The multi-period $p$-center problem with time-dependent travel times

TL;DR

This paper extends the p-center problem to multiple periods with time-dependent travel times and mobile facilities, providing analysis, a heuristic solution method, and computational validation on realistic road network data.

Contribution

It introduces a multi-period p-center model with time-varying travel times and develops a decomposition heuristic for solving it efficiently.

Findings

The heuristic finds high-quality solutions within reasonable time.

The problem structure analysis reveals relationships with single-period models.

Computational tests on Paris road data demonstrate effectiveness.

Abstract

This paper deals with a multi-period extension of the p-center problem, in which arc traversal times vary over time, and facilities are mobile units that can be relocated multiple times during the planning horizon. The problem arises in several applications, such as emergency services, in which vehicles can be relocated in anticipation of traffic congestion. First, we analyze the problem structure and its relationship with its single-period counterpart, including a special case. Then, the insight gained with this analysis is used to devise a decomposition heuristic. Computational results on instances based on the Paris (France) road graph indicate that the algorithm is capable of determining good-quality solutions in a reasonable execution time.