A Benders decomposition algorithm for the maximum availability service facility location problem

This paper introduces the maximum availability service facility location problem, which integrates the set covering and flow capturing problems to service both stationary and mobile demand in an urban region. The problem has applications in location of government offices, medical facilities and polling stations. We present a mixed-integer linear programming formulation and develop a Benders decomposition algorithm. We implement several acceleration techniques including multi-cut and Pareto-optimal cut generation. We construct these cuts analytically using closed-form expressions for subproblem solutions. Our best algorithm can optimally solve randomly generated instances with up to one thousand nodes, one million commuting customers and one hundred candidate facilities. We also conduct a case study with real data from the city of Chicago and show an application of our model for the location of medical facilities in a pandemic situation. We find that confinement restrictions in a pandemic do not significantly affect the total demand coverage, but facility layout may be significantly different under different confinement levels.