Fuzzy integer transportation problem

Chanas, Stefan; Kuchta, Dorota

doi:10.1016/s0165-0114(96)00380-6

Cited by 94 publications

(39 citation statements)

References 3 publications

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“…In the first step, based on the extension principle [5],the membership function of supply and demand can be defined as:…”

Section: Constraintsmentioning

confidence: 99%

“…Ahlatcioglu, Sivri and Güzel [1] proposed a solution algorithm finding all fuzzy optimal solution of the transportation problem that the cost coefficients and the supply and demand quantities are fuzzy numbers. Chanas and Kuchta [5] proposed an algorithm that solves the transportation problem with fuzzy supply and demand values and integrality condition imposed on the solution. Ammar and Youness [2] investigated the efficient solutions and stability of fuzzy multi-objective transportation problem and proposed an algorithm for the determination of the stability set.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy Cost Analysis In A Fuzzy Transportation System A Study Of The Supply Chain Management In A General Contractor Company

Barough¹

2011

J. Math. Computer Sci.

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Transportation models play an important role in logistics and supply chain management for reducing cost and improving services. In this paper, the author presented a fuzzy transportation problem, in which the cost coefficients and supply and demand quantities are fuzzy numbers. The problem is solved in two stages. First, calculating the maximum satisfactory level and achieving balances between fuzzy supplies and demands. Second, the problem is solved by considering the unit of transportation costs and optimal solutions which are connected with fuzzy quantities' satisfactory level are founded. The author used two different satisfactory levels for the problem: The transportation costs breaking points (γp) and the values that have violated positive condition of optimal solutions in the intervals of [γp-1, γp]. A new method is proposed in this paper to find optimal solutions. The proposed method is then illustrated through a numerical example.

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“…In the first step, based on the extension principle [5],the membership function of supply and demand can be defined as:…”

Section: Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fuzzy Cost Analysis In A Fuzzy Transportation System A Study Of The Supply Chain Management In A General Contractor Company

Barough¹

2011

J. Math. Computer Sci.

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“…Chanas and Kuchta [25] developed a new method for solving fuzzy integer transportation problem by representing the supply and demand parameters as L-R type fuzzy numbers. Chiang [26] proposed a method to find the optimal solution of transportation problems with fuzzy requirements and fuzzy availabilities.…”

Section: Introductionmentioning

confidence: 99%

A Simple Method for Solving Type-2 and Type-4 Fuzzy Transportation Problems

Kumar¹

2016

IJFIS

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In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer's over time work, unexpected failures in machine, seasonal changes and many more. To counter these problems, depending on the nature of the parameters, the TP is classified into two categories namely type-2 and type-4 fuzzy transportation problems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992) is used to transform the type-2 and type-4 FTPs into a crisp one so that the conventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.

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“…For example, FLP is used to solve problems in agricultural economics [55,38,16,41,48,71,70], network location [17], banking and finance [53,54,38,27,84,37,40], environment management [72,52,42], inventory management [49,66,65], manufacturing and production [78,76,80,59,30,75,81,82,32,56], resource allocation [1,36], supply chain management [14,57,58,6,85], personnel management [73], media selection [83], trade balance [9], management of the reservoir watershed [12], dimension design [13], transportation management [78,94,10,11,22,…”

Section: Introductionmentioning

confidence: 99%

Duality in fuzzy linear programming: a survey

Schryen

Hristova

2013

OR Spectrum

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The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed, comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For example, there are no consistent concepts of weak duality and strong duality. The contributions of this survey are (1) to provide the first comprehensive overview of literature results on duality in FLP, (2) to analyze these results in terms of research gaps in FLP duality theory, and (3) to show avenues for further research. We systematically analyze duality in fuzzy linear programming along potential fuzzifications of linear programs (fuzzy classes) and along fuzzy order operators. Our results show that research on FLP duality is fragmented along both dimensions, more specifically duality approaches and related results vary in terms of homogeneity, completeness, consistency with crisp duality, and complexity. Fuzzy linear programming is still far away from a unifying theory as we know it from crisp linear programming. We suggest fur- ther research directions, including the suggestion of comprehensive duality theories for specific fuzzy classes while dispensing with restrictive mathematical assumptions, the development of consistent duality theories for specific fuzzy order operators, and the proposition of a unifying fuzzy duality theory.

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Fuzzy integer transportation problem

Cited by 94 publications

References 3 publications

Fuzzy Cost Analysis In A Fuzzy Transportation System A Study Of The Supply Chain Management In A General Contractor Company

Fuzzy Cost Analysis In A Fuzzy Transportation System A Study Of The Supply Chain Management In A General Contractor Company

A Simple Method for Solving Type-2 and Type-4 Fuzzy Transportation Problems

Duality in fuzzy linear programming: a survey

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