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2690. Exact solution approaches for the nested p-center problem

Invited abstract in session MA-61: Advances in Location Analysis , stream Locational Analysis.

Monday, 8:30-10:00
Room: S10 (building: 101)

Authors (first author is the speaker)

1. Christof Brandstetter
Institute of Business Analytics and Technology Transformation, Johannes Kepler University Linz
2. Markus Sinnl
Institute of Business Analytics and Technology Transformation, Johannes Kepler University Linz

Abstract

Consistent solutions are vital in multi-period facility location problems, especially for long-term planning. In this work, we present various exact solution approaches
on the nested p-center problem, a recently introduced variation of the well-known (vertex) p-center problem, which can be defined as follows:
Given a set of locations and a finite time horizon, in each time period, a set of open facilities needs to be opened, where the set of a time period, needs to be a subset of
the set of open facilities in the following period. The goal is to minimize the sum of the maximal distance between any customer and its nearest open facility over the time horizon.

In our work, we present different mixed integer linear programming formulations on the nested p-center problem, which are solved using exact
solution methods like Bender's Decomposition or branch-and-bound. Furthermore, we have developed a solution framework to increase the performance in terms
of runtime on all formulations by adopting a diverse set of methods, like cut separation, lifted optimality cuts or preprocessing.

The different formulations and methods used are analyzed in a computational study on benchmark
instances, known from previous literature and the managerial implications of the nesting property are analyzed.

Keywords

Status: accepted

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