Sink location to find optimal shelters in evacuation planning

Abstract

The sink location problem is a combination of network flow and location problems: From a given set of nodes in a flow network a minimum cost subset W has to be selected such that given supplies can be transported to the nodes in W . In contrast to its counterpart, the source location problem which has already been studied in the literature, sinks have, in general, a limited capacity. Sink location has a decisive application in evacuation planning, where the supplies correspond to the number of evacuees and the sinks to emergency shelters.We classify sink location problems according to capacities on shelter nodes, simultaneous or non-simultaneous flows, and single or multiple assignments of evacuee groups to shelters. Resulting combinations are interpreted in the evacuation context and analyzed with respect to their worst-case complexity status.There are several approaches to tackle these problems: Generic solution methods for uncapacitated problems are based on source location and modifications of the network. In the capacitated case, for which source location cannot be applied, we suggest alternative approaches which work in the original network. It turns out that latter class algorithms are superior to the former ones. This is established in numerical tests including random data as well as real world data from the city of Kaiserslautern, Germany.

Optimising shelter location and evacuation routing operations: The critical issues

“…As to be expected considering the difficulty of these models, five case studies developed ad-hoc heuristics, such as simulated annealing and genetic algorithms (Li et al 2012;Goerigk, Deghdak and Heßler 2014;Gama, Santos and Scaparra 2016;Heßler and Hamacher 2016;Shahparvari et al 2016). In some cases, heuristic solutions have been compared with those of commercial optimisation software (Gama, Santos and Scaparra 2016) or exact methods, such as source location algorithms (Heßler and Hamacher 2016) and -constraint techniques (Shahparvari et al 2016). None of the nine case studies included the development of a user-friendly GIS-based interface (Q24) as a supporting tool for using the models.…”

“…The model is solved with a Simulated Annealing algorithm whose applicability is tested on a realistic case study for Wake County, North Carolina (USA). Heßler and Hamacher (2016) propose a sink location problem to mimic a self-evacuation process,…”

“…Six of the case studies have attempted at incorporating congestion issues (Q16). Goerigk, Deghdak and Heßler (2014), Heßler and Hamacher (2016) and Shahparvari et al (2016) tackle congestion in a simplified way by using capacitated network arcs. In Li et al (2012), congestion is captured in the dynamic UE model, which computes time-dependent travel times.…”

“…Our analysis of the nine case studies shows that three different categories of evacuees can be identified: SES, SED, and SE. However, these evacuee categories have been considered either as separate ones (Coutinho-Rodrigues, Tralhão and Alçada-Almeida 2012; B T Y K K a and Bozkaya 2015; Gama, Santos and Scaparra 2016;Shahparvari et al 2016;Bayram and Yaman 2017) or as a combination of two out of three (Li et al 2012;Goerigk, Deghdak and Heßler 2014;Heßler and Hamacher 2016). To be more comprehensive, even if undoubtedly more complex, all the three different categories should be considered in an integrated manner given that they share common resources.…”

“…The remaining three case studies integrate two categories of evacuees together. Li et al(2012) andHeßler and Hamacher (2016) deal with both SES and SED whileGoerigk, Deghdak and…”