Solution of multi-objective solid transportation problem in fuzzy approach

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

2022

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.

“…Singh et al (2019) developed a generalized model for MSTP with some random parameters. Anuradha et al (2019) have utilized a row maxima procedure to solve the bi-objective STP.…”

Section: Introductionmentioning

confidence: 99%

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

Kara¹,

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

2022

A Fuzzy Approach to Multi-Objective Solid Transportation Problem with Mixed Constraints Using Hyperbolic Membership Function

Kara

Cybernetics and Information Technologies

2021

Multi-objective Solid Transportation Problem (MSTP) is known as a special class of vector-minimization (or maximization) problems and has three parameters: source, destination, and conveyance. The objectives such as transportation cost, transportation time, transportation safety level, and objectives in terms of environmental and social issues are generally in conflict with each other. In this paper, we present a fuzzy approach to bring these conflicting objectives together as high as possible. Instead of using the linear membership function, which is frequently used in the literature for ease of use, we use the hyperbolic membership function in our approach. Also, while most of the papers in the literature deal with the standard equality constrained form of MSTP, the mixed constrained form is addressed in this paper. Finally, a numerical example from the literature is used to illustrate the construction of the hyperbolic membership function and how well it represents the objective functions’ degree of satisfaction.

An Approach for a Multi-Objective Capacitated Transportation Problem

Kara

Encyclopedia of Data Science and Machine Learning

2022

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.