Solution of multi-item interval valued solid transportation problem with safety measure using different methods

Baidya, Abhijit; Bera, Uttam Kumar; Maiti, Manoranjan

doi:10.1007/s12597-013-0129-2

Cited by 24 publications

(6 citation statements)

References 20 publications

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“…The main objective of this paper is to present a solution procedure of a solid transportation problem under various precise and imprecise environments. In this paper, we formulated (4,5,6,11) C 211 (7,10,11,17) C 311 (6,8,9,10) C 121 (5,6,8,12) C 221 (10,11,12,14) C 321 (12,14,17,18) C 131 (13,14,15,20) C 231 (15,17,19,21) C 331 (15,17,19,21) C 112 (3,5,7,9) C 212 (13,15,19,20) C 312 (11,13,14,22) C 122 (9,10,…”

Section: Discussionmentioning

confidence: 99%

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A solid transportation problem with safety factor under different uncertainty environments

Baidya

Bera

Maiti

2013

J. Uncertain. Anal. Appl.

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In this paper, we introduce a new concept 'safety factor' in a transportation problem. When items are transported from plants to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency, land slide, etc. in some routes. Due to these, a desired total safety factor is being introduced, and depending upon the nature of the safety factor, we develop five models. In this paper, a solid transportation problem (STP) with imprecise unit costs is considered. The sources' availabilities, destinations' demands, and capacities of conveyances are also represented by fuzzy numbers like trapezoidal and triangular numbers. The transportation problem has been formulated with and without a safety factor. To reduce the different models into its crisp equivalent, we introduce different methods as chance-constraint programming, an approach using interval approximation of fuzzy numbers and the application of the expected value model. Generalized reduced gradient technique is used to find the optimal solutions for a set of given numerical data. To illustrate the model, a numerical example has been presented and solved using LINGO.12 software. The effect of safety factors on transported amount is illustrated.

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Section: Discussionmentioning

confidence: 99%

“…Our aim is to formulate and solve solid transportation problems with safety constraints with different types of uncertain (fuzzy, random, and hybrid) parameters. Recently, Baidya et al [7,8] solved two problems based on safety factors and uncertainty in transportation problem.…”

Section: Introductionmentioning

confidence: 99%

A solid transportation problem with safety factor under different uncertainty environments

Baidya

Bera

Maiti

2013

J. Uncertain. Anal. Appl.

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“…Recently, Kundu et al [13] have proposed a method to find the crisp optimal compromise solution of the fuzzy MOMISTP, using the fuzzy programming technique and global criterion method. Solid transportation problems are also studied by Baidya et al [14] and Kundu et al [15]. Ebrahimnejad [16] studied the transportation problem with generalized trapezoidal fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Uncertain multi-objective multi-product solid transportation problems

Rani

Gulati

2016

Sādhanā

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The solid transportation problem is an important generalization of the classical transportation problem as it also considers the conveyance constraints along with the source and destination constraints. The problem can be made more effective by incorporating some other factors, which make it useful in real life situations. In this paper, we consider a fully fuzzy multi-objective multi-item solid transportation problem and present a method to find its fuzzy optimal-compromise solution using the fuzzy programming technique. To take into account the imprecision in finding the exact values of parameters, all the parameters are taken as trapezoidal fuzzy numbers. A numerical example is solved to illustrate the methodology.

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“…Expected-constrained programming for an uncertain solid transportation problem is given by Cui and Sheng [15]. Baidya et al have discussed the multi-item interval valued solid transportation problem in [16,17]. A method to solve multiobjective solid transportation problems in uncertain environment has been presented in [18].…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Multiobjective Multi-Item Solid Transportation Problem

Rani

Gulati

Kumar

2015

Journal of Optimization

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A transportation problem involving multiple objectives, multiple products, and three constraints, namely, source, destination, and conveyance, is called the multiobjective multi-item solid transportation problem (MOMISTP). Recently, Kundu et al. (2013) proposed a method to solve an unbalanced MOMISTP. In this paper, we suggest a method, which first converts an unbalanced problem to a balanced one. In one case of an example, while the method proposed by Kundu et al. concludes infeasibility, our method gives a feasible solution.

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Solution of multi-item interval valued solid transportation problem with safety measure using different methods

Cited by 24 publications

References 20 publications

A solid transportation problem with safety factor under different uncertainty environments

A solid transportation problem with safety factor under different uncertainty environments

Uncertain multi-objective multi-product solid transportation problems

On Fuzzy Multiobjective Multi-Item Solid Transportation Problem

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