Solving the fully fuzzy multi-objective transportation problem based on the common set of weights in DEA

2020 ◽  
Vol 39 (3) ◽  
pp. 3099-3124
Author(s):  
M. Bagheri ◽  
A. Ebrahimnejad ◽  
S. Razavyan ◽  
F. Hosseinzadeh Lotfi ◽  
N. Malekmohammadi
Keyword(s):  
Relative Efficiency ◽  
Transportation Problem ◽  
Real Life ◽  
Transportation Cost ◽  
Multi Objective ◽  
Decision Making Unit ◽  
Common Set Of Weights ◽  
The Common ◽  
Total Transportation Cost ◽  
Fuzzy Dea

A transportation problem basically deals with the problem which aims to minimize the total transportation cost or maximize the total transportation profit of distributing a product from a number of sources or origins to a number of destinations. While, in general, most of the real life applications are modeled as a transportation problem (TP) with the multiple, conflicting and incommensurate objective functions. On the other hand, for some reason such as shortage of information, insufficient data or lack of evidence, the data of the mentioned problem are not always exact but can be fuzzy. This type of problem is called fuzzy multi-objective transportation problem (FMOTP). There are a few approaches to solve the FMOTPs. In this paper, a new fuzzy DEA based approach is developed to solve the Fully Fuzzy MOTPs (FFMOTPs) in which, in addition to parameters of the MOTPs, all of the variables are considered fuzzy. This approach considers each arc in a FFMOTP as a decision making unit which produces multiple fuzzy outputs using the multiple fuzzy inputs. Then, by using the concept of the common set of weights (CSW) in DEA, a unique fuzzy relative efficiency is defined for each arc. In the following, the unique fuzzy relative efficiency is considered as the only attribute for the arcs. In this way, a single objective fully fuzzy TP (FFTP) is obtained that can be solved using the existing standard algorithms for solving this kind of TPs. A numerical example is provided to illustrate the developed approach.

scholarly journals Application of fuzzy programming techniques to solve solid transportation problem with additional constraints

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Sharmistha Halder (Jana) ◽  
Biswapati Jana
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Transportation Cost ◽  
Fuzzy Programming ◽  
Solid Transportation Problem ◽  
Generalized Gradient ◽  
Proposed Model ◽  
Programming Techniques ◽  
Total Transportation Cost ◽  
Additional Constraints

An innovative, real-life solid transportation problem is explained in a non-linear form. As in real life, the total transportation cost depends on the procurement process or type of the items and the distance of transportation. Besides, an impurity constraint is considered here. The proposed model is formed with fuzzy imprecise nature. Such an interesting model is optimised through two different fuzzy programming techniques and fractional programming methods, using LINGO-14.0 tools followed by the generalized gradient method. Finally, the model is discussed concerning these two different methods.

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. 

Fuzzy Transportation Problem by Using Triangular, Pentagonal and Heptagonal Fuzzy Numbers With Lagrange's Polynomial to Approximate Fuzzy Cost for Nonagon and Hendecagon

2020 ◽  
Vol 9 (1) ◽  
pp. 112-129
Author(s):  
Ashok Sahebrao Mhaske ◽  
Kirankumar Laxmanrao Bondar
Keyword(s):  
Transportation Problem ◽  
Operational Research ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Transportation Cost ◽  
Fuzzy Transportation Problem ◽  
Total Transportation Cost ◽  
Fuzzy Cost

The transportation problem is a main branch of operational research and its main objective is to transport a single uniform good which are initially stored at several origins to different destinations in such a way that the total transportation cost is minimum. In real life applications, available supply and forecast demand, are often fuzzy because some information is incomplete or unavailable. In this article, the authors have converted the crisp transportation problem into the fuzzy transportation problem by using various types of fuzzy numbers such as triangular, pentagonal, and heptagonal fuzzy numbers. This article compares the minimum fuzzy transportation cost obtained from the different method and in the last section, the authors introduce the Lagrange's polynomial to determine the approximate fuzzy transportation cost for the nanogon (n = 9) and hendecagon (n = 11) fuzzy numbers.

scholarly journals Optimization of total transportation cost

2020 ◽  
Vol 26 (1) ◽  
pp. 57-63
Author(s):  
Adamu Isah Kamba ◽  
Suleiman Mansur Kardi ◽  
Yunusa Kabir Gorin Dikko
Keyword(s):  
Transportation Problem ◽  
Research Work ◽  
Minimum Cost ◽  
Transportation Cost ◽  
Strategic Decision ◽  
Distribution Method ◽  
North West ◽  
Total Transportation Cost ◽  
Transportation Schedule ◽  
Furniture Factory

In this research work, the study used transportation problem techniques to determine minimum cost of transportation of Gimbiya Furniture Factory using online software, Modified Distribution Method (MODI). The observation made was that if Gimbiya furniture factory, Birnin Kebbi could apply this model to their transportation schedule, it will help to minimize transportation cost at the factory to ₦1,125,000.00 as obtained from North west corner method, since it was the least among the two methods, North west corner method and Least corner method. This transportation model willbe useful for making strategic decision by the logistic managers of Gimbiya furniture factory, in making optimum allocation of the production from the company in Kebbi to various customers (key distributions) at a minimum transportation cost. Keywords: North West corner, Least corner, Transportation problem, minimum transportation.

scholarly journals Mathematical Modeling for Routes and Cost of Local Transports in Pune City

2020 ◽  
Vol 9 (8) ◽  
pp. 25-28
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Transportation Cost ◽  
Transportation Model ◽  
Air Suspension ◽  
Life Problems ◽  
Wide Range ◽  
Trip Distance ◽  
Research Domains

Transportation problem is considered a vitally important aspect that has been studied in a wide range of operations including research domains. As such, it has been used in simulation of several real life problems. The transportation model is for the optimization of routes, cost and travelling of peoples with the help of public transport buses from the source to the destination by road. The data is collected which includes number of trips per day, cost of trips per trip ,distance between source and destination etc. manually through the questionery interview with the conductors drivers and the regular travelling peoples travelling on that route as well as data collection from PMPML office and calculation for minimizing the transportation cost have been done. The result of the research with proper scheduling, proper routing of buses can save Rs. 48865.875 in a 1 day. The saving of the transportation cost increases the profit of the PMPML. The total saving amount profit percentage is about 18.15% increase from saving transportation cost. The parameters as discussed above are considered and collected manually with the help of survey sheet and transportation model is prepared and after that calculation for minimizing the transportation cost have been done. The methods used for minimization of transportation of cost are Northwest corner method, Least count method etc. The result of the research gives with proper scheduling, routing of buses can save generate so much of revenue with saving of cost.. The amount saved from the transportation cost is utilized for increase the facilities in bus such as A.C, Automatic door system, Air suspension, Good quality of seats etc.

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 Fixed-Charge Solid Transportation Problem with Budget Constraints Based on Carbon Emission in Neutrosophic Environment

2021 ◽  
Author(s):  
Shyamali Ghosh ◽  
Sankar Kumar Roy ◽  
Jose Luis Verdegay
Keyword(s):  
Measurement Errors ◽  
Transportation Problem ◽  
Carbon Emission ◽  
General Structure ◽  
Real Life ◽  
Transportation System ◽  
Neutrosophic Set ◽  
Budget Constraints ◽  
Solid Transportation Problem ◽  
Multi Objective

Abstract This paper is to integrate among solid transportation problem, budget constraints and carbon emission with probable maximum profit. The limits of air pollution and climate variation are solely dependent by exerting CO 2 gas and rest greenhouse gases due to myriad transportation system. Henceforth, it is our apt mission to minimize carbon emission for pollution free environment. Again transportation system with single objective is hardly applicable to the situation with more than one criterion. Therefore multi- objective decision making is incorporated for designing real-life transportation problem. Due to time pressure, data limitation, lack of information or measurement errors in practical problems, there exist some hesitations or suspicions. Based on the fact, decision maker considers indeterminacy in the designed problems. To overcome the restriction on occurrence and non-occurrence of fuzzy and intuitionistic fuzzy, neutrosophic set is very important and suitable to accommodate such general structure of problems. Therefore neutrosophic environment with neutrosophic linear programming, fuzzy programming and global criterion method are profiled to search the compromise solution of the multi- objective transportation problem ( MOTP ). Thereafter, the performance of the considered model is useful by evaluating a numerical example; and then the derived results are compared. Finally sensitivity analysis and conclusions with upcoming works of this research are stated hereafter.

On Solving Fuzzy Multi-Objective Multi-Choice Stochastic Transportation Problems

2019 ◽  
pp. 332-378
Keyword(s):  
Probability Distributions ◽  
Transportation Cost ◽  
Transportation Problems ◽  
Multi Objective ◽  
Fuel Prices ◽  
Product Availability ◽  
Road Congestion ◽  
Total Transportation Cost ◽  
Cost Parameters ◽  
The Cost

This chapter presents solution procedures for solving unbalanced multi-objective multi-choice stochastic transportation problems in a hybrid fuzzy uncertain environment. In this chapter, various types of unbalanced multi-objective fuzzy stochastic transportation models are considered with the assumption that the parameters representing supplies of the products at the origins and demands of the products at the destinations, capacity of the conveyances, associated with the system constraints are either fuzzy numbers (FNs) or fuzzy random variables (FRVs) with some known continuous fuzzy probability distributions. The multi-choice cost parameters are considered as FNs. In this chapter, two objectives are considered: total transportation cost and total transportation time. As the transportation cost mainly depends on fuel prices and since fuel prices are highly fluctuating, the cost parameters are taken as multi-choice cost parameters with possibilistic uncertain nature. The time of transportation mainly depends on vehicle conditions, quality of roads, and road congestion. Due to these uncertain natures, the parameters representing time of transportation are also taken as fuzzy uncertain multi-choice parameters. In this transportation model, these objectives are minimized satisfying the constraints: product availability constraints, requirement of the product constraints, and capacity of the conveyance constraints. Numerical examples are provided for the sake of illustration of the methodology presented in this chapter, and also achieved solutions are compared with the solutions obtained by some existing methodologies to establish its effectiveness.

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