Interactive solutions for the linear multiobjective transportation problem

Ringuest, Jeffrey L.; Rinks, Dan B.

doi:10.1016/0377-2217(87)90274-8

Cited by 113 publications

(37 citation statements)

References 7 publications

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“…Step 5: We get an equivalent crisp model, which can be formulated as: Maximize Xmn+1 subject to The example is solved by the given interactive approach in [6]. The procedure begins with constructing a linear compromise solution and a search is conducted among all non-dominated solutions corresponding to extreme points adjacent to the most preferred extreme point.…”

Section: Theorem: Definementioning

confidence: 99%

“…can write k L ( λ, K) with p = 1,2,and ∞ as follows: The family of distance functions for solutions of the given fuzzy linear membership approach and the interactive procedure [6] are summarized in table 3. Table 3 Objective function The family of the distance functions for solutions of the given fuzzy approach and the interactive procedure [6] are summarized in table 3.…”

Section: Theorem: Definementioning

confidence: 99%

“…Table 3 Objective function The family of the distance functions for solutions of the given fuzzy approach and the interactive procedure [6] are summarized in table 3. In above example it is observed that the fuzzy approach gives compromise solution better than the interactive compromise solution with respect to L1.…”

Section: Theorem: Definementioning

confidence: 99%

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Fuzzy Programming Technique to Solve Bi-Objective Transportation Problem

SG¹,

VH²,

RM³

2010

Int J Mach Intell

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Abstract-In a transportation problem generally a single criterion of minimizing the total transportation cost is considered but in certain practical situations two or more objectives are relevant. For example, the objectives may be minimization of total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation etc. Clearly, this problem can be solved using any of the multiobjective linear programming techniques, but the computational efforts needed would be prohibitive in many cases. In this paper, The Bi-objective transportation problem, where only objectives are considered as fuzzy. We apply the fuzzy programming technique with hyperbolic membership function to solve a biobjective transportation problem as vector minimum problem.

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Section: Theorem: Definementioning

confidence: 99%

Section: Theorem: Definementioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Programming Technique to Solve Bi-Objective Transportation Problem

SG¹,

VH²,

RM³

2010

Int J Mach Intell

View full text Add to dashboard Cite

show abstract

“…The multi-objective optimization problem is solved using some relatively simple methods and the solution is presented to DM. The methods in this category include the Method of Global Criterion (e.g., Ringuest & Rinks, 1987;Miettinen, 1999;Caballero, Luque, Molina, & Ruiz, 2005) and Proximal Bundle Method (e.g., Kiwiel, 1990;Miettinen & Mäkelä, 1995).…”

Section: No-preference Methodsmentioning

confidence: 99%

“…A comparison has been made with the approaches of Li and Lai (2000), Bit, Biswal, and Alam (1992), Ringuest and Rinks (1987), Quddoos, Javaid, Ali, and Khalid (2013), and Quddoos, Javaid, and Khalid (2013) in Table 4. (Bit, Biswal, & Alam, 1992); c (Ringuest & Rinks, 1987); d (Quddoos, Javaid, Ali, & Khalid, 2013); e (Quddoos, Javaid, & Khalid, 2013) Figure 6. Graphical representation of solutions at different priorities Now consider the second example of a multi-objective assignment problem using the proposed model.…”

Section: Graphical Representation Of Consistencymentioning

confidence: 99%

A Distance Based Method for Solving Multi-Objective Optimization Problems

Kamal

Jalil

Muneeb

et al. 2018

J. Mod. Appl. Stat. Methods

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A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective subproblems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. Numerical illustrations are given for the proposed model.

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Multi‐objective combinatorial optimization problems: A survey

Ulungu

Teghem

1994

Multi Criteria Decision Anal

271

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In the last 20 years many multi‐objective linear programming (MOLP) methods with continuous variables have been developed. However, in many real‐world applications discrete variables must be introduced. It is well known that MOLP problems with discrete variables can have special difficulties and so cannot be solved by simply combining discrete programming methods and multi‐objective programming methods. The present paper is intended to review the existing literature on multi‐objective combinatorial optimization (MOCO) problems. Various classical combinatorial problems are examined in a multi‐criteria framework. Some conclusions are drawn and directions for future research are suggested.

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Interactive solutions for the linear multiobjective transportation problem

Cited by 113 publications

References 7 publications

Fuzzy Programming Technique to Solve Bi-Objective Transportation Problem

Fuzzy Programming Technique to Solve Bi-Objective Transportation Problem

A Distance Based Method for Solving Multi-Objective Optimization Problems

Multi‐objective combinatorial optimization problems: A survey

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