Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment

Gupta, Srikant; Ali, Irfan; Ahmed, Aquil

doi:10.1007/s12597-018-0330-4

Cited by 23 publications

(8 citation statements)

References 25 publications

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“…Let us consider the quantity of the item available at m sources (origins) O i (i = 1, 2, 3, ...., m) to be delivered to the n location D j (j = 1, 2, 3, ....., n) to meet the b j requirement. With this assumption, the three different mathematical model for the multi-objective capacitated TP with mixed constraints is formulated as follows [34,35]:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…To demonstrate the practical use and the computational details of working out the suggested quantity to be shipped from different sources to a different destination, the following numerical example is provided. Parts of the data are from Gupta et al [34,35] in which they considered three origins and three destinations with the objective of how much should they ship from origin to destination to minimize the cost of damage, cost of labouring, total transportation time, total transportation costs and also maximize the discount on shipping costs. The information simulated by DM are summarized below in the Tables 3, 4, 5, 6, 7, 8, 9, and 10.…”

Section: Examplementioning

confidence: 99%

“…Among all the used distributions such as Pareto, Weibull, Normal and Gamma, the least value of AIC and BIC has been correspond to the GD that shows the efficiency of our proposed work. The above defined capacitated TP with linear and fractional objective functions was first formulated by Gupta et al [34] in which they considered the three different types of real life situations in their formulated model. They present the ambiguity in the paper with fuzzy numbers, multi-choices and randomness and used fuzzy goal programming approach for getting the desired result.…”

Section: Examplementioning

confidence: 99%

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Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution

Gupta

Garg

Chaudhary

2020

Complex Intell. Syst.

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The transportation problem in real life is an uncertain problem with multi-objective decision-making. In particular, by considering the conflicting objectives/criteria such as transportation costs, transportation time, discount costs, labour costs, damage costs, decision maker searches for the best transportation setup to find out the optimum shipment quantity subject to certain capacity restrictions on each route. In this paper, capacitated stochastic transportation problem is formulated as a multi-objective optimization model along with some capacitated restrictions on the route. In the formulated problem, we assume that parameters of the supply and demand constraints' follow gamma distribution, which is handled by the chance constrained programming approach and the maximum likelihood estimation approach has been used to assess the probabilistic distributions of the unknown parameters with a specified probability level. Furthermore, some of the objective function's coefficients are consider as ambiguous in nature. The ambiguity in the formulated problem has been presented by interval type 2 fuzzy parameter and converted into the deterministic form using an expected value function approach. A case study on transportation illustrates the computational procedure.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

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Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution

Gupta

Garg

Chaudhary

2020

Complex Intell. Syst.

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“…Some other notable works have been done by [21][22][23][24][25][26]; all have established different kinds of transformation techniques to select the most suitable choice with the help of the utility function procedure, binary variables technique, interpolating method, Lagrange's interpolating polynomial. Recently, [27,28] formulated a capacitated transportation problem under certain and uncertain environments. These uncertainties in the formulated problem had been tackled by fuzziness, multi-choice, and randomness, respectively.…”

Section: Multi-choice Programming Problemmentioning

confidence: 99%

Bi-Level Multi-Objective Production Planning Problem with Multi-Choice Parameters: A Fuzzy Goal Programming Algorithm

et al. 2019

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This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.

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“…ey considered an application in the area of hybrid multicriteria group decision-making with hesitant fuzzy truth degrees. Gupta et al [29] formulated a new model of MOCTP considering the mixed constraints in which few objective functions are linear, while the others are assumed to be fractional. is situation is conflicting by nature.…”

Section: Introductionmentioning

confidence: 99%

Enhancement of Capacitated Transportation Problem in Fuzzy Environment

Khalifa

Kumar

Alharbi

2020

Advances in Fuzzy Systems

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This research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. Through the use of the α‐level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker’s choice between intervals. The maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.

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Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment

Cited by 23 publications

References 25 publications

Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution

Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution

Bi-Level Multi-Objective Production Planning Problem with Multi-Choice Parameters: A Fuzzy Goal Programming Algorithm

Enhancement of Capacitated Transportation Problem in Fuzzy Environment

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