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Logistics Hub Location Optimization: A K-Means and P-Median Model Hybrid Approach Using Road Network Distances

Muhammad Abdul Rahman, Muhammad Aamir Basheer, Zubair Khalid, Muhammad Tahir, Momin Uppal

TL;DR

This paper tackles the problem of last-mile hub placement by measuring distances over an actual road network rather than Euclidean space. It introduces a hybrid workflow that clusters delivery points with K-Means using road-network distances, followed by hub localization via a P-Median model, with weights drawn from delivery counts and population (via WorldPop). On a Lahore case study using Muller & Phips data and NTRC road networks, the approach reduces the average distance per delivery from 7801 m to 6986 m (a gain of 815 m), demonstrating the value of road-aware optimization for urban logistics. The method offers a practical, data-driven pathway to lower fuel use and emissions while improving delivery efficiency in developing-city contexts, and it can be extended with rider allocation and additional hub-relevant criteria.

Abstract

Logistic hubs play a pivotal role in the last-mile delivery distance; even a slight increment in distance negatively impacts the business of the e-commerce industry while also increasing its carbon footprint. The growth of this industry, particularly after Covid-19, has further intensified the need for optimized allocation of resources in an urban environment. In this study, we use a hybrid approach to optimize the placement of logistic hubs. The approach sequentially employs different techniques. Initially, delivery points are clustered using K-Means in relation to their spatial locations. The clustering method utilizes road network distances as opposed to Euclidean distances. Non-road network-based approaches have been avoided since they lead to erroneous and misleading results. Finally, hubs are located using the P-Median method. The P-Median method also incorporates the number of deliveries and population as weights. Real-world delivery data from Muller and Phipps (M&P) is used to demonstrate the effectiveness of the approach. Serving deliveries from the optimal hub locations results in the saving of 815 (10%) meters per delivery.

Logistics Hub Location Optimization: A K-Means and P-Median Model Hybrid Approach Using Road Network Distances

TL;DR

This paper tackles the problem of last-mile hub placement by measuring distances over an actual road network rather than Euclidean space. It introduces a hybrid workflow that clusters delivery points with K-Means using road-network distances, followed by hub localization via a P-Median model, with weights drawn from delivery counts and population (via WorldPop). On a Lahore case study using Muller & Phips data and NTRC road networks, the approach reduces the average distance per delivery from 7801 m to 6986 m (a gain of 815 m), demonstrating the value of road-aware optimization for urban logistics. The method offers a practical, data-driven pathway to lower fuel use and emissions while improving delivery efficiency in developing-city contexts, and it can be extended with rider allocation and additional hub-relevant criteria.

Abstract

Logistic hubs play a pivotal role in the last-mile delivery distance; even a slight increment in distance negatively impacts the business of the e-commerce industry while also increasing its carbon footprint. The growth of this industry, particularly after Covid-19, has further intensified the need for optimized allocation of resources in an urban environment. In this study, we use a hybrid approach to optimize the placement of logistic hubs. The approach sequentially employs different techniques. Initially, delivery points are clustered using K-Means in relation to their spatial locations. The clustering method utilizes road network distances as opposed to Euclidean distances. Non-road network-based approaches have been avoided since they lead to erroneous and misleading results. Finally, hubs are located using the P-Median method. The P-Median method also incorporates the number of deliveries and population as weights. Real-world delivery data from Muller and Phipps (M&P) is used to demonstrate the effectiveness of the approach. Serving deliveries from the optimal hub locations results in the saving of 815 (10%) meters per delivery.
Paper Structure (8 sections, 3 equations, 4 figures, 1 table)

This paper contains 8 sections, 3 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Description and Formulation
  4. Cluster Formation
  5. Hub Location Optimization
  6. Application and Analysis
  7. Results
  8. Conclusion

Figures (4)

  • Figure 1: Comparison of Euclidean and road network distances. The road network distance is 926 meters while the Euclidean distance is 290 meters.
  • Figure 2: (a) - (e) Convex hull of each cluster formed from iteration 1 to 5. (f) Monotonically decreasing curve showing the change in average distance per delivery with each iteration.
  • Figure 3: Data sources used for the proposed approach.
  • Figure 4: Centroids of clusters for phase 1 and phase 2.