Scheduling activities with time-dependent durations and resource consumptions

TL;DR

This paper addresses complex time-dependent scheduling problems involving resource constraints, proposing a dynamic discretization algorithm and preloading techniques to improve computational efficiency, demonstrated through electric vehicle routing scenarios.

Contribution

It introduces a novel dynamic discretization discovery algorithm and preloading techniques for efficient scheduling with time-dependent durations and resource consumptions.

Findings

The proposed methods effectively reduce computational effort.

The approach successfully models electric vehicle routing with recharging.

Results show improved scheduling efficiency in case studies.

Abstract

In this paper we study time-dependent scheduling problems where activities consume a resource with limited availability. Activity durations as well as resource consumptions are assumed to be time-dependent and the resource can be replenished between activities. Because of the interaction of time-dependent activity durations and resource consumptions, scheduling policies based on starting all activities as early as possible may fail due to unnecessarily high resource consumptions. We propose a dynamic discretization discovery algorithm that generates a partially time-expanded network during the search. We propose preloading techniques allowing to significantly reduce the computational effort if the approach is embedded in an iterative solution procedure that frequently evaluates activity sequences that start with the same activities. We evaluate our approaches on a case of routing a fleet of electric vehicles in which vehicles can recharge batteries during the route.