Fair facility allocation in emergency service system

The request of equal accessibility must be respected to some extent when dealing with problems of designing or rebuilding of emergency service systems. Not only the disutility of the average user but also the disutility of the worst situated user must be taken into consideration. Respecting this principle is called fairness of system design. Unfairness can be mitigated to a certain extent by an appropriate fair allocation of additional facilities among the centres. In this article, two criteria of collective fairness are defined in the connection with the facility allocation problem. To solve the problems, we suggest a series of fast algorithms for solving of the allocation problem. This article extends the family of the original solving techniques based on branch-and-bound principle by newly suggested techniques, which exploit either dynamic programming principle or convexity and monotony of decreasing nonlinearities in objective functions. The resulting algorithms were tested and compared performing numerical experiments with real-sized problem instances. The new proposed algorithms outperform the original approach. The suggested methods are able to solve general min-sum and min-max problems, in which a limited number of facilities should be assigned to individual members from a finite set of providers.