Title: A mixed integer programming model and a hybrid VNS/TS algorithm for GVRP with the heterogeneous fleet, time windows, and vehicle selection
Authors: Emine Akyol Özer; Melis Alpaslan Takan; Tuğba Saraç
Addresses: Department of Industrial Engineering, Eskisehir Technical University, 26555, Eskisehir, Turkey ' Department of Industrial Engineering, Faculty of Engineering, Bilecik Şeyh Edebali University, TR, 11100 Bilecik, Turkey ' Industrial Engineering Department, Eskisehir Osmangazi University, Eskisehir, Turkey
Abstract: The green vehicle routing problem (GVRP) is a logistical problem considering environmental effects. Existing GVRP studies considered important constraints such as time windows (TW) or heterogeneous fleets (HF), but mostly, they assumed that there is an available fleet where all vehicles can be used. However, some companies build their fleets using rented cars by selecting the vehicle numbers and types. Therefore, we focus on GVRP with the HF, TW, and vehicle selection to minimise travel, rental, and emission costs. A MIP model, and a hybrid algorithm combining variable neighbourhood search with the tabu search algorithm are proposed. The performance of the algorithm is demonstrated by using the modified Solomon test instances. The proposed algorithm could produce high-quality solutions within a short computation time. In addition, an average improvement of 45.49% and 16.69% are achieved respectively compared to the first scenario and the second scenario where the vehicles are held constant. [Submitted: 6 February 2023; Accepted: 9 January 2024]
Keywords: heterogeneous fleet green vehicle routing problem; HFGVRP; green vehicle routing problem with time window; GVRPTW; vehicle selection; variable neighbourhood search; VNS; tabu search; TS.
European Journal of Industrial Engineering, 2025 Vol.19 No.4, pp.429 - 453
Received: 06 Feb 2023
Accepted: 03 Jan 2024
Published online: 02 Jun 2025 *