Fair emergency system design under uncertainty

In host situations, a public service system is designed so that the average disutility is minimized. In this paper, we deal with a special member of a category of public service systems known as the emergency service system. Designers of this sort of service system must take into consideration not only the disutility of the average user, but also the disutility of the worst situated user. Optimization of the average user disutility relates to the large weighted p-median problem. The necessity of solving large instances has led to the approximate approach based on a radial formulation, which enables the solving of larger instances in admissible time and making use of a universal IP-solver. The p-median problem objective denoted as a min-sum criterion often causes a situation where the average user’s disutility is minimal, but the disutility of the worst situated user can nonetheless be extremely high, which is considered unfair. The objective of a fair emergency service system design is to minimize perceived disutility of the worst situated system users under various scenarios, where the model uncertainty is connected with randomly occurring events. In this paper, we focus on two different modelling techniques, which enables designing a fair emergency service system under uncertainty with minimal disutility perceived by the worst situated users. We also deal with processing uncertainty, which can be modelled either by a finite set of scenarios or using fuzzy values.