Improving fairness in ambulance planning by time sharing |
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| Institution: | 1. HEC Liège, Management School of the University of Liège, Liège, Belgium;2. School of Business and Economics, Maastricht University, Maastricht, the Netherlands;1. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern 67663 Germany;2. CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisboa 1049-001, Portugal;1. Université Laval, 2325 rue de la Terrasse, Québec G1V 0A6, Canada;2. CIRRELT, Université Laval, Pavillon Palasis-Prince, bureau 2415, 2325 rue de la Terrasse, Québec G1V 0A6, Canada;3. École Polytechnique de Montréal, C.P. 6079, succursale Centre-ville, Montréal H3C 3A7, Canada;4. GERAD, 3000 chemin de la Côte-Sainte-Catherine, Montréal H3T 2A7, Canada;1. Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand;2. RWTH Aachen University, Templergraben 64, Aachen 52056, Germany;3. Innsbruck University, Universitätsstr. 15, Innsbruck 6020, Austria;4. University of Portsmouth, Portland Street, Portsmouth PO1 3DE, United Kingdom;1. Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università degli Studi di Siena, Via Roma 56, Siena 53100, Italy;2. Warwick Business School, University of Warwick, Coventry, CV4 7AL England, United Kingdom;3. Dipartimento di Ingegneria, Università degli studi Roma Tre, Via della Vasca Navale 79, Roma 00146, Italy;4. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università degli Studi di Roma “Tor Vergata”, via del Politecnico 1, Roma 00133, Italy |
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| Abstract: | Most literature on the ambulance location problem aims to maximize coverage, i.e., the fraction of people that can be reached within a certain response time threshold. Such a problem often has one optimum, but several near-optimal solutions may exist. These may have a similar overall performance but provide different coverage for different regions. This raises the question: are we making ‘arbitrary’ choices in terms of who gets coverage and who does not? In this paper we propose to share time between several good ambulance configurations in the interest of fairness. We argue that the Bernoulli–Nash social welfare measure should be used to evaluate the fairness of the system. Therefore, we formulate a nonlinear optimization model that determines the fraction of time spent in each configuration to maximize the Bernoulli–Nash social welfare. We solve this model in a case study for an ambulance provider in the Netherlands, using a combination of simulation and optimization. Furthermore, we analyze how the Bernoulli–Nash optimal solution compares to the maximum-coverage solution by formulating and solving a multi-objective optimization model. |
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