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Improving fairness in ambulance planning by time sharing. (English) Zbl 1430.90378
Summary: 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.
MSC:
90B80 Discrete location and assignment
90B06 Transportation, logistics and supply chain management
90C29 Multi-objective and goal programming
90C90 Applications of mathematical programming
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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