Optimal Solution of the Planar Four Index Transportation Problem

Sarode, Deepali; Tuli, Renu

doi:10.1109/aicai.2019.8701265

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…In [13], the researchers implemented the modified distribution method to obtain an optimal solution for the four-index transportation problem. Djamel et al [14] focused on the theoretical study and numerical solution of a capacitated four-index transportation problem, and constructed an algorithm for solving the problem.…”

Section: Introductionmentioning

confidence: 99%

Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

et al. 2021

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Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.

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Section: Introductionmentioning

confidence: 99%

Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

et al. 2021

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New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators

Kara¹,

Köçken

2022

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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A solid transportation problem emerges when the decision variables are represented by three items: the source, the destination, and the mode of transport. In applications, the STP generally requires considering multiple objectives such as cost minimization, time minimization, security level maximization, etc. In this way, a multi-objective solid transportation problem arises. This paper deals with the solution of the problem and analyzes the effect of several important fuzzy aggregation operators on the solution of the problem. In this context, the most commonly used aggregation operators are investigated for this problem. To explain the solution approach, a numerical example from the literature is given and a Pareto-optimal solution set is provided to offer the decision-maker. Furthermore, graphical comparisons and sensitivity analysis are presented with the solution obtained.

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An Approach for a Multi-Objective Capacitated Transportation Problem

Kara

Köçken

2022

Encyclopedia of Data Science and Machine Learning

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The multi-objective solid transportation problem is a special class of vector-minimum linear programming problems in which the objectives are often in conflict. Furthermore, the supply, demand, and conveyance constraints in MSTP may not be only of equality type but also of inequality type. The fuzzy programming approach is one of the most common solution methods for multi-objective programming problems. In this approach, linear membership functions are generally used in the literature. In this study, the fuzzy programming approach is applied by utilizing a special type of non-linear (exponential) membership functions to solve the multi-objective capacitated solid transportation problem (MCSTP) and a Pareto-optimal solution is obtained. Finally, an application from the literature is provided to illustrate the efficiency of the exponential membership function. Also, a comparison is presented with the solution obtained by using a linear membership function.

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Optimal Solution of the Planar Four Index Transportation Problem

Cited by 3 publications

References 12 publications

Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators

An Approach for a Multi-Objective Capacitated Transportation Problem

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