An integer L-shaped algorithm for the vehicle routing problem with time windows and stochastic demands

Author(s)

De La Vega, Jonathan ; Gendreau, Michel ; Morabito, Reinaldo ; Munari, Pedro ; Ordonez, Fernando

• Document type: Journal article
• Source: European Journal of Operational Research; v. 308, n. 2, p. 20-pg., 2023-02-28.

Abstract

This paper addresses the vehicle routing problem with time windows and stochastic demands (VRPTWSD). The problem is modeled as a two-stage stochastic program with recourse, in which routes are designed in the first stage and executed in the second. A failure occurs if the load of the vehicle is insufficient to meet the observed demand of a customer, implying recourse actions to recover feasibility. We consider the classical recourse policy where reactive trips to the depot are made in case of failures and a fixed rule-based recourse policy where, in addition, preventive trips are allowed. These recourse actions delay the vehicle and may cause further failures if the arrival times on the remaining customers of the planned route do not satisfy their time windows. An additional recourse action is used to service the customers whose time windows would be violated in the planned routes. We propose an Integer L-shaped algorithm considering the mentioned recourse actions. To the best of our knowledge, this is the first tailored exact approach for the VRPTWSD. Computational experiments using 112 benchmark in-stances evaluate the performance of this algorithm as well as the quality of the stochastic problem solu-tions. The results indicate significant savings in the solutions when using the fixed rule-based policy and round-trip recourse actions instead of the classical policy. Additionally, the algorithm performed better with the fixed rule-based policy, solving to optimality all instances with up to 34 customers, and taking less time on instances that were solved to optimality with both policies.(c) 2022 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 18/01523-0 - Benders-branch-and-cut for the vehicle routing problem with multiple deliverymen and stochastic demand
• Grantee: Jonathan Justen de La Vega Martínez
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 19/23596-2 - Rich vehicle routing problems: models and algorithms for deterministic and stochastic variants
• Grantee: Pedro Augusto Munari Junior
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/14582-7 - Stochastic Programming and Robust Optimization to Variants of Vehicle Routing Problem: Formulations and Exact Methods
• Grantee: Jonathan Justen de La Vega Martínez
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 17/06434-3 - Two-stage robust optimization with recourse for the vehicle routing problem with time windows and multiple deliverymen
• Grantee: Jonathan Justen de La Vega Martínez
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate