Optimal Solution of Linear Programming Problem Using Python And TORA: A Comparative Analysis

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Special Issue | Volume XIV, Issue XIII, October 2025

www.ijltemas.in Page 198

Optimal Solution of Linear Programming Problem Using Python
and TORA: A Comparative Analysis

Mayuri B. Babar*, Varsha J. Patil

Department of Mathematics, Dr. D. Y. Patil Arts, Commerce and Science College, Pimpri, Pune-18, Maharashtra, India

DOI: https://doi.org/10.51583/IJLTEMAS.2025.1413SP040

Received: 26 June 2025; Accepted: 30 June 2025; Published: 25 October 2025

Abstract: Linear Programming (LP) is a mathematical method to optimize results under certain constraints. With the improvement
of computational aids, LP problems have become easy to solve. This study compares two well-known aids: Python's PULP Library
and the TORA software. Applying a new LP problem, both aids are compared for accuracy, usability and application for various
user groups. The research aims to guide students, teachers and practitioners on choosing the best tool depending on their
requirements.

Keywords: Linear Programming Problem, TORA Software, Python Software

I. Introduction

Linear Programming problem (LPP) has wide applications in logistics, finance, operations management and production. Solving
LP problems calculative is time-consuming and prone to errors. Thus, software tools such as Python and TORA have gained
popularity. As real-world LP problems often involve numerous variables and constraints, solving them manually not only become
tedious and time-consuming but also increase the likelihood of errors in calculation and interpretation. To overcome these
limitations, software tools have become integral in solving LP models efficiently and accurately. Among these tools, Python and
TORA have emerged as popular choices for both academic and practical applications. Python, a versatile programming language,
offers powerful libraries like PULP. On the other hand, TORA provides a user-friendly graphical interface, primarily used in
educational settings to illustrate the steps of the Simplex method and other operations research algorithms.

This paper evaluates both tools by solving the same LP problem using Python’s programmatic approach using PULP library and
TORA’s Simplex method interface.

Problem Formulation

The new Linear Programming Problem is:

Maximize �� = �� + �� + ��

Subject to constraints:
3��1 + 3��2 + ��3 ≤ 10

��1 + 2��2 + 3��3 ≤ 15

��1, ��2, ��3 ≥ 0

This problem represents an optimization scenario such as resource allocation or production planning.

II. Methodology

Solving with Python

Input

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Special Issue | Volume XIV, Issue XIII, October 2025

www.ijltemas.in Page 200

III. Results:

Both tools gives the same optimal solution:
Optimal Solution by using Python

��1 = 0.00, ��2 = 3.3333333, ��3 = 0.00
�� = 19.9999998 ~ 20

Optimal Solution by using TORA

��1 = 0.00, ��2 = 3.33, ��3 = 0.00
�� = 20

Comparison Table:

IV. Discussion:

Both software show efficacy in identifying the best solution. Python’s programmatic style provides us with speed, automation,
and interfacing into real-world systems such as logistics systems and business application.

TORA, however, is useful for teaching and learning. It decomposes every step of the Simplex method so that a learner can see
how the algorithm unfolds internally.

Python does need minimum programming skill but has high scalability and customizability. TORA is ideal for low-scale
Problems.

V. Conclusion:

This comparative analysis concludes that Python and TORA are both great tools to solve LP Problems. Yet, their usability
is context-dependent: For students and teachers, TORA is perfect as it involves visual, step-by-step learning of the Simplex
method. Python is better for researchers, engineers and analysts who require

Scalability and integration with larger systems. Overall, Python is the best choice for professional and industrial use, while
TORA is best used in academic environments.

References:

1. Hamdy A. TAHA, Operations Research (Seventh Edition)
2. Introduction to Machine Learning with Python

Criteria Python (PULP) TORA Software

Ease of Use Requires programming Skills Simple GUI, ideal for beginners

Output
Detail

Code-based output Step-by-step tableau

Speed Very fast Fast for small problems

Flexibility High, allows for automation/scripting Limited to small-scale problems

Graphical
Support

Needs extra libraries (e.g., matplotlib) Built-in for 2-variable cases

Suitability Research, automation, large datasets Education, small manual problems