scholarly journals Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables

2021 ◽  
Vol 6 (5) ◽  
pp. 1406-1422
Author(s):  
Vandana Y. Kakran ◽  
Jayesh M. Dhodiya
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Solid Transportation Problem ◽  
Programming Technique ◽  
Distance Method ◽  
Multi Objective ◽  
Uncertain Variables ◽  
Value Model ◽  
Single Objective

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.

scholarly journals Multi-Objective Faculty Course Assignment Problem with Result and Feedback Based Uncertain Preferences

2021 ◽  
Vol 6 (4) ◽  
pp. 1055-1075
Author(s):  
Sunil B. Bhoi ◽  
Jayesh M Dhodiya
Keyword(s):  
Deterministic Model ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Programming Technique ◽  
Feedback Analysis ◽  
Multi Objective ◽  
Ranking Criteria ◽  
Uncertain Preferences ◽  
Single Objective ◽  
Optimistic Value

In this paper, a multi-objective faculty course allocation problem with result analysis and feedback analysis based on uncertain preferences mathematical model is presented. To deal with an uncertain model, three different ranking criteria are being used to develop: a) Expected value, b) Optimistic value, c) Dependent optimistic value criterion. These mathematical models are transformed into their corresponding deterministic forms using the basic concepts of uncertainty theory. The deterministic model of DOCM consists of fractional objectives which are converted into their linear form using Charnes and Cooper’s transformation. These deterministic formulations MOFCAP are converted into a single objective problem by using the fuzzy programming technique with linear and exponential membership functions. Further, the single objective problem for all the defined models is solved in the Lingo 18.0 software to derive the Pareto-optimal solution. The sensitivity of the models is also performed to examine the variation in the objective function due to the variation in parameters. Finally, a numerical example is given to exhibit the application and algorithm of the models.

scholarly journals Geometric Mean Method to Solve Multi-Objective Transportation Problem Under Fuzzy Environment

2020 ◽  
Vol 9 (5) ◽  
pp. 1739-1744
Keyword(s):  
Transportation Problem ◽  
Geometric Mean ◽  
Method Comparison ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Numerical Examples ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Single Objective

Transportation problem is a very common problem for a businessman. Every businessman wants to reduce cost, time and distance of transportation. There are several methods available to solve the transportation problem with single objective but transportation problems are not always with single objective. To solve transportation problem with more than one objective is a typical task. In this paper we explored a new method to solve multi criteria transportation problem named as Geometric mean method to Solve Multi-objective Transportation Problem Under Fuzzy Environment. We took a problem of transportation with three objectives cost, time and distance. We converted objectives into membership values by using a membership function and then geometric mean of membership values is taken. We also used a procedure to find a pareto optimal solution. Our method gives the better values of objectives than other methods. Two numerical examples are given to illustrate the method comparison with some existing methods is also made.

Multi-Objective Fixed-Charge Transportation Problem with Random Rough Variables

2018 ◽  
Vol 26 (06) ◽  
pp. 971-996 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Sudipta Midya ◽  
Vincent F. Yu
Keyword(s):  
Transportation Problem ◽  
Deterministic Model ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Fixed Charge ◽  
Optimal Solutions ◽  
Multi Objective ◽  
Proposed Model ◽  
Fixed Charge Transportation Problem

This paper considers a multi-objective fixed-charge transportation problem (MOFCTP) in which the parameters of the objective functions are random rough variables, while the supply and the demand parameters are rough variables. In real-life situations, the parameters of a multi-objective fixed-charge transportation problem may not be defined precisely, because of globalization of the market, uncontrollable factors, etc. As such, the multi-objective fixed-charge transportation problem is proposed under rough and random rough environments. To tackle uncertain (rough and random rough) parameters, the proposed model employs an expected value operator. Furthermore, a procedure is developed for converting the uncertain multi-objective fixed-charge transportation problem into a deterministic form and then solving the deterministic model. Three different methods, namely, the fuzzy programming, global criterion, and ϵ-constrained methods, are used to derive the optimal compromise solutions of the suggested model. To provide the preferable optimal solution of the formulated problem, a comparison is drawn among the optimal solutions that are extracted from different methods. Herein, the ϵ-constrained method derives a set of optimal solutions and generates an exact Paretofront. Finally, in order to show the applicability and feasibility of the proposed model, the paper includes a real-life example of a multi-objective fixed-charge transportation problem. The main contribution of the paper is that it deals with MOFCTP using two types of uncertainties, thus making the decision making process more flexible.

scholarly journals An Empirical Study on Multi-objective Transportation Problem in Fuzzy Environment

2018 ◽  
Vol 7 (4.38) ◽  
pp. 748
Author(s):  
Manoranjan Mishra ◽  
Debdulal Panda
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Fuzzy Rule ◽  
Transportation Cost ◽  
Transportation System ◽  
Vital Role ◽  
Multi Objective ◽  
Transportation Models ◽  
Total Transportation Cost ◽  
Single Objective

For both in economical and social development of country transportation system plays a vital role. As it is directly involved with financial growth of the country, for that a complete well planned transportation infrastructure is necessary. Most of the transportation models are formulated with minimization of transportation cost as the basic objective. But consideration of transportation system with a single objective is not able to meet the various requirements of transportation industry for which it may not lead to the practical optimal solution. It bounds the decision makers (DMs) to consider several objectives at a time instead of single objective. To handle a multi-objective transportation problem with fixed parameters is a challenging issue; rather it is easy to consider all parameters in terms of linguistic variables. In this paper, a multi criteria multi-objective transportation models is formulated based on fuzzy relations under the fuzzy logic with several objectives like (i) minimization of total transportation cost and (ii) minimization of total transportation time. Another objective, maximization of the transported amount from a source to a destination is determined on the basis of previous two objectives. All the objectives are associated with multiple numbers of criteria like breakable items, shipping distance, service charge, mode of transportation etc. These relations are imprecise in nature and represented in terms of verbal words such as low, medium, high and very high. The fuzzy rule based multi-objective transportation problem is formulated and result is discussed. 

scholarly journals A New Method to Solve Interval Transportation Problems

2020 ◽  
pp. 802-811
Author(s):  
Abdul Quddoos ◽  
Ummey Habiba
Keyword(s):  
Comparative Study ◽  
Transportation Problem ◽  
Solution Method ◽  
Fuzzy Programming ◽  
Solution Procedure ◽  
Programming Technique ◽  
Left Limit ◽  
Objective Model ◽  
The Cost ◽  
Single Objective

transportation problem (ITP) in which the cost-coefficients of the objective function, source and destination parameters are all in the form of interval. In this paper, the single objective interval transportation problem is transformed into an equivalent crisp bi-objective transportation problem where the left-limit and width of the interval are to be minimized. The solution to this bi-objective model is then obtained with the help of fuzzy programming technique. The proposed solution procedure has been demonstrated with the help of a numerical example. A comparative study has also been made between the proposed solution method and the method proposed by Das et al.(1999) .

scholarly journals Multi-Objective Restricted Solid Transportation Problem in Intuitionistic Fuzzy Environment with Emission Cost

2019 ◽  
Vol 8 (2S3) ◽  
pp. 722-727 ◽  
Keyword(s):  
Transportation Problem ◽  
International Energy Agency ◽  
Optimal Solution ◽  
Transport Sector ◽  
Solid Transportation Problem ◽  
Energy Agency ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Weighted Sum Method ◽  
Fuzzy Environment

Transportation plays key role in logistic and supply chain management for decreasing cost and enhances service. The transport sector contributes 23% of the total CO2 emissions in the world according to the latest estimates of the International Energy Agency (IEA).There is a direct link between weight of the quantity transported and co2 emission for the freight transport. This paper presents multi objective restricted solid transportation problem in intuitionistic fuzzy ambiance with emission cost which is based on weight of the quantity transported and vehicle cost under some restriction on transported amount. An extra constraint on the total budget at each destination is imposed. Transportation models are formulated under crisp and fuzzy environments and fuzzy models are converted into crisp using average method. The total time and emission cost based on weight of the quantity transported for restricted and unrestricted models are compared. The optimal solution is obtained by using weighted sum method and Lingo 13.0 Software. Mathematical example is given to validate the proposed mode

A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment

2021 ◽  
pp. 1-18
Author(s):  
Xiang Jia ◽  
Xinfan Wang ◽  
Yuanfang Zhu ◽  
Lang Zhou ◽  
Huan Zhou
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Sets ◽  
Regret Theory ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Objective Model ◽  
Single Objective

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach.

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