Title: Clustering-based CVRP model for route optimisation in urban LPG distribution

Authors: Danışment Vural; Anıl Uyanık; Aylin Güler; Seda Koldemir; Selinay Akdeniz

Addresses: Department of Industrial Engineering, Atılım University, Gölbaşı 06836 Ankara, Turkey ' Department of Industrial Engineering, Atılım University, Gölbaşı 06836 Ankara, Turkey ' Department of Industrial Engineering, Atılım University, Gölbaşı 06836 Ankara, Turkey ' Department of Industrial Engineering, Atılım University, Gölbaşı 06836 Ankara, Turkey ' Department of Industrial Engineering, Atılım University, Gölbaşı 06836 Ankara, Turkey

Abstract: This study presents a two-phase optimisation framework for improving urban liquefied petroleum gas (LPG) distribution efficiency. The approach integrates k-means clustering for customer segmentation with a capacitated vehicle routing problem (CVRP) formulated as a mixed integer programming (MIP) model. The model, implemented in GAMS, accounts for vehicle capacity, daily distance limits, and depot return constraints. Using real-world operational data from 22 customers, the Elbow method identified four spatially compact clusters, reducing computational complexity and enabling locally optimised routing. Each cluster was solved independently, yielding a 15.9% reduction in total travel distance compared to current routes, without increasing fleet size. The proposed method produced more balanced and non-overlapping delivery routes. Overall, the results demonstrate that combining clustering with mathematical optimisation enhances delivery efficiency, reduces operational costs, and provides a scalable framework applicable to medium-sized fuel distribution networks.

Keywords: capacitated vehicle routing problem; CVRP; clustering; k-means; Elbow method; mixed integer programming; MIP; route optimisation; liquefied petroleum gas; LPG.

DOI: 10.1504/IJBPIM.2026.155183

International Journal of Business Process Integration and Management, 2026 Vol.13 No.2, pp.153 - 161

Received: 23 Oct 2025
Accepted: 12 Mar 2026
Published online: 28 Jul 2026 *

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