INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025

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Optimization of Courier Delivery Route among Hubs in Johor by

Using Mixed Integer Programming, Genetic Algorithm and Ant

Colony Optimization

Vevina Yau Jing Rou, Suliadi Firdaus Sufahani*

Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun

Hussein Onn Malaysia, Pagoh Edu Hub, 84600, Johor, Malaysia

*Corresponding Author

DOI: https://dx.doi.org/10.47772/IJRISS.2025.910000481

Received: 02 November 2025; Accepted: 08 November 2025; Published: 17 November 2025

ABSTRACT

The quick growth of e-commerce has significantly increased demand for courier services, creating pressure on

logistics infrastructure to manage delivery operations efficiently. This study focuses on the optimization of

courier delivery routes for GDex Express to determine the optimal delivery route based on distance and time

travelled among hubs in Johor. Mixed Integer Programming, Genetic Algorithm, and Ant Colony Optimization

were proposed in this study in order to solve the travelling salesman problem (TSP) by using Python software.

This study mainly focuses on 13 GDex Express delivery hubs in Johor with the data based on total distance

travelled and average time travelled that selected into three different time periods at 8.00 a.m., 1.00 p.m. and

6.00 p.m. for weekdays and weekends. There are two optimal delivery routes generated respectively in terms

of total distance travelled and average time travelled. The results shows that Mixed Integer Programming

provided optimal solution as benchmarking, while Genetic Algorithm outperformed Ant Colony Optimization

in comparing which algorithm is more closer to the optimal solution. Thus, this study provides solutions to the

GDex Express in order to improving the delivery effectiveness and reducing the operating costs by reducing

the travel time and distance.

Keywords – Courier services, GDex Express, Optimization, Mixed Integer Programming, Genetic Algorithm,

Ant Colony Optimization, Travelling Salesman Problem

INTRODUCTION

The quick growth of e-commerce has significantly impacted global logistics and delivery systems. E-

commerce, defined as the online purchasing and selling of products and services, has enabled businesses to

reach more customers through cost-effective and efficient means. The proliferation of digital devices such as

computers, tablets, and smartphones has further facilitated this trend. As a result, traditional business

operations have undergone radical changes, with the transportation and delivery sectors being among the most

affected (1). The need for reliable, fast, and efficient courier services has risen dramatically to meet the

demands of customers purchasing goods online (2).

Courier services play a crucial role in this ecosystem, offering specialized shipping solutions that prioritize

speed, reliability, and security. Unlike traditional postal services, courier services provide enhanced features

such as real-time tracking, customization options, and faster deliveries (3). In Malaysia, the evolution of

courier services dates to the British colonial era, with the establishment of Pos Malaysia in 1985 to facilitate

communication and package delivery. The advent of private courier companies in the 1980s brought more

efficient and professional delivery options, driven by technological advancements and growing economic

demands (4). Today, major courier service providers in Malaysia, such as GDex Express, Pos Laju, and DHL

Express, operate in a highly competitive market.

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025

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However, the rapid expansion of e-commerce has introduced challenges to the logistics infrastructure,

including bottlenecks in warehouses, sorting facilities, and delivery networks. Route optimization, a critical

aspect of courier operations, has become increasingly complex due to factors such as multiple hubs, variable

delivery quantities, and geographic constraints (5). Addressing these challenges requires innovative solutions

like the travelling salesman problem (TSP), an optimization problem focused on determining the optimal

courier delivery route among hubs in Johor based on distance and time. Previous studies have applied methods

such as Mixed Integer Programming, Genetic Algorithm, and Ant Colony Optimization to solve TSP,

demonstrating significant improvements in route planning and cost efficiency (6).

This study aims to determine the optimal delivery routes among courier hubs in Johor using advanced

optimization techniques. There are four objectives in this study, as gathering the data of distance and time

travelled among hubs for courier delivery of GDex Express in Johor, applying the modelling of mixed integer

programming, genetic algorithm and ant colony optimization to find the optimal delivery route in Johor. The

study also seeks to determine the optimal courier delivery route among hubs in Johor based on distance and

time and compare the performance of approximate algorithm against the benchmark optimal solutions

provided by mixed integer programming method on which provides solutions closet to the optimal outcomes.

By achieving these objectives, this research will provide valuable insights for enhancing operational efficiency,

reducing costs, and improving service reliability in Malaysia’s courier industry.

Materials and Methods

In this study, the location of 13 GDex Express delivery hubs in Johor were collected from the GDex Express

website (https://gdexpress.com/), while the distance and time travelled data among hubs were collected from

the Google Maps (https://www.google.com/maps). The distance travelled data among hubs is illustrated in

kilometer (km), while the time travelled data among hubs is illustrated in minutes (min). The time travelled

data were collected at three different times which are 8.00 a.m., 1.00 p.m. and 6.00 p.m. for weekdays and

weekends. The average time travelled data among hubs on weekdays is calculated by using the data from

Sunday to Thursday, while the average time travelled data among hubs on weekends is calculated by using the

data on Friday and Saturday. Then, the distance and time travelled data were used for future analysis.

Data Description

This study mainly focused on the courier delivery hubs in Johor state. There was a total of 13 courier delivery

hubs in the Johor area to be considered. The list of transit hubs is shown in Table 1, while the location of the

listed hubs is illustrated in Figure 1.

Table 1 List of Transit Hubs

Node

Name of Hub

Tangkak Hub

Muar Hub

Batu Pahat Hub

Pagoh Hub

Segamat Hub

Yong Peng Hub

Kluang Hub

Kulai Hub

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

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Senai Hub

Tampoi Hub

Pasir Gudang Hub

Kota Tinggi Hub

Pontian Hub

Fig. 1 Location of The Listed Hubs on Google Maps

Travelling Salesman Problem (TSP)

In this study, the travelling salesman problem (TSP) known as an optimization problem that aims for

determining the optimal delivery route with the least amount of travel distance, time, and cost in travelling

every location and returning to the beginning point at the end (7). The distance or time to travel between two

hubs is where 𝑖 is the origin and 𝑗 is the destination. The binary variable that considers value 1 if the

salesman travel from 𝑖 to 𝑗 and 0 as otherwise is . The general TSP model in this study is constructed as

below which was mentioned by (8):

Eq.

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

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Mixed Integer Programming

Mixed Integer Programming known as a mathematical optimization method that used for solving the

optimization problem applied in this formulation where the determination of the optimal solution depends on

the discrete integer values of some of the decision variables and continuous values of others (9). The objective

of mixed integer programming is to find the optimal values of the decision variable that in turn either minimize

or maximize an objective function constraint that subject to certain number of constraints. Solving Mixed

Integer Programming problems involves specialized algorithms and software tools, such as Branch-and-Bound.

Branch-and-Bound is known as a general algorithmic technique which is mainly used for optimization

problems, especially those based on combinatorial optimizations and mathematical programming. It

systematically explores the solution space of a problem to find the optimal solution or prove its infeasibility or

optimality. Figure 2 showed the general flow chart of Branch-and-Bound which was mentioned by (10).

Fig. 2 Flowchart of Branch-and-Bound

Genetic Algorithm

Genetic Algorithm is a type of metaheuristic algorithm that gets inspiration from the principles of genetics and

natural selection. It aims to mimic the process of evolution observed in natural systems, so that it will solve the

optimization and search problems (11). There are five steps in the process of Genetic Algorithm which are

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025

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initial population, fitness function, selection, crossover, and mutation. Figure 3 showed the process of Genetic

Algorithm which was mentioned by (12).

Fig. 3 Process of Genetic Algorithm

Ant Colony Optimization

Ant Colony Optimization is known as a metaheuristic algorithm extracted based on the strategy of ants

searching for food sources (13). It is a probabilistic technique used for solving computational problems that

can be reduced to finding good paths through graphs. Figure 4 showed the process of Ant Colony Optimization

which was mentioned by (14).

Fig. 4 Process of Ant Colony Optimization

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025

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RESULTS AND DISCUSSION

Delivery Route Based on Distance Travelled

In this study, three methods were used to determine the delivery routes based on distance travelled among hubs

in Johor which are Mixed Integer Programming, Genetic Algorithm and Ant Colony Optimization. The

delivery route with the minimum distance travelled and fulfilling all the travelling salesman problem (TSP)

constraints is the optimal delivery route for the distance factor. Table 2 showed the total distance travelled of

Mixed Integer Programming, Genetic Algorithm and Ant Colony Optimization.

Table 2 Total Distance Travelled of Mixed Integer Programming, Genetic Algorithm and Ant Colony

Optimization

Method

Total distance travelled (km)

Mixed Integer Programming

569.7

Genetic Algorithm

569.8

Ant Colony Optimization

582.4

Based on Table 2, the total distance travelled of Mixed Integer Programming is 569.7 km. Next, the total

distance travelled of Genetic Algorithm is 569.8 km. Then, the total distance travelled of Ant Colony

Optimization is 582.4 km. The overall results showed that Mixed Integer Programming obtained the minimum

total distance travelled in this study with the delivery route sequence from Muar - Tangkak - Segamat - Yong

Peng - Kluang - Kota Tinggi - Pasir Gudang - Tampoi - Senai - Kulai - Pontian - Batu Pahat - Pagoh - Muar.

Delivery Route Based on Time Travelled

In this study, three methods were used to determine the delivery routes based on time travelled among hubs in

Johor which are Mixed Integer Programming, Genetic Algorithm and Ant Colony Optimization. The delivery

route with the minimum total time travelled and fulfilling all the travelling salesman problem (TSP) constraints

is the optimal delivery route for the time factor. There was total six different sets of time travelled data based

on three different time periods at 8.00 a.m., 1.00 p.m. and 6.00 p.m. for both weekdays and weekends. Table 3

showed the total time travelled of Mixed Integer Programming, Genetic Algorithm and Ant Colony

Optimization at 8.00 a.m., 1.00 p.m. and 6.00 p.m. for both weekdays and weekends.

Table 3 Total Time Travelled of Mixed Integer Programming, Genetic Algorithm and Ant Colony

Optimization at 8.00 a.m., 1.00 p.m. and 6.00 p.m. for Both Weekdays and Weekends

Total time travelled

(min)

Mixed Integer

Programming

Genetic Algorithm

Ant Colony Optimization

Weekdays

8.00 a.m.

608.8

611.0

612.0

1.00 p.m.

625.4

629.2

631.8

6.00 p.m.

635.6

640.8

640.0

Weekends

8.00 a.m.

606.5

609.5

607.5

1.00 p.m.

666.0

672.0

685.5

6.00 p.m.

676.5

677.5

682.5

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

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Based on Table 3, the minimum total time travelled for the optimal delivery route at 8.00 a.m. on weekdays

was 608.8 min which was produced by using Mixed Integer Programming. The minimum total time travelled

for the optimal delivery route at 1.00 p.m. on weekdays was 625.4 min which was produced by using Mixed

Integer Programming. The minimum total time travelled for the optimal delivery route at 6.00 p.m. on

weekdays was 635.6 min which was produced by using Mixed Integer Programming. Moreover, the minimum

total time travelled for the optimal delivery route at 8.00 a.m. on weekends was 606.5 min which was produced

by using Mixed Integer Programming. The minimum total time travelled for the optimal delivery route at 1.00

p.m. on weekends was 666.0 min which was produced by using Mixed Integer Programming. The minimum

total time travelled for the optimal delivery route at 6.00 p.m. on weekends was 676.5 min which was

produced by using Mixed Integer Programming. By comparison between each different time, the results

showed that the most suitable time for delivery is 8.00 a.m. in weekends based on time factor since the total

time travelled is the least compared to other time. The delivery route sequence is Tangkak - Muar - Batu Pahat

- Pontian - Kulai - Senai - Tampoi - Pasir Gudang - Kota Tinggi - Kluang - Yong Peng - Pagoh - Segamat –

Tangkak.

Comparison Among the Algorithms

Based on the results, Mixed Integer Programming is the most suitable algorithm for solving the travelling

salesman problem (TSP) in this study with 13 delivery hubs, due to it can generated the optimal solution for

total seven different sets of distance and time travelled data.

Since the exact algorithm, Mixed Integer Programming can provide the optimal solution as benchmarking,

therefore the performances of the approximate algorithms, Genetic Algorithm and Ant Colony Optimization

will be compared. The comparison was summarized in Table 4.

Table 4 Comparison Among the Algorithms

Mixed Integer

Programming

Genetic Algorithm

Ant Colony

Optimization

Total distance travelled

569.7 km

569.8 km

582.4 km

Total time

travelled

Weekdays

8.00 a.m.

608.8 min

611.0 min

612.0 min

1.00 p.m.

625.4 min

629.2 min

631.8 min

6.00 p.m.

635.6 min

640.8 min

640.0 min

Weekends

8.00 a.m.

606.5 min

609.5 min

607.5 min

1.00 p.m.

666.0 min

672.0 min

685.5 min

6.00 p.m.

676.5 min

677.5 min

682.5 min

According to Table 4, it clearly shows that Genetic Algorithm provided the solutions that better than the Ant

Colony Optimization based on total seven different sets of distance and time travelled data. This is because the

results obtained from Genetic Algorithm is closer to the optimal solution compared to the results obtained from

Ant Colony Optimization, especially Genetic Algorithm has obtained five solutions that are closer to the

optimal solution. Thus, it can be concluded that Genetic Algorithm can obtained better solution than Ant

Colony Optimization.

CONCLUSION

This study successfully demonstrated the application of Mixed Integer Programming, Genetic Algorithm and

Ant Colony Optimization for optimizing the courier delivery routes based on distance and time travelled

INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN SOCIAL SCIENCE (IJRISS)

ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025

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among hubs in Johor. The results shows that Mixed Integer Programming provided optimal solution as

benchmarking, while Genetic Algorithm outperformed Ant Colony Optimization in comparing which

algorithm is more closer to the optimal solution. Thus, Mixed Integer Programming was the most effective

method for GDex Express to plan their delivery routes followed by Genetic Algorithm and Ant Colony

Optimization in order to improving the delivery effectiveness and reducing the operating costs by reducing the

travel time and distance.

Additionally, this study provides solutions to the courier companies in improving their delivery routes by

reducing the travel time and distance for 13 delivery hubs in Johor. The delivery effectiveness is improved by

shorter delivery times, while the operating costs are reduced by shorter distance. Since this study uses the real-

world data from GDex Express, therefore the results are practical and reliable. The models can help the courier

companies in selecting more efficient routes. Besides, the models developed in this study are not just for

courier companies. They can also be used for other industries that require optimization, such as food delivery,

waste collection, and supply chains logistics. These models can be modified to improve the operations of the

companies in various types of industries.

ACKNOWLEDGEMENT

This research was supported by University Tun Hussein Onn Malaysia (UTHM) through Tier 1 (vot H785).

The authors are extremely thankful to the reviewers for their beautiful remarks.

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