Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters

Anukokila, P.; Radhakrishnan, B.; Anju, A.

doi:10.1051/ro/2019005

Cited by 16 publications

(13 citation statements)

References 23 publications

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“…There exist some researches studying on multi-objective transportation problem (MOTP) in some realistic environments. A few of them [1,2,15,19,25,32] are presented including their works. Most of them were analyzed by fuzzy programming (FP), rough programming, neutrosophic linear programming (NLP), goal programming (GP), etc.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station

Ghosh

Roy

2021

RAIRO-Oper. Res.

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In this contribution, for the first time, an efficient model of multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station is formulated. Transfer station inserts transfer cost and type-I fixed-charge. Our aim is to analyze an extra cost that treats as type-II fixed-charge and truck load constraints in the designed model that required when the amount of items exceeds the capacity of vehicle for fulfilling the shipment by more than one trip. Type-II fixed-charge is added with transportation cost and other cost from transfer station. We consider here an important issue of the multi-objective transportation problem as product blending constraints for transporting raw materials with different purity levels for customers' satisfaction. In realistic point of view, the parameters of the model are imprecise in nature due to existing several unpredictable factors. These factors are apprehended by incorporating the fuzzy-rough environment on the parameters. Expected-value operator is utilized to derive the deterministic form of fuzzy-rough data, and the model is experienced with help of fuzzy programming, neutrosophic linear programming and global criteria method. Two numerical examples are illustrated to determine the applicability of the proposed model.

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Section: Introductionmentioning

confidence: 99%

“…Allah et al [1] defined a multi-objective transportation model in the presence of neutrosophic environment. Anukokila and Radhakrishan [2] formulated multi-objective fractional TP in fuzzy environment and then solved it by GP approach. Li and Lai [15] analyzed multi-objective problem on transportation system using FP.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station

Ghosh

Roy

2021

RAIRO-Oper. Res.

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“…Using fuzzy goal programming, the degree of satisfaction of each objective function is maximized which helps the decision maker to decide the best efficient solution. Many researchers proposed and applied fuzzy goal programming models, for example Aköz and Petrovic [16], Anukokila et al [17], Chen and Tsai [18], Cheng [19], Dalman and Bayram [20], Díaz-Madroñero et al [21], Hocine et al [22], Jadidi et al [23], Jamalnia and Soukhakian [24], Jiménez et al [25], Pramanik and Roy [26], and Jana et al [27]. It is not always possible that the goals priority is symmetric in nature.…”

Section: Introductionmentioning

confidence: 99%

Goal Programming Models with Linear and Exponential Fuzzy Preference Relations

et al. 2020

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Goal programming (GP) is a powerful method to solve multi-objective programming problems. In GP the preferential weights are incorporated in different ways into the achievement function. The problem becomes more complicated if the preferences are imprecise in nature, for example ‘Goal A is slightly or moderately or significantly important than Goal B’. Considering such type of problems, this paper proposes standard goal programming models for multi-objective decision-making, where fuzzy linguistic preference relations are incorporated to model the relative importance of the goals. In the existing literature, only methods with linear preference relations are available. As per our knowledge, nonlinearity was not considered previously in preference relations. We formulated fuzzy preference relations as exponential membership functions. The grades or achievement function is described as an exponential membership function and is used for grading levels of preference toward uncertainty. A nonlinear membership function may lead to a better representation of the achievement level than a linear one. Our proposed models can be a useful tool for different types of real life applications, where exponential nonlinearity in goal preferences exists. Finally, a numerical example is presented and analyzed through multiple cases to validate and compare the proposed models. A distance measure function is also developed and used to compare proposed models. It is found that, for the numerical example, models with exponential membership functions perform better than models with linear membership functions. The proposed models will help decision makers analyze and plan real life problems more realistically.

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“…Lee and Moore [3] applied GP to find a solution of MOTP. Anukokila and Radhakrishnan [4] studied a GP approach for solving multi-objective fractional transportation problem by representing the parameters (γ , δ) in terms of interval valued fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%