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A COMPARATIVE ANALYSIS OF STEPPING STONE AND DHOUIB-

MATRIX-TP1 METHODS IN OPTIMIZING TRANSPORTATION COST IN

NEUTROSOPHIC ENVIRONMENT

NUR AIN SYAZWANI BINTI ASMAWI (2022836006) (K242/50)

SUPERVISOR : MADAM MAZIAH BINTI MAHMUD

ABSTRACT METHOD & IMPLEMENTATION

In transportation and logistics, determining the most efficient allocation PHASE 1 : Formulate the NTP as a neutrosophic linear PHASE 6: Apply Dhouib-Matrix-TP1 to obtain

of resources while minimizing total cost is a common challenge in programming problem. optimal solution

logistics and transportation, particularly in uncertain and imprecise

environments. In order to handle uncertainty in cost estimation, this study

focusses on optimizing transportation costs using SVTN data. This study

involves applying LCM to obtain an IBFS, followed by optimization using

the Stepping Stone and DM-TP1 method. SVTN data is first transformed

into crisp numbers using the sign distance method for easier

computation. According to the findings, the DM-TP1 offers a quicker,

simplified method slightly higher cost, while Stepping Stone method gives PHASE 2 : Compile the transportation matrix and the Discard row 2

the lower transportation cost at 618.36. The comparison highlights the initial table

trade-off between cost minimization and computational efficiency. It is

recommended that decision-makers choose optimization techniques

according to the context by using SVTN-based modeling to represent real-

world uncertainty. This study shows that the accuracy of decisions in

uncertain environments is improved by applying neutrosophic concept to

classical transportation problems. Discard column 1

PROBLEM STATEMENT

In daily life, products often need to be moved from multiple suppliers to PHASE 3 : Apply sign distance method to convert SVTN

different destinations. Organizations aim to do this in the most efficient to crisp numbers

and cost-effective way. The main challenge is finding the cheapest way to

transport goods from factories to warehouses, especially since Discard column 3

transportation costs can vary across routes. The situation can be solved

by using traditional transportation method but real-world transportation

problems often involve uncertainties that can arise in inconsistent

transportation costs, fluctuating supply and demand, or capacities issues. PHASE 4 : Apply LCM to obtain IBFS

Traditional methods struggle with this uncertainty, making neutrosophic

sets which handle truth, indeterminacy, and falsity more suitable for

modelling such problems. This study focuses on the application of the Discard row 1

LCM, which finds an IBFS by allocating supplies to the lowest-cost routes

first, and the comparison of Stepping stone method and DM-TP1, which

optimizes that solution by evaluating unoccupied routes through closed-

loop paths to minimize total cost. By applying these methods within a

neutrosophic environment, this study aims to develop a more accurate

and practical approach for optimizing transportation cost under Initial solution = 657.06

uncertainty.

PHASE 5 : Apply Stepping Stone Method to obtain Discard column 4

optimal solution
OBJECTIVES Iteration-1

To transform the Single-Valued Trapezoidal Neutrosophic (SVTN)

numbers to crisp numbers using sign distance method.

To obtain an Initial Basic Feasible Solution (IBFS) using Least

Cost Method (LCM). Discard column 2

To compare the optimal transportation cost between Stepping

Stone and Dhouib Matrix-TP1 method. The highest negative net cost change : -3.76

Updated table after ±10

RESULT & DISCUSSION

Optimal solution : 805.46

CONCLUSION

This study successfully addressed a transportation

Iteration-2 problem under a Single-Valued Trapezoidal

Neutrosophic (SVTN) environment, demonstrating how

uncertainty in cost parameters can be effectively

managed. By converting SVTN data into crisp values

using the sign distance method, classical optimization

techniques like Least Cost Method (LCM), Stepping

Stone, and Dhouib-Matrix-TP1 (DM-TP1) were applied

effectively. The results showed that while DM-TP1 offers

faster computation, the Stepping Stone Method provides

It shows that the Stepping Stone The highest negative net cost change : -0.58 a more optimal solution with the lowest transportation

method yields a reliable minimum cost It shows that the DM-TP1 method gives a cost. These findings confirm that all research objectives

with high confidence and minimal reliable cost within the core range, Updated table after ±2 were achieved by optimizing transportation costs under

uncertainty, as indicated by zero though with slightly higher uncertainty uncertainty, comparing solution methods, and validating

indeterminacy and strong rejection of compared to the Stepping Stone method.

values outside the core cost range. the practical value of neutrosophic modeling. Overall,
the study proves that integrating neutrosophic with
Although the Stepping Stone

method offers a more classical methods enhances decision-making in real-

accurate solution, it requires world logistics problems.

more manual effort. In

contrast, DM-TP1 is faster RECOMMENDATION

and easier, making it suitable

for large-scale problems Iteration-3 It is recommended that SVTN representations be

needing quick decisions. incorporated in future transportation models to better

Both methods effectively handle uncertainty in cost estimation. While LCM

minimized costs under remains a reliable method for initial allocation, Stepping

uncertainty, with a trade-off Stone is preferred for higher accuracy, whereas DM-TP1

between accuracy and is suitable for faster solutions in large-scale problems.

computational efficiency. The

use of SVTN data helped Future studies may explore integrating SVTN with other

manage uncertainty, showing heuristics or machine learning for improved efficiency

how traditional optimization and robustness. Finally, supply chain and logistics

can be adapted to uncertain No negative net cost change. professionals are encouraged to adopt neutrosophic-

environments through crisp Optimal solution : 618.36 based approaches for more flexible, cost-effective, and

conversion. data-informed planning strategies.