Initial Basic Feasible Solution Research Articles

A NEW DUAL HEURISTIC ALGORITHM FOR FINDING THE INITIAL BASIC FEASIBLE SOLUTION FOR A TRANSPORTATION PROBLEM

Because determining the best initial basic feasible solution (IBFS) for a transportation problem is so crucial, numerous authors have expended a great deal of energy developing effective algorithms that will result in the lowest possible cost of moving products from a given source to a destination. The goal of this work was to develop an efficient dual algorithm for finding an initial basic feasible solution to a transportation problem (TP). Two distinct algorithms that produce the same IBFS make up our suggested approach. Compared to some popular methods in the literature, Using four numerical examples, the Row Minimum Method (RMM), Column Minimum Method (CMM), Least Cost Method (LCM), Extremum Difference Method (EDM), Northwest Corner Method (NWCM), Vogel's Approximation Method (VAM), etc. In comparison to the other heuristic techniques compared with the optimal dictate solution modified distribution (MODI), the proposed heuristic approach (PS-DESPAN) approximation was shown to provide a better starting solution (a solution that is extremely close to the optimal solution)

Advanced method for solving the transportation problem

Transportation problem is one of the predominant areas of operations research. It is a type of linear programming problem designed to minimize the cost of distributing a single product from m sources to n destinations. Transportation problem is widely used as a decision making tool in different fields such as engineering, business management and many others. These types of problems can be solved by general network methods. In this paper The Advanced Method for Solving the Transportation Problem (AMSTP) is proposed to find initial basic feasible solution and optimal solution of transportation problem and compared its results with other existing methods.

To Solve Pythagorean Fuzzy Decagonal Transportation Problem Using Bipartite Graph with Optimal Solution

Objectives: This study aims to solve the Pythagorean fuzzy transportation problem by means of providing a novel approach. Methods: To determine the optimum decision-making, we applied the MODI approach. To illustrate the proposed approach, we applied several types of numerical issues. An algorithm for solving the suggested technique is described. Findings: This study presents a bipartite graph-based strategy to the Pythagorean fuzzy transportation problem. Applying TORA statistical software, the data analysis discovered that the crisp model becomes linear when the membership function is applied. Novelty: This study has paved a way for better optimal results to obtain when the Pythagorean fuzzy set is converted using the score function instead of the standard techniques for Defuzzification. Keywords: Score Function, Pythagorean Fuzzy, Defuzzification, Pythagorean Fuzzy Transportation Problem, Decagonal Fuzzy Number, Ranking Method, Initial Basic Feasible Solution, and Optimal Solution

Transportation Problem via Median Approximatiom Technique for IBFS and Revised Modi’s Technique

The work sought to improve the modified distribution method (MODI) and propose an approach for estimating the initial basic feasible solution (IBFS) for a transportation problem. The Median Approximation Technique (MAT), an explicit and effective approach for locating an IBFS to a transportation problem, was created and successfully tested on 10 problem sets. The created methodology, MAT, was compared to the five existing approaches for obtaining the IBFS: Vogel Approximation Method{VAM}; North West Corner Method {NWCM}; Least Cost Method{LCM}; Column Minimum Method{CMM}; and Row Minimum Method{RMM} in terms of iterations’ number required to reach the optimum stage. Conclusively, the MAT under development provided a better IBFS across the board, as it produced optimum solutions for around 60% of the solved problem cases, as opposed to the IBFS created by the five existing approaches employed in this study, which gave optimum solutions for roughly 0%, 20%, 20%, 10%, and 10% of the examples, respectively.

Optimal value determination using traditional and newly developed method based on using initial basic feasible solution of a transportation problem using northwest and Russell method

Optimal value determination using traditional and newly developed method based on using initial basic feasible solution of a transportation problem using northwest and Russell method

A new approach for finding an initial basic feasible solution to a transportation problem

A new approach for finding an initial basic feasible solution to a transportation problem

New Methods to Solve and Find Initial Basic Feasible Solution of Transportation Problems

In this paper to solve the initial basic solution for transportation problem and Minimizing transportation time and getting optimal solutions are always considered as important factors while solving transportation problem. This paper shows a new approach for finding initial basic solution for transportation problem which reduces cost of transportation more than any transportation method such as Northwest Corner Method(NCM), Least Cost Method(LCM), northwest, Vogel’s approximation, Total Opportunity Cost Matrix-Minimal Total (TOCM-MT) and so on. This method has been illustrated by taking an Numerical example.

Pythagorean fuzzy transportation problem: New way of ranking for Pythagorean fuzzy sets and mean square approach

The predominant domain for optimization in the current situation is the transportation problem (TP). In the majority of cases, accurate data have been employed, yet in reality, the values are vague and imprecise. In any decision-making process, imprecision is a significant issue. To deal with the ambiguous setting of collective decision-making, many tools and methods have been established. The Pythagorean fuzzy set is an extension of fuzzy sets that successfully handles ambiguity and fuzziness. To overcome the shortcomings of intuitionistic fuzzy context, Pythagorean fuzzy sets are considered to be the most recent tools. This study proposes a new method for addressing the uncertain Pythagorean transportation issue. In this study, we created a novel sorting technique for Pythagorean fuzzy sets that converts uncertain quantities into crisp numbers. We developed an innovative mean square strategy for obtaining the initial basic feasible solution (IBFS) for a Pythagorean Fuzzy Transit Issue (PyFTP) of three types (I, II, III) wherein the requirement, availability, and unit of transportation expenses are all in Pythagorean uncertainty. In addition, we used the MODI technique to find the best option. To demonstrate the suggested strategy, we used numerical problems of three distinct kinds. A comparison table with the results of the previous strategy and the suggested method is created to state the benefits of the ranking methodology with the proposed algorithm. The discussion of future research and conclusions is the final step.

An application of generalized symmetric type-2 intuitionistic fuzzy variables to a transportation problem with the effect of a new ranking function

The primary objective of this study is to establish and introduce generalized symmetric type-2 intuitionistic fuzzy set, a type-2 fuzzy set extension. The major goal of such an extension is to enable the concept of fuzzy outranking relation which is known as foot print of uncertainty (FOU) to be employed in generalized symmetric type-2 intuitionistic fuzzy number (GST2IFN) for the first time. This is interesting to deal this GST2IFNs and it is complicated to find the equivalent crisp quantities due to this special structure. Hence, we have introduced a new ranking function using the mean level set of membership and non-membership functions. Besides, the arithmetic operations of the GST2IFNs are discussed. To express the effectiveness and application of the proposed GST2IF variables, a transportation problem (TP) is formulated with all cost parameters are GST2IFNs. In addition, few different algorithmic approaches are applied to find the initial basic feasible solution (IBFS) and optimal solution of the TP. Finally, the feasibility and richness of the obtained optimal solution is discussed.

An Efficient Method to Obtain Initial Basic Feasible Solution of a Transportation Problem

Transportation Problem (TP) is the study of strategy for shipping the product from the origin (supplier) to the destination (consumers) and the optimal shipment cost of the TP obtained from the initial basic feasible solution (IBFS). IBFS is the prime element of TP which helps to optimize the TP objective function. Existing methods for finding IBFS could not give the nearest value to minimal cost everywhere. Hence an innovative technique Known as TOCM-MT provides IBFS, which is the closest to an optimal solution. Many researchers have used this TOCM-MT technique through thousands of real-life TP problems, in every time got a better result than VAM, JHM, and TDM1 techniques. Hence, this technique is best for obtaining IBFS. This research is illustrated the TOCM-MT approach through time minimizing, transshipment, and profit maximization problems with some numerical examples.

A NEW APPROACH FOR FINDING MINIMIZATION COST IN TRANSPORTATION PROBLEM – AN ALGORITHM BY USING PYTHON LANGUAGE

In this paper the package Numpy from the programing language Python is presented as a computational tool that can help to solve the initial basic feasible solution involving transportation problem. This is also extension of our previous paper. The objective of this paper is to find how to minimize the transportation cost (TC) and to save a significant amount of time.

Investigating the Pitfalls of the Least Cost and Vogel’s Approximate Methods: Understanding the Impact of Cost Matrix Patterns

To obtain an optimal solution for any Transportation Problem (TP), the first step is to find an Initial Basic Feasible Solution (IBFS). A better IBFS requires fewer iterations to reach an optimal solution. The Least Cost Method (LCM) and Vogel’s Approximate Method (VAM) are commonly used approaches to finding IBFS due to their ease of implementation. Researchers frequently propose various methods to discover IBFS, but most of them are modifications of LCM or VAM. While VAM generally performs better, there are instances where it produces worse results compared to LCM and other approaches. Additionally, although researchers have developed new approaches, mainly modified versions of VAM, and demonstrated improved solutions with a few numerical instances, they have not yet identified the causes behind these results. The reasons for LCM and VAM's inability to obtain better IBFS have not been fully determined. This article aims to uncover the causes of pitfalls and the mechanisms of the allocation flow in both LCM and VAM through hypothetical and experimental domains. Several typical numerical instances have been conducted to demonstrate the causes of pitfalls and the allocation flow mechanisms of these methods. Journal of Engineering Science 14(1), 2023, 123-135

On solving fully intuitionistic fuzzy transportation problem via branch and bound technique

In dealing with real world transportation problems, several issues are frequently encountered as a result of uncontrollable factors. To deal this uncertainties, many authors have suggested transportation problems with intuitionistic fuzzy parameters. In this article, fully intuitionistic fuzzy transportation problem (InFTP) is considered in which the parameters are triangular intuitionistic fuzzy numbers. To solve this, initially intuitionistic fuzzy branch and bound technique are applied to get the initial basic feasible solution and then intuitionistic fuzzy modified distribution (InFMODI) method is applied to acquire the optimal solution of the fully InFTP. Also, a new ordering is developed here in which some properties of compensation, linearity, additive and partial order relations are satisfied. The optimal solution obtained from the proposed method satisfies the condition of optimality and feasibility. Finally, two numerical examples are provided to show the effectiveness of the proposed method.

New Approach to Find Initial Basic Feasible Solution (IBFS) for Optimal Solution in Transportation Problem

Minimizing transportation time and getting optimal solutions are always considered as important factors while solving transportation problem. This paper shows a new approach for finding initial basic solution for transportation problem which reduces cost of transportation more than any transportation method such as LCM, northwest, Vogel’s approximation and so on. This method has been illustrated by taking an example; afterwards, it compares basic initial feasible solution with other methods IBF and optimal dictate solutions such as MODI and Steppingstone method.

Minimum demand supply based stepping stone approach to solve a special trapezoidal fuzzy transportation problem

ABSTRACT In literature, a variety of fuzzy transportation problems are discussed and solved by defuzzification of the fuzzy input values to the crisp values. This crisp-valued conversion, in the beginning, limits the features of fuzziness as it does not take into account the uncertainties occurring in the course of intermediate calculations. The present study is a successful effort to overcome this limitation by proposing a minimum demand supply-based methodology to obtain a fuzzy initial basic feasible solution (FIBFS) of the problem. A unique ordering of trapezoidal fuzzy numbers is proposed to make the demand and supply allocation in a fuzzy form. The proposed method has been applied to a special class of fuzzy transportation problems, having all the inputs viz. demand, supply, and cost as trapezoidal fuzzy numbers. Further, the incenter fuzzy ranking process is used to convert FIBFS in a crisp initial basic feasible solution (IBFS). The optimality of the IBFS thus obtained is tested through the stepping stone method. The results obtained by the proposed approach are compared with the fuzzy Hungarian-MODI approach and the presence of inherent uncertainties in FIBFS makes the former approach superior to the latter.

Proposed Method for Solving Transportation Problems

The transportation problem (TP) is a frequently used optimization technique in operations research for studying difficulties involving the transportation of commodities from manufacturing locations to retail outlets. Lowering transportation costs is one possible purpose of the TP, reducing the distance travelled in terms of time, and so on. Solving such issues can be done systematically. We do this by determining the problem's Initial Basic Feasible Solution (IBFS). The usual methods for determining the IBFS are Vogel's Approximation technique, Least Cost technique, and the North-West Corner technique. Several more techniques to handle such difficulties have been proposed in recent years. In this article, we offer a new technique for solving the transportation problem, and its efficacy is compared to that of existing solutions. Calculation of the result shows that it is straightforward and close to the ideal solution to the issue.

Using the largest difference method to find the initial basic feasible solution to the transportation problem

The largest difference approach is a new method to find an initial basic feasible solution (IBFS) to transportation problems, this new method is presented in this study, for obtaining a reasonable primary answer to a wide range of transportation issues. Numerical examples and optimality testing of the conclusions justify these methodologies. The most enticing feature of these methods is that they just necessitate a few simple calculations.

A Novel Approach Algorithm for Determining the Initial Basic Feasible Solution for Transportation Problems

In optimization, the transportation problem is of utmost significance. The fundamental idea for solving the transportation problem is to develop methods that lower the overall cost between the source and the destination. Numerous research techniques are given in the literature as solutions to transportation problems. The majority of strategies focus on locating the initial basic, feasible solution to the transportation problem, while some techniques concentrate on locating an optimal solution. To find an initial, basic, feasible solution, Vogel's approximation, the least-cost method, the northwest method, and other methods are used. The Modified Distribution Method and the Stepping Stone Method are gaining acceptance as the optimal solution to the transportation problem. In this research study, a model approach to figuring out the basic, feasible solution for transportation problems with balanced and unbalanced components is proposed based on the average unit cost value of columns and rows. A new table is created using the unit cost values and average unit cost values in the columns and rows and compared to the transportation problem to solve the problem by balancing demand and supply. The proposed methodology is effortless, easy to understand, and simple to use. Comparatively speaking, the algorithmic technique suggested by this work is less complex than the well-known meta-heuristic algorithms in the literature. Finally, provide a case study to demonstrate the proposed approach.

A new LCM modification for finding an IBFS for fuzzy transportation problems

In this research, we present a modified approach to “the least cost method” (LCM) of finding “the initial basic feasible solution” (IBFS) to the fuzzy transportation problem (FTP). The problem is in a foggy environment where the cost of transporting the product, the resources, and the demand in the destinations are fuzzy numbers. We solved the (FTP) by converting it to an equivalent crisp form using (a robust ranking technique). A numerical example is presented to demonstrate the suggested approach.

Employing the arithmetic mean to find the IBFS for transportation problems

Transportation Problem (TP) cost is a term that refers to the operating costs associated with transportation. The cost of transportation is critical in order to optimize profit. In recent time, competitive global market and enterprises must carefully organize their transportation systems in order to keep transportation costs low. Modeling this transport channel is a management choice that entails determining the most cost-effective distribution strategy for a single homogenous item. This is referred to as a transportation issue, which may be expressed mathematically as a linear programming problem. A fundamental practicable solution is always necessary in the solution method of a transportation issue in order to reach the best solution. There several classic methods to find initial basic feasible solution (IBFS). In this work, a novel strategy for obtaining (IBFS) to (TP) is presented. Numerical examples are used to explain the suggested technique.