On single-source capacitated facility location with cost and fairness objectives

We consider a location problem where a planner has to decide where to open facilities which have to be reached by customers at their own cost. The planner has two objectives: cost minimization and customer satisfaction. We argue that performance and fairness, as structural components of customer satisfaction, are both captured by an equity measure called conditional β-mean. We thus formulate the Fair Single-Source Capacitated Facility Location (F-SSCFL) problem, where the cost minimization objective is paired with the conditional β-mean minimization objective. The resulting formulation is a bi-objective mixed-integer linear program. A weighted sum method is developed to generate a small representative set of efficient solutions to the F-SSCFL problem, and a Benders decomposition approach is implemented to handle large-scale instances. On small/medium-scale instances, we analyse the trade-off between cost and conditional β-mean, showing that the model may be used as a managerial tool to balance direct costs and customer service. We also compare the quality of the solutions obtained with those obtained using alternative equity measures. On large-scale instances, we test Benders decomposition, showing that it is able to find good quality solutions in a relatively short computing time.