Fuzzy programming approach to multiobjective solid transportation problem

1993 ◽  
Vol 57 (2) ◽  
pp. 183-194 ◽  
Author(s):  
A.K. Bit ◽  
M.P. Biswal ◽  
S.S. Alam
Keyword(s):  
Transportation Problem ◽  
Fuzzy Programming ◽  
Programming Approach ◽  
Solid Transportation Problem

Solving Solid Transportation Problems With Multi-Choice Cost and Stochastic Supply and Demand

2018 ◽  
pp. 137-170 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into a solid transportation problem, and this new problem is called Multi-Choice Stochastic Solid Transportation Problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique that will select an appropriate choice from a set of multi-choice, which optimize the objective function. The stochastic constraints of STP converts into deterministic constraints by stochastic programming approach. Finally, the authors construct a non-linear programming problem for MCSSTP, and by solving it, they derive an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

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.

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 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.

Solving Solid Transportation Problem with Multi-Choice Cost and Stochastic Supply and Demand

2014 ◽  
Vol 5 (3) ◽  
pp. 1-26 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

This paper proposes a new approach to analyze the solid transportation problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming which is incorporated in three constraints namely sources, destinations and capacities constraints followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into solid transportation problem and this new problem is called multi-choice stochastic solid transportation problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique which will select an appropriate choice from a set of multi-choice which optimizes the objective function. The stochastic constraints of STP convert into deterministic constraints by stochastic programming approach. Finally, the authors have constructed a non-linear programming problem for MCSSTP and have derived an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

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