Workload Equity in Multi-Period Vehicle Routing Problems

TL;DR

This paper presents a two-phase method for multi-period vehicle routing that achieves workload equity over several days without increasing transportation costs, especially effective for horizons of five days or more.

Contribution

The paper introduces a novel two-phase approach to achieve workload equity in multi-period vehicle routing problems without cost trade-offs for sufficiently long planning horizons.

Findings

Workload equity improves with longer planning horizons.

Near-optimal workload equity and routing costs are achievable for horizons of five days or more.

The proposed method effectively balances workloads over multiple days.

Abstract

An equitable distribution of workload is essential when deploying vehicle routing solutions in practice. For this reason, previous studies have formulated vehicle routing problems with workload-balance objectives or constraints, leading to trade-off solutions between routing costs and workload equity. These methods consider a single planning period; however, equity is often sought over several days in practice. In this work, we show that workload equity over multiple periods can be achieved without impact on transportation costs when the planning horizon is sufficiently large. To achieve this, we design a two-phase method to solve multi-period vehicle routing problems with workload balance. Firstly, our approach produces solutions with minimal distance for each period. Next, the resulting routes are allocated to drivers to obtain equitable workloads over the planning horizon. We conduct extensive numerical experiments to measure the performance of the proposed approach and the level of workload equity achieved for different planning-horizon lengths. For horizons of five days or more, we observe that near-optimal workload equity and optimal routing costs are jointly achievable.