EURO 2025 Leeds
Abstract Submission

2659. Ordinal Location Problems and Consistent Shortest Paths

Invited abstract in session MD-48: Applications of Location Methods, stream Locational Analysis.

Monday, 14:30-16:00
Room: Parkinson B09

Authors (first author is the speaker)

1. Renée Lamsfuß
2. Kathrin Klamroth
Department of Mathematics and Informatics, University of Wuppertal
3. Michael Stiglmayr
School of Mathematics and Natural Sciences, University of Wuppertal
4. Julia Sudhoff
Bergische Universität Wuppertal

Abstract

We consider ordinal location problems on graphs, where in addition to the edge length, a category is associated with each edge. We assume that we have two categories to choose from, where one category is strictly preferred over the other. As an example, we consider the safety of an edge and categorize edges as safe (green) and unsafe (red) from the perspective of a cyclist.
Although a value function that assigns monetary costs to the categories is not known in general, we can still formulate a biobjective optimization problem using the preference information from the ordering of the categories.
We are now not only interested in finding an optimal location, but also require the shortest paths to be consistent. Specifically, a particular decision to choose an efficient customer-to-facility path must align with all other customer-to-facility paths. Speaking of safe and unsafe edges, choosing a longer path over safe edges once induces that choosing a shorter, but unsafe customer-to-facility route is prohibited in the following.
In this talk, we introduce a notion of consistency and analyze the solutions in terms of supportedness. We propose an algorithmic approach to construct consistent solutions iteratively and demonstrate it at a medium size instance in the city of Wuppertal, Germany.

Keywords

Status: accepted

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