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

TL;DR

The paper tackles the multi-compartment vehicle routing problem with multiple time windows (MCVRPMTW), a challenging integration of loading constraints, time-window flexibility, and daily driver regulations. It develops an exact branch-and-price algorithm with a labeling-based pricing subproblem that handles time windows, compartments, and compatibility, augmented by dominance and resource-extension mechanisms. To scale to large instances, the authors introduce a rolling-space extension using overlapping clusters and a post-processing feasibility check for multi-compartment constraints, along with acceleration strategies across pricing, Master, and branching stages. Computational experiments on industrial-inspired data demonstrate the method’s effectiveness and scalability, yielding substantial reductions in vehicles and total distance and providing actionable managerial insights. The proposed RS-B&P approach shows promise for practical deployment in complex logistics settings and offers a robust framework for future enhancements in multi-constraint VRP variants.

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.

Figures (3)

• Figure 1: MCVRPMTW Example
• Figure 2: Rolling Space Example
• Figure 3: Evolution of the Objective and Execution Time with the Number of Compartments for Instances L4 to L7

Theorems & Definitions (5)

• Example 1
• Proposition 1
• proof
• Proposition 2
• proof