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Solving multi-choice multi-objective transportation problem: a utility function approach

Journal of Uncertainty Analysis and Applications 2014年第1期2卷 1-20页

作者： Gurupada Maity Sankar Kumar Roy Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the environment of utility function approach. MCMTP is converted to multi-objective transportation problems (MOTP) by transforming the multi-choice parameters like cost, demand, and supply to real-valued parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTP are solved by goal programming (GP) approach. Using GP, the solution of MOTP may not be satisfied all the time by the decision maker (DM) when the proposed problem contains interval-valued aspiration level. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and utility function into the MOTP and then compared the solution between them. Finally, numerical examples are presented to show the feasibility and usefulness of our paper.

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Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach

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Journal of Industrial Engineering International 2016年第3期12卷 287-298页

作者： Maiti, Sumit Kumar Roy, Sankar Kumar School of Applied Sciences and Humanities Haldia Institute of Technology Purba Midnapore Haldia 721 157 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

In this paper, a Multi-Choice Stochastic Bi-Level programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general transformation technique with the help of binary variables is used to transform the multi-choice type cost coefficients of the objective functions of Decision Makers(DMs). Then the transformed problem is considered as a deterministic multi-choice bi-level programming problem. Finally, a numerical example is presented to illustrate the usefulness of the paper. © 2016, The Author(s).

关键词： Bi-level programming Fuzzy programming Multi-choice programming Non-linear programming Stochastic programming

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Sustainable Manufacturing Model with Considering Greenhouse Gas Emission and Screening Process of Imperfect Items Under Stochastic Environment

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International Journal of applied and Computational mathematics 2022年第3期8卷 1-21页

作者： Dolai, Madhusudan Manna, Amalesh Kumar Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore 721102 India Department of Mathematics C. V. Raman Global University Bhubaneswar 752054 India

In this work, a production model with screening of imperfect product and green house gas emission has been developed. Here, it has been considered that the manufacturing process transfer from in-control situation to out-of-control situation after an uncertain time, which is a random variable. In the out-of-control situation, a part of produced items are imperfect. For this reason, the manufacturer decides to check each item through screening process before sale the perfect items to the market. The screening and production rates are not equal and new type of screening process has been considered here. The imperfect rate depends on the length of out-of-control situation and its random nature. Also, the manufacturer sales the imperfect items by reducing the selling price. The greenhouse gas (GHG) emission tax has been considered here and its rate depends on the production rate. The objective of this study is to find the optimal business and production period, optimal production rate which maximizes the expected average profit of the model. Two numerical examples have been considered to illustrate the feasibility of the model. Finally, the sensitivity analysis have been carried out to get the effect of some important parameters on the optimization problem related to the proposed model. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Greenhouse gas emission Imperfect production Price discount Screening

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Modeling of Memory Dependent Derivative Under Three-Phase Lag in Generalized Thermo-Viscoelasticity

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International Journal of applied and Computational mathematics 2021年第6期7卷 1-20页

作者： Singh, Biswajit Sarkar, Smita Pal Barman, Krishnendu Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur Howrah 711103 West Bengal India Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Paschim Medinipur 721102 West Bengal India

In this study, a new generalized model of thermo-viscoelasticity with three phase-lag (TPL) theory concerning memory-dependent derivative (MDD) theory is emphasized. The governing combined equations of the novel model associated with kernel function and time delay are considered in a two-dimensional semi-infinite space. The bounding surface of the medium is assumed to be free of traction and subjected to time-dependent thermal loading. Using Laplace and Fourier Transform techniques, the problem is transformed from the space–time domain and then solved numerically. Suitable numerical technique is used to find the inversion of Fourier and Laplace transforms. In the simulation, the effects of the time-delay parameter and kernel function on the distributions of the displacement components, stresses and temperature field are studied and represented graphically. The results shows that the presence of TPL, the time-delay and kernel function extensively affect all the distributions. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Laplace and Fourier transform Memory dependent derivative Thermo-viscoelasticity Three phase-lag Vector matrix differential equation

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A study on pentagonal fuzzy number and its corresponding matrices

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Pacific Science Review B: Humanities and Social Sciences 2015年第3期1卷 131-139页

作者： Apurba Panda Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

In this article, the notion of pentagonal fuzzy number (PFN) is introduced in a generalized way. A few articles have been published based on this topic, but they have some ambiguities in defining this type of fuzzy number. Here, we proposed the logical definition in developing a pentagonal fuzzy number, along with its arithmetic operations. Based on PFN, the structure of pentagonal fuzzy matrices (PFMs) is studied, together with their basic properties. Some special type of PFMs and their algebraic natures (trace of PFM, adjoint of PFM, determinant of PFM, etc.) are discussed in this article. Finally, the notion of nilpotent PFM, comparable PFM, and constant PFMs, with their many properties, are highlighted in this article.

关键词： Pentagonal fuzzy number Arithmetic of pentagonal fuzzy number Pentagonal fuzzy matrices Pentagonal fuzzy determinant Nilpotent pentagonal fuzzy matrices

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Generalised multi-fuzzy soft set and its application in decision making

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Pacific Science Review A: Natural Science and Engineering 2015年第1期17卷 23-28页

作者： Asit Dey Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

The aim of this paper is to introduce the concept of generalised multi-fuzzy soft set. We also define several generalised multi-fuzzy soft set operations and study their properties, and applications of generalised mul... 详细信息

关键词： Soft sets Fuzzy soft sets Multi-fuzzy sets Multi-fuzzy soft sets Generalised multi-fuzzy soft sets Decision making

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Analysis of pricing decision for substitutable and complementary products with a common retailer

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Pacific Science Review A: Natural Science and Engineering 2016年第3期18卷 190-202页

作者： Raghu Nandan Giri Shyamal Kumar Mondal Manoranjan Maiti Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

In this paper, a competition of selling two substitutable products and one complementary product has been studied in two-echelon supply chain systems in which one of these three products is produced by one manufacturer separately, and all produced items are sold through a common retailer in the market. The demand of each product depends linearly on prices of these three products as per their nature. In this study, four different decision scenarios are developed mathematically under the game theory framework to maximize the profit function of each participant of the supply chain, and a number of pricing strategies are subsequently worked out for manufacturers and retailer. Finally, the model under different scenarios is illustrated with numerical data to study the feasibility of the model exploring the managerial insights, as well. Different marketing policies are predicted for maximum individual and system profits.

关键词： Supply chain Substitutable products Complementary products Stackelberg game

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On hesitant multi-fuzzy soft topology

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Pacific Science Review B: Humanities and Social Sciences 2015年第3期1卷 124-130页

作者： Asit Dey Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

The aim of this paper is to introduce and study the concept of hesitant multi-fuzzy soft topological space and some of its structural properties, such as the neighbourhood of hesitant multi-fuzzy soft sets and interior hesitant multi-fuzzy soft sets, the hesitant multi-fuzzy soft basis and hesitant multi-fuzzy soft subspace topology. Additionally, we introduce and define the hesitant multi-fuzzy soft cover, hesitant multi-fuzzy soft open cover, and hesitant multi-fuzzy soft compactness, and some important results on them are presented.

关键词： Hesitant multi-fuzzy soft basis Hesitant multi-fuzzy soft subspace topology Hesitant multi-fuzzy soft cover Hesitant multi-fuzzy soft open cover Hesitant multi-fuzzy soft compactness 54A05 54A40 03E72 54D30 54A10

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Multi-item EPQ model with learning effect on imperfect production over fuzzy-random planning horizon

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Journal of Management Analytics 2017年第1期4卷 80-110页

作者： Amalesh Kumar Manna Barun Das Jayanta Kumar Dey Shyamal Kumar Mondal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnapore-721102WBIndia Department of Mathematics Sidho-Kanho-Birsha UniversityPuruliaWBIndia Department of Mathematics Mahishadal Raj CollegeMahishadal721628WBIndia

Uncertainty is certain in the world of *** study revisits an economic production quantity(EPQ)model with shortages for stock-dependent demand of the items with reworking and disposing of the imperfect ones over a random planning horizon under the joint effect of inflation and time value of money,where the expected time length is imprecise in *** of learning effect has been incorporated to reduce the defective *** total expected profit over the random planning horizon is maximized subject to the imprecise space *** possibility,necessity and credibility measures have been introduced to defuzzify the *** simulation-based genetic algorithm is used to make decision for the above EPQ model in different measures of *** model is illustrated through an *** analysis shows the impacts of different parameters on the objective function in the model.

关键词： imperfect production rework shortage learning effect random planning horizon genetic algorithm

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Scheduling Algorithm to Select Optimal Programme Slots in Television Channels: A Graph Theoretic Approach

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International Journal of applied and Computational mathematics 2017年第3期3卷 1931-1950页

作者： Pal, Madhumangal Pal, Anita Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India Department of Mathematics National Institute of Technology Durgapur Mahatma Gandhi Avenue Durgapur 713 209 West Bengal India

In this paper, it is shown that all programmes of all television channels can be modelled as an interval graph. The programme slots are taken as the vertices of the graph and if the time duration of two programme slots have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a programme is taken as the weight of the vertex. A set of programmes that are mutually exclusive in respect of time scheduling is called a session. We assume that a company sets the objective of selecting the popular programmes in k parallel sessions among different channels so as to make its commercial advertisement reach the maximum number of viewers, that is, a company selects k suitable programme slots simultaneously for advertisement. The aim of the paper is, therefore, to help the companies to select the programme slots, which are mutually exclusive with respect to the time schedule of telecasting time, in such a way that the total number of viewers of the selected programme in k parallel slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight k-colouring problem on an interval graph. An algorithm is designed to solve this just-in-time optimization problem using O(kMn ² ) time, where n and M represent the total number of programmes of all channels and the upper bound of the viewers of all programmes of all channels respectively. The problem considered in this paper is a daily life problem which is modeled by k-colouring problem on interval graph. © 2016, Springer India Pvt. Ltd.

关键词： Design and analysis of algorithms Graph colouring Graph theory Interval graphs Modelling

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