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Inventory of deteriorating complementary and substitute items with stock dependent demand

American Journal of Mathematical and Management Sciences 2005年第1-2期25卷 83-96页

作者： Maity, K. Maiti, M. Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore - 721 102 India

The optimal production for an inventory control system of deteriorating multi-items where items are of complementary or substitute types is formulated with a resource constraint. Here, it is assumed that substitute products have linearly negative effect on one another's demands and this effect is positive for the complementary items. The effect of an item on the demand of the other item depends on the inventory level of the first item. The rate of deterioration of the items is stock dependent. An item's own demand is also stock dependent, shortages are not allowed, and deteriorated items are salvaged. The total profit which consists of the sales proceeds, production cost, inventory holding cost, salvage value is formulated as a Pontryagin Optimal Control problem for both steady and transient states and evaluated using optimal control theory satisfying the Generalized Legendre condition. The model is formulated in general form for n-items and in particular, is illustrated with two items for some numerical data. The optimum results are presented both in tabular form and graphically. Copyright © 2005 by American Sciences Press, Inc.

关键词： Inventory control

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Numerical approach of multi-objective optimal control problem in imprecise environment

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Fuzzy Optimization and Decision Making 2005年第4期4卷 313-330页

作者： Maity, K. Maiti, M. Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

In this paper, realistic production-inventory models without shortages for deteriorating items with imprecise holding and production costs for optimal production have been formulated. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is time dependent and known. The imprecise holding and production costs are assumed to be represented by fuzzy numbers which are transformed to corresponding interval numbers. Following interval mathematics, the objective function is changed to respective multi-objective functions and thus the single-objective problem is reduced to a multi-objective decision making(MODM) problem. The MODM problem is then again transformed to a single objective function with the help of weighted sum method and then solved using global criteria method, calculus method, the Kuhn-Tucker conditions and generalized reduced gradient(GRG) technique. The models have been illustrated by numerical data. The optimum results for different objectives are obtained for different types of production function. Numerical values of demand, production function and stock level are presented in both tabular and graphical forms. © 2005 Springer Science+Business Media, Inc.

关键词： Problem solving

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Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply

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Journal of the Operations Research Society of China 2016年第2期4卷 193-204页

作者： Sankar Kumar Roy Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnaporeWest Bengal 721102India

This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice *** that the supply parameters of the constraints in a transportation problem(TP)follow logistic *** main objective of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function and the demand of the constraints in the TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimized and satisfies the required *** stochastic programming,the stochastic supply constraints of the TP are transformed into deterministic ***,a non-linear deterministic model is *** Lingo software,the optimal solution of the proposed problem is *** illustrate the methodology,a real-life problem on the TP is considered.

关键词： Transportation problem Multi-choice programming Lagrange’s interpolating polynomial Stochastic programming

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CI-MM-Dombi operator based on interval type-2 spherical fuzzy set and its applications on sustainable supply chain with risk criteria: using CI-TODIM-MARCOS method

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Soft Computing 2024年第17-18期28卷 10023-10056页

作者： Giri, Binoy Krishna Roy, Sankar Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India

Sustainable supplier selection and optimal quantity transportation (S3OQT) play an important role in supply chain management. This research represents a new four-stage solution approach for S3OQT where the multi-criteria decision making (MCDM) methods are integrated through an optimization model. In first stage, a new uncertainty interval type-2 spherical fuzzy set (IT2SFS) is introduced to help the decision-makers (DMs) for securing and reliable results in hesitancy situations. We develop a new operator on IT2SFS under Dombi t-norm and t-conorm by integrating Muirhead mean (MM) operator based on Choquet integral (CI). The preferences and priorities to the sustainable criteria based on interaction and interrelationship are represented by CI. Thereafter, the weights of the criteria and sub-criteria are determined by CI-indifference threshold-based attribute ratio analysis (ITARA) method by utilizing the proposed operator. In second stage, to evaluate the weights of the suppliers and to rank these, we construct a new MCDM method CI-TODIM (an acronym in Portuguese of interactive multi-criteria decision-making)-measurement alternatives and ranking according to compromise solution (MARCOS) method by utilizing the proposed operator and then finally design a new ranking function. In third stage, a new model on stochastic multi-objective mixed-integer non-linear solid transportation problem (SM2NSTP) is established to identify suitable supplier under sustainable risk criteria, and then, optimal quantity of products are transported from each supplier. Thereafter, we propose TOPSIS-neutrosophic-game theoretic approach (TNGTA) to obtain Pareto-optimal solution. We apply Ε-constraint method to obtain Pareto-optimal solution from SM2NSTP model. In the fourth stage, a comparative study is drawn among the obtained Pareto-optimal solutions that are extracted from TNGTA and Ε-constraint method. Finally, two MCDM models, CRITIC-TOPSIS and CRITIC-MARCOS, are used to help the DMs for s

关键词： Fuzzy sets

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Analysis of prey-predator three species models with vertebral and invertebral predators

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International Journal of Dynamics and Control 2015年第3期3卷 306-312页

作者： Roy, Banani Roy, Sankar Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University MidnaporeWest Bengal721102 India

In this paper, we consider a mathematical model involving three species namely prey, predator and super predator. Different type functional responses have been considered to formulate the mathematical model for predator and super predator. Main intention of this study is to establish the local and global stabilities for the proposed model around its interior equilibrium points. A numerical example is considered to illustrate the proposed system of our paper. The stability of the system has been analyzed using some graphical representation. © 2015, Springer-Verlag Berlin Heidelberg.

关键词： Hopf bifurcation

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Solving single-sink, fixed-charge, multi-objective, multi-index stochastic transportation problem

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American Journal of Mathematical and Management Sciences 2014年第4期33卷 300-314页

作者： Midya, Sudipta Roy, Sankar Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore West-Bengal721102 India

The aim of this article is to present a fuzzy programming approach to a singlesink, fixed-charge, multiobjective, multi-index stochastic transportation problem (SSMISTP). This article focuses on the minimization of the transportation cost, deterioration rate, and underused capacity for transportation of raw materials from different sources to the "Single-Sink " by different transportation modes. The parameters of the proposed problem are transportation cost, fixed-charge, deterioration rate, and underused capacity. These parameters are to be treated here as random variables. Because of the globalization of the market, assume that the "Sink" demand is an interval representing the inexact demand component for the SSMISTP. By considering the uncertainties of these parameters, we formulate the mathematical model of the proposed problem. Using a stochastic programming approach, all the stochastic objective functions are converted into deterministic objective functions. Again using the interval concept, the proposed intervalvalued sink constraint decomposes into two deterministic constraints. Finally, using all deterministic objective functions and constraints, we design a multiobjective transportation problem(MOTP). The optimal compromise solution to the MOTP has been obtained by using a fuzzy programming technique. We demonstrate the feasibility of the proposed problem using a real-life practical example. Copyright © Taylor & Francis Group, LLC.

关键词： Stochastic programming

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The optimal sequential and parallel algorithms to compute all hinge vertices on interval graphs

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Journal of applied mathematics and Computing 2001年第2期8卷 295-309页

作者： Bera, Debashis Pal, Madhumangal Pal, Tapan K. Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore - 721 102 West-Bengal India

If the distance between two vertices becomes longer after the removal of a vertex u, then u is called a hinge vertex. In this paper, a linear time sequential algorithm is presented to find all hinge vertices of an interval graph. Also, a parallel algorithm is presented which takes O(n/P + logn) time using P processors on an EREW PRAM. © 2001 Korean Society for Computational & applied mathematics and Korean SIGCAM.

关键词： Consensus algorithm

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A supply chain model for imperfect production system with stochastic lead time demand

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Journal of Management Analytics 2018年第4期5卷 309-333页

作者： Rabin Kumar Mallick Amalesh Kumar Manna Shyamal Kumar Mondal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnaporeIndia

This study deals an integrated manufacturer-buyer supply chain system for imperfect production under stochastic lead time ***,defective rate has been followed as a function of production ***,the produced units have been inspected in order to screen the defective units but screening rate is less than the production rate and greater than the demand *** purchases the products from the ***,we assume that shortage during the lead time is permitted and demand during the shortage period is fully *** objective is to derive the optimal production rate,ordering quantity and to maximize joint total ***,two different models for different probability distribution functions of stochastic lead time demand have been *** numerical examples are provided to show the applicability of the proposed models comparing the optimum average ***,sensitive analysis,conclusion and future researches are presented.

关键词： supply chain imperfect production stochastic lead time demand back order

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Multi-attribute decision making for power Dombi operators under Pythagorean fuzzy information with MABAC method

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Journal of Ambient Intelligence and Humanized Computing 2023年第8期14卷 10761-10778页

作者： Jana, Chiranjibe Garg, Harish Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India Punjab Patiala147004 India

Pythagorean fuzzy sets have a lot of applications in the field of engineering and scientific problems. Also, besides, the power averaging (PA) operator can reduce the influence of evaluating extreme data from some bias experts. Dombi operator has flexibility in working on parameter evaluation. Here, Dombi operations combined with PA operator are used to construct some Pythagorean fuzzy power Dombi operators, i.e. Pythagorean fuzzy power Dombi weighted averaging (PFPDWA), order weighted averaging and hybrid weighted averaging operators have been introduced. Further, Pythagorean fuzzy power Dombi weighted geometric (PFPDWG), order weighted geometric and hybrid weighted geometric operators have been considered. Meanwhile, some properties of these operators have been established in detail. To solve the Pythagorean fuzzy multiple attribute decision making problem by using PFPDWA and PFPDWG operators to design an algorithm for the proposed approach. At the same time, a novel approach is proposed to design multiple attribute border approximation area comparison approached with Pythagorean fuzzy numbers to justify the feasibility of the proposed approach. Finally, we compare the developed approach with some existing operators to show its efficiency. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Decision making

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Scoring rule and its application in intuitionistic fuzzy parameterized soft set-based decision-making problem

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Journal of Ambient Intelligence and Humanized Computing 2023年第10期14卷 14209-14224页

作者： Paik, Biplab Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University W.B. Midnapore721 102 India

There is an importance of multi-criteria group decision-making (MCGDM) problems based on soft set theory in decision analysis. This article focuses on MCGDM problems based on intuitionistic fuzzy parameterized soft sets (IFPSS) structure. Our goal in decision-making is to select an object by verifying all the parameters. Fuzzy ranking is one of the essential critical tools used in the MCGDM process. The ranking system plays a vital role in the comparison of Intuitionistic fuzzy numbers (IFN) in MCGDM, like fuzzy numbers. However, most of the ranking methods on IFN mentioned in the literature have some limitations. By addressing the limitations of existing score functions and proposing a new and improved method for ranking IFNs, this article can make a significant contribution to the field of MCDM and decision-making under uncertainty. We have also introduced a new similarity measure of two intuitionistic fuzzy soft sets (IFSS). Using the concept of scoring rule, we have defined the reduced FP-soft set of an IFPSS. Additionally, we have calculated the adequate standard of a decision-maker in MCGDM problems under the IFPSS environment. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Decision theory

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