A Rolling-Space Branch-and-Price Algorithm for the Multi-Compartment Vehicle Routing Problem with Multiple Time Windows

TL;DR

This paper introduces a novel branch-and-price algorithm with a rolling-space approach for solving the complex multi-compartment vehicle routing problem with multiple time windows, considering practical operational constraints.

Contribution

It develops an exact algorithm with acceleration strategies and a rolling-space framework to efficiently solve large-scale, real-world instances of the multi-compartment vehicle routing problem.

Findings

The proposed method effectively solves large instances.

Acceleration strategies improve computational stability.

Real-world inspired instances demonstrate practical applicability.

Abstract

This paper investigates the multi-compartment vehicle routing problem with multiple time windows (MCVRPMTW), an extension of the classical vehicle routing problem with time windows that considers vehicles equipped with multiple compartments and customers requiring service across several delivery time windows. The problem incorporates three key compartment-related features: (i) compartment flexibility in the number of compartments, (ii) item-to-compartment compatibility, and (iii) item-to-item compatibility. The problem also accommodates practical operational requirements such as driver breaks. To solve the MCVRPMTW, we develop an exact branch-and-price (B&P) algorithm in which the pricing problem is solved using a labeling algorithm. Several acceleration strategies are introduced to limit symmetry during label extensions, improve the stability of dual solutions in column generation, and enhance the branching process. To handle large-scale instances, we propose a rolling-space B&P algorithm that integrates clustering techniques into the solution framework. Extensive computational experiments on instances inspired by a real-world industrial application demonstrate the effectiveness of the proposed approach and provide useful managerial insights for practical implementation.