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

2021 ◽  
Vol 13 (3) ◽  
pp. 1372
Author(s):  
Abd Elazeem M. Abd Elazeem ◽  
Abd Allah A. Mousa ◽  
Mohammed A. El-Shorbagy ◽  
Sayed K. Elagan ◽  
Yousria Abo-Elnaga
Keyword(s):  
Transportation Problem ◽  
Efficient Solution ◽  
Efficient Solutions ◽  
Nondominated Solutions ◽  
Multi Index ◽  
Transportation Problems ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Nondominated Set ◽  
The Stability

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.

scholarly journals A review on fuzzy and stochastic extensions of the multi index transportation problem

2017 ◽  
Vol 27 (1) ◽  
pp. 3-29 ◽  
Author(s):  
Sungeeta Singh ◽  
Renu Tuli ◽  
Deepali Sarode
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Review Article ◽  
Fixed Charge ◽  
Fixed Cost ◽  
Multi Index ◽  
Transportation Problems ◽  
Single Criterion ◽  
Fixed Charge Transportation Problem

The classical transportation problem (having source and destination as indices) deals with the objective of minimizing a single criterion, i.e. cost of transporting a commodity. Additional indices such as commodities and modes of transport led to the Multi Index transportation problem. An additional fixed cost, independent of the units transported, led to the Multi Index Fixed Charge transportation problem. Criteria other than cost (such as time, profit etc.) led to the Multi Index Bi-criteria transportation problem. The application of fuzzy and stochastic concept in the above transportation problems would enable researchers to not only introduce real life uncertainties but also obtain solutions of these transportation problems. The review article presents an organized study of the Multi Index transportation problem and its fuzzy and stochastic extensions till today, and aims to help researchers working with complex transportation problems.

scholarly journals A Multi-Objective Stochastic Model for an Earthquake Relief Network

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zeren D. Yenice ◽  
Funda Samanlioglu
Keyword(s):  
Pareto Frontier ◽  
Efficient Solutions ◽  
Earthquake Damage ◽  
Mixed Integer ◽  
Penalty Cost ◽  
Earthquake Scenario ◽  
Earthquake Scenarios ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Damage Risk

Earthquake relief network involves storage and distribution of relief aid to people in need. In this paper, a new stochastic multi-objective mixed integer mathematical model is developed and implemented in Kadikoy municipality of Istanbul, Turkey in order to configure part of the earthquake relief network. The aim of the model is to help decision makers decide on the locations of storage areas for shelters pre-earthquake and distribution of shelters from these areas to temporary shelter areas post-earthquake while minimizing earthquake scenario-specific total expected distribution distance, total expected earthquake damage risk factor of storage areas and expected total penalty cost related to unsatisfied demand at temporary shelter areas, simultaneously. In the model, storage area capacity and coverage distance restrictions are taken into consideration. The data related to potential storage areas and shelter locations were obtained from Kadikoy municipality of Istanbul and Istanbul Metropolitan Municipality (IMM). The earthquake damage risk factors were determined based on possible earthquake scenarios given in Japan International Cooperation Agency’s (JICA) report. Four event scenarios with two different earthquake scenario likelihoods were considered and sample efficient solutions from the Pareto frontier were obtained implementing the normalized (scaled) weighted sum method.

A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

2021 ◽  
pp. 1-14
Author(s):  
Mojtaba Borza ◽  
Azmin Sham Rambely
Keyword(s):  
Programming Problem ◽  
Efficient Solution ◽  
Fuzzy Numbers ◽  
Parametric Approach ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Multi Objective Programming ◽  
Linear Fractional Program ◽  
Interval Valued ◽  
Linear Fractional Programming Problem

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of α - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly ɛ - efficient solution. Two examples are given to illustrate the method.

scholarly journals On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment

2021 ◽  
Vol 30 (1) ◽  
pp. 620-635
Author(s):  
Hamiden Abd El-Wahed Khalifa ◽  
Pavan Kumar ◽  
Majed. G. Alharbi
Keyword(s):  
Membership Function ◽  
Transportation Problem ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
Two Stage ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
The Stability ◽  
Fuzzy Cost ◽  
Necessary And Sufficient

Abstract This article attempts to study cost minimizing multi-objective fractional solid transportation problem with fuzzy cost coefficients c ˜ i j k r {\tilde{c}}_{ijk}^{r} , fuzzy supply quantities a ˜ i {\tilde{a}}_{i} , fuzzy demands b ˜ j {\tilde{b}}_{j} , and/or fuzzy conveyances e ˜ k {\tilde{e}}_{k} . The fuzzy efficient concept is introduced in which the crisp efficient solution is extended. A necessary and sufficient condition for the solution is established. Fuzzy geometric programming approach is applied to solve the crisp problem by defining membership function so as to obtain the optimal compromise solution of a multi-objective two-stage problem. A linear membership function for the objective function is defined. The stability set of the first kind is defined and determined. A numerical example is given for illustration and to check the validity of the proposed approach.

On Solving Bottleneck Bi-Criteria Fuzzy Transportation Problems

2018 ◽  
Vol 7 (4.10) ◽  
pp. 547
Author(s):  
V. E. Sobana ◽  
D. Anuradha ◽  
. .
Keyword(s):  
Transportation Problem ◽  
Efficient Solutions ◽  
Compromise Solution ◽  
Transportation Problems ◽  
Numerical Example

A fuzzy block–dripping method (FBDM) has been proposed to find the best compromise solution and efficient solutions of the bottleneck bi-criteria transportation problem under uncertainty. The procedure of the proposed method is illustrated by numerical example. 

scholarly journals Multi-Objective Optimization Methods for Transportation Network Problems

2020 ◽  
Vol 11 (1) ◽  
pp. 1-36
Author(s):  
Mouna Gargouri Mnif ◽  
Sadok Bouamama
Keyword(s):  
Transportation Problem ◽  
Transportation Network ◽  
Optimization Methods ◽  
Multi Objective Optimization ◽  
Multimodal Transportation ◽  
Literature Research ◽  
Transportation Problems ◽  
Multi Objective ◽  
Network Problems

This article recapitulates literature research solving transportation problems and these variants, notably the multimodal transportation problems variants. Moreover, the existing optimization methods critiqued and synthesized their efficiency to solve the transportation problem. This problem can be identified by various criteria and objectives functions that distinguished according to the case study. Based on the existing literature research, a taxonomy is proposed to distinguish different factors and criteria that perform and influence the multi-objective optimization on the transportation network planning problems. The transportation problems are cited according to these objective functions, and the variant of the problem by referring to the previous studies. In this article, the authors have focused their attention on a recent multi-objective mathematical model to solve the planning network of the multimodal transportation problem.

scholarly journals An Improved Vogel's Approximation Method for the Transportation Problem

2011 ◽  
Vol 16 (2) ◽  
pp. 370-381 ◽  
Author(s):  
Serdar Korukoğlu ◽  
Serkan Ballı
Keyword(s):  
Approximation Method ◽  
Operations Research ◽  
Opportunity Cost ◽  
Transportation Problem ◽  
Large Scale ◽  
Efficient Solutions ◽  
Important Task ◽  
Computational Experiments ◽  
Optimal Solutions ◽  
Transportation Problems

Determining efficient solutions for large scale transportation problems is an important task in operations research. In this study, Vogel’s Approximation Method (VAM) which is one of well-known transportation methods in the literature was investigated to obtain more efficient initial solutions. A variant of VAM was proposed by using total opportunity cost and regarding alternative allocation costs. Computational experiments were carried out to evaluate VAM and improved version of VAM (IVAM). It was seen that IVAM conspicuously obtains more efficient initial solutions for large scale transportation problems. Performance of IVAM over VAM was discussed in terms of iteration numbers and CPU times required to reach the optimal solutions.

scholarly journals EFFICIENT SOLUTION OF A MULTI-OBJECTIVE BULK TRANSPORTATION PROBLEM.

2017 ◽  
Vol 5 (6) ◽  
pp. 2337-2341 ◽  
Author(s):  
Sungeeta Singh ◽  
◽  
SudhirKumar Chauhan ◽  
Kuldeep A ◽  
◽  
...  
Keyword(s):  
Transportation Problem ◽  
Efficient Solution ◽  
Multi Objective

New Unconventional Technique to Decipher MOTP in Neutrshopic Environment

2020 ◽  
pp. 244-257
Author(s):  
Krishna Prabha Sikkannan ◽  
Vimala Shanmugavel
Keyword(s):  
Transportation Problem ◽  
Transportation Problems ◽  
Multi Objective ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Innovative Technique ◽  
The Mean

Many papers have been proposed so far in the field of fuzzy and intuitionistic fuzzy multi-objective transportation problems. An innovative technique to unravel multi-objective neutroshopic (NS) transportation problem called mean method is proposed in this chapter. The objectives which have different units to membership values are aggregated by finding the mean of the values. A new algorithm is developed in order to solve the problems of this type is explained in this work. A numerical example is instigated to demonstrate the technique and the consequence is compared with VAM's method.

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