The minimum p-envy location problem with requirement on minimum survival rate

• Survival function was incorporated into the model for evaluating system performance.
• The objective is to minimize total envy among customers weighted by demand proportion.
• Vehicle busy probabilities estimated by hypercube model are used as server weights.
• Results in non-dominated solutions—lowest total envy and most number of lives saved.

In location problems for the public sector such as emergency medical service (EMS) systems, the issue of equity is an important factor for facility design. Several measures have been proposed to minimize inequity of a system. This paper considers an extension to the minimum p-envy location model by evaluating the objective of the model based on a survival function instead of on a distance function since survival probability is directly related to patient outcomes with a constraint on minimum survival rate. The model was tested on a real world data set from the EMS system at Hanover County, VA, and also compared to other location models. The results indicate that, not only does the enhanced p-envy model reduce inequity but we also find that more lives can be saved by using the survival function objective. A sensitivity analysis on different quality of service measures (survival probability and traveled distance) and different choices of priority assigned to serving facility is discussed.