed the Resource-Constrained Queue-based Maximum Availability Location Problem (RC-QMALP). This model is based on a location-allocation framework that (1) assigns workload from neighborhoods to ambulances located within s and ambulance idle capacity to neighborhoods and (2) includes additional constraints designed to help ensure the validity of the original MALP and QMALP constraints used to establish whether a neighborhood can find an available ambulance with α-reliability. We also implemented a secondary minsum objective that minimizes the average travel distance between ambulances and the neighborhoods they service while maintaining the priority of the MALP and QMALP coverage objective. In this thesis, we validated RC-QMALP by comparing the reliable coverage levels predicted by the RC-QMALP to the ambulance system simulations that used the locational configurations suggested by the RC-QMALP. We found that MALP 2 and QMALP provided higher levels of reliable coverage and that RC-QMALP’s secondary objective has a negligible impact on system performance. However, RC-QMALP-based models provide more accurate estimates of reliable coverage and location solutions whose simulated reliable coverage performance was always within 5% of the optimal solution with the same system parameters (we tested 1,080 different model configurations). Our work suggests that (1) more work is needed on developing simulation models that can accommodate the modeling assumptions that underlie location optimization models and that (2) service vi reliability location models should consider additional factors such as ambulance workloads (and their distribution). vii TABLE OF CONTENTS 1. Introduction ........................................................................................................................................ 1 1.1 Thesis Scope and Motivation ....................................................................................................... 5 1.2 Thesis Organization ...................................................................................................................... 7 2. History of Emergency Medical Service System Planning .................................................................. 8 2.1 Early EMS Systems in the United States ..................................................................................... 8 2.2 Prelude to the Quantitative Revolution in EMS System Planning and Management ................. 11 2.3 Developments in Emergency Medical Service Policy ............................................................... 28 2.4 The Systems Approach for Planning and Managing Emergency Medical Services .................. 35 2.5 Location Science and EMS Systems .......................................................................................... 40 2.6 Discussion .................................................................................................................................. 64 3. Model Formulation Background ...................................................................................................... 65 3.1 Fundamental Models .................................................................................................................. 66 3.2 Modeling Capacity and Congestion in Location Models ........................................................... 74 3.3 Essential Probabilistic and Stochastic Location Models ............................................................ 94 4. The Resource Constrained Queuing Maximum Availability Location Problem ............................ 135 4.1 Model Formulation ................................................................................................................... 138 4.2 Model Components .................................................................................................................. 141 4.3 Discussion ................................................................................................................................ 144 5. Results and Analysis ...................................................................................................................... 154 5.1 Experiments .............................................................................................................................. 155 5.2 Results ...................................................................................................................................... 160 viii 6. Conclusion ...................................................................................................................................... 214 References .......................................................................................................................................... 216 Appendix