Publications

Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media

Journal

Journal NameMathematics and Computers in Simulation

Title of PaperStudy and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media

Volume Number192

Page Number491-500

Published YearFebruary 2022

ISSN/ISBN No0376-4754

Indexed INScopus, Web of Science

Study of one-dimensional space-time fractional-order Burgers-Fisher and Burgers-Huxley fluid models

Journal

Journal NameMathematical Methods in the Applied Sciences

Title of PaperStudy of one-dimensional space-time fractional-order Burgers-Fisher and Burgers-Huxley fluid models

Volume Number44

Page Number2455-2467

Published YearFebruary 2021

ISSN/ISBN No2455-2467

Indexed INScopus, Web of Science

Study and analysis of a two-dimensional non-conservative fractional order aerosol transport equation

Journal

Journal NameMathematical Methods in the Applied Sciences

Title of PaperStudy and analysis of a two-dimensional non-conservative fractional order aerosol transport equation

Volume Number42

Page Number2939-2948

Published YearJune 2019

ISSN/ISBN No1099-1476

Indexed INScopus, Web of Science

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

Journal

Journal NameJournal of Computational and Nonlinear Dynamics-ASME

Title of PaperNumerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

Volume Number14

Page Number041003-041009

Published YearApril 2019

ISSN/ISBN No1555-1423

Indexed INScopus, Web of Science

Study and analysis of spatial-time nonlinear fractional order reaction-advection diffusion equation

Journal

Journal NameJournal of Porous Media

Title of PaperStudy and analysis of spatial-time nonlinear fractional order reaction-advection diffusion equation

Volume Number22

Page Number787-798

Published YearJanuary 2019

ISSN/ISBN No1934-0508

Indexed INScopus, Web of Science

Numerical Solution of Fractional Order Advection-Reaction-Diffusion Equation

Journal

Journal NameSerbian Society of Heat Transfer Engineers

Title of PaperNumerical Solution of Fractional Order Advection-Reaction-Diffusion Equation

Volume Number22

Page NumberS309-S316

Published YearJanuary 2018

ISSN/ISBN No2334-7163

Indexed INScopus, Web of Science

VERTICAL TRANSMISSION OF HIV-HBV CO-INFECTION WITH LIQUOR HABIT AND VACCINATION

Journal

Journal NameMALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES

Title of PaperVERTICAL TRANSMISSION OF HIV-HBV CO-INFECTION WITH LIQUOR HABIT AND VACCINATION

Volume Number16

Page Number1

Published YearApril 2021

ISSN/ISBN No1823-8343

Indexed INScopus, Web of Science, Indian citation Index

Abstract

In this paper, the transmission of HIV-HBV co-infection is carried out. The individuals who are infected with both diseases HIV and HBV simultaneously, are said to be HIV-HBV co-infected. These infected individuals have high risk of liver failure. It is the main cause for serious liver complications like cirrhosis and liver cancer at younger age. A deterministic model is considered with liquor habit in men and vaccination to new-borns and carrier mother. Carrier class results in the vertical transmission. In this paper, the transmission dynamics of the model is analyzed. The total population is divided in to twenty eight class viz. Susceptible, HBV Vaccinated, HBV-infected female, HBV-carrier female, HBV infected alcoholic male, HBV carrier alcoholic male, HBV infected non-alcoholic male, HBV carrier non-alcoholic male, HBV recovered class, pre-AIDS female, AIDS female, pre-AIDS-HBV co-infected female, AIDS-HBV co-infected female, pre-AIDS-HBV carrier female, AIDS-HBV carrier female, pre-AIDS alcoholic male, AIDS alcoholic male, pre-AIDS non-alcoholic male, AIDS non-alcoholic male, pre-AIDS-HBV co-infected alcoholic male, pre-AIDS-HBV co-infected non-alcoholic male, pre-AIDS-HBV carrier alcoholic male, pre-AIDS-HBV carrier non-alcoholic male, AIDS-HBV co-infected alcoholic male, AIDS-HBV co-infected non-alcoholic male, AIDS-HBV carrier non-alcoholic male, HIV infected -HBV recovered classes. The basic reproduction numbers for HIV, for HBV and for HIV-HBV are found using next generation matrix. Local and global stability of HIV-HBV disease free equilibrium is worked out. Model is validated with the numerical simulation.

TRANSMISSION DYNAMICS OF COVID-19 FROM ENVIRONMENT WITH RED ZONE, ORANGE ZONE, GREEN ZONE USING MATHEMATICAL MODELLING

Book Chapter

Book NameMATHEMATICAL ANALYSIS FOR TRANSMISSION OF COVID-19

Publisherspringer

Author NameBijal Yeolekar, Nita Shah

Page Number61-76

Chapter TitleTRANSMISSION DYNAMICS OF COVID-19 FROM ENVIRONMENT WITH RED ZONE, ORANGE ZONE, GREEN ZONE USING MATHEMATICAL MODELLING

Published YearMarch 2021

ISSN/ISBN No978-981-336-264-2

Indexed INScopus

Abstract

The novel corona virus or Covid-19 spread had its inception in November of 2019, and in March 2020, it was declared as a pandemic. Since its initial stage, it has now already infected over 5 million people, leading to the lockdown of countries around the world, and a halt on global as well as national travel across the globe. Based on this, the research proposes a mathematical Covid-19 model to study the outcome of these classified zones under different control strategies. In the nonlinear mathematical model, the total population has been divided into seven compartments, namely Susceptible, Exposed, Red zone, Orange zone, Green zone, Hospitalized, and Recovered. The spectral radius is calculated to analyze dynamics of the Covid-19. To control the spread of the virus, the parameters of controls are Medical Intervention, Partial Lockdown, and Strict Lockdown. This model has been validated with …

OPTIMAL CONTROL MODEL FOR BLINDNESS DUE TO DEFICIENCY OF VITAMIN-A

Journal

Journal NameDYNAMICS OF CONTINUOUS, DISCRETE AND IMPULSIVE SYSTEMS SERIES B: APPLICATIONS & ALGORITHMS

Title of PaperOPTIMAL CONTROL MODEL FOR BLINDNESS DUE TO DEFICIENCY OF VITAMIN-A

Publisherwatman press

Volume Number28

Page Number4b

Published YearMarch 2021

ISSN/ISBN No1492-8760

Indexed INScopus, PubMed

STABILITY OF LIMIT CYCLES OF PASSIVE DYNAMIC KNEED BIPED

Journal

Journal NameSTRUCTURAL INTEGRITY AND LIFE

Title of PaperSTABILITY OF LIMIT CYCLES OF PASSIVE DYNAMIC KNEED BIPED

PublisherDIVK

Volume Number20

Page Numbersp11-sp17

Published YearNovember 2020

ISSN/ISBN NoPrint ISSN 0973-6107 Online ISSN 0974-4738

Indexed INScopus, Web of Science

MATHEMATICAL MODEL TO ANALYZE EFFECT OF DEMONETIZATION

Book Chapter

Book NameMATHEMATICAL MODELS OF INFECTIOUS DISEASES AND SOCIAL ISSUES

PublisherIGI GLOBAL

Author NameN H Shah, Bijal Yeolekar, Z A patel

Page Number270-286

Chapter TitleMATHEMATICAL MODEL TO ANALYZE EFFECT OF DEMONETIZATION

Published YearApril 2020

ISSN/ISBN No9781799837411

Indexed INScopus

Abstract

Demonetization is a fundamental regulatory act of stripping in which a currency unit's status as an exchange is professed worthless. Generally, it is done whenever there is a change of national currency, often to be replaced of the old notes or coins with a new one. Sometimes, a country totally replaces the old currency with new currency. For example, in India recently the government demonetized RS. 500 and 1000 notes. So, one has to deposit their cash within limited time in the banks. The demonetization affects individuals mildly or potentially, which in turn affects banking sector. So, SMPB-model is proposed and analyzed for demonetization. The SMP-model is formulated with the system of nonlinear differential equations. The effect of demonetization is studied by calculating threshold using next generation matrix. The local and global stability for demonetization free equilibrium and demonetization equilibrium is …

GLOBAL ANALYSIS OF ELECTRONIC ITEMS WITH RE-MANUFACTURING TO CONTROL E-WASTE

Journal

Journal NameINTERNATIONAL JOURNAL OF ENVIRONMENT AND WASTE MANAGEMENT

Title of PaperGLOBAL ANALYSIS OF ELECTRONIC ITEMS WITH RE-MANUFACTURING TO CONTROL E-WASTE

PublisherInderscience Publishers (IEL)

Volume Number24

Page Number3

Published YearOctober 2019

Indexed INScopus, Web of Science

Abstract

E-waste is electronic items that have become useless or have reached to the end of their life-span. The maximum e-waste is produced by electronic industry in comparison to vendor and customer. E-waste contains many harmful chemicals which can be absorbed by humans and landfills and floats in the environment. The best solution to control e-waste is re-manufacturing. Re-manufacturing preserves natural resources, saves landfills, reduces greenhouse gas emissions and consequently controls pollution. It also consumes fewer inventories so that it pays less cost. To investigate this e-waste problem and advocating re-manufacturing, we have developed a mathematical model of three compartments viz. manufacturing unit, vendor and customer comprising of re-manufacturing at player's ends. To examine the stability of e-waste model, the local and global stability is considered. Threshold and numerical simulation …

VERTICAL DYNAMICS OF EBOLA WITH MEDIA IMPACT

Journal

Journal NameJOURNAL OF KING SAUD UNIVERSITY-SCIENCE

Title of PaperVERTICAL DYNAMICS OF EBOLA WITH MEDIA IMPACT

PublisherElsevier

Volume Number31

Page Number567-574

Published YearOctober 2019

ISSN/ISBN No1018-3647

Indexed INScopus, Web of Science

Abstract

The Ebola virus disease (EVD) is one of the deadly diseases amongst human and non-human primates caused by most virulent pathogens Ebola virus. Socio-economic impacts of Ebola is very high. In 2014, the latest and largest major outbreak occurred in West African countries Guinea, Sierra Leone, and Liberia. During the outbreak, cases were reported about presence of Ebola virus in semen and breast milk of individuals after recovery. Vertical transmission of disease spread and its impacts on population are studied in this research. How effectively early diagnosis, isolation, awareness campaigns break the chain of infectious cases and control disease spread is studied. Mathematical model for vertical transmission of Ebola with media effect is developed using seven compartments namely susceptible, exposed, infectious, Hospitalised/Isolated, Convalescent, Dead (not properly buried dead bodies of Ebola …

Stability of ‘GO-CLEAN’Model Through Graphs

Journal

Journal NameJournal of Computer and Mathematical Sciences

Title of PaperStability of ‘GO-CLEAN’Model Through Graphs

PublisherJournal of Computer and Mathematical Sciences

Volume Number9(2)

Page Number79-93

Published YearSeptember 2018

ISSN/ISBN No0976 - 5727

Indexed INUGC List

Abstract

Cleanliness is the habit of keeping the dirt away, to maintain the good health and make environment hygiene. In simple words, cleanliness is very important factor in our life from all the aspects to keep society healthy. The aim of this study is to motivate the drives of cleanliness in India. However, some individuals do no support these kinds of drives which makes them passive cleaners. Therefore, we have formulated the system of non-linear differential equations to study passive cleaners turning into active ones. The stability is derived to understand the behaviour of potential cleaners through weighted graph having only two cycles. The model is validated by numerical simulation.

Epidemics Of Corruption Using Incidence Function

Journal

Journal NameEconomic Computation & Economic Cybernetics Studies & Research

Title of PaperEpidemics Of Corruption Using Incidence Function

Volume Number51(2)

Page Number165-180

Published YearJanuary 2018

ISSN/ISBN No0424-267X

Indexed INEBSCO, UGC List

Abstract

Corruption is a slow poison damaging individuals and consequently society and nation. This is a global issue. Any individual can be exposed to the corruption. Slowly and steadily, an individual turns out to be most corrupted. In this study, an attempt is made to formulate the dynamics of corruption. The non-linear system of differential equations constructed for different compartments viz. Susceptible, Exposed, Infected and Punished. The punishment in terms of transfers from one place to another is defined in exposed and infected classes. These transfers lead the vertical transmission in both the classes. The threshold in terms of reproduction number is computed to make society corruption free. The local and global stability is analyzed. The proposed model is supported by numerical simulation. The observations and suggestions are outlined to have corruption free society or reduced corruption.

Congenital Transmission of Chagas with Control Dropouts and Spraying

Journal

Journal NameInternational Journal of Applied and Computational Mathematics

Title of PaperCongenital Transmission of Chagas with Control Dropouts and Spraying

PublisherSpringer India

Volume Number3 (1)

Page Number185-201

Published YearDecember 2017

ISSN/ISBN No2349-5103

Indexed INScopus

Abstract

Vector-borne diseases are the leading causes of death amongst all disease. They remain as highest risk for lives of millions of people in many countries of the world. Scientific and economic impacts of vector-borne disease are significant. Chagas is one of the vector-borne diseases found in Latin American countries with its large impact. Studies indicate that vector control is the most convergent way to control vector-borne diseases. To control vectors, spraying insecticide is the easiest and safest way, but sometimes it is cost worthy for long period of spraying. Also, for most of the Vector-borne diseases treatments are available, but because of unawareness they spread at high frequency. People may start to opt the treatment but the side effects or cost of treatment, force them to left treatment in between and that create larger dropouts. Vertical transmission of disease also plays vital role in spreading disease as …

Threshold for vaccination in measles and its vertical transmission

Journal

Journal NameInternational Journal of Dynamical Systems and Differential Equations

Title of PaperThreshold for vaccination in measles and its vertical transmission

PublisherInderscience Publishers (IEL)

Volume Number7 (2)

Page Number157-168

Published YearJune 2017

ISSN/ISBN No1752-3583

Indexed INScopus, UGC List

Abstract

This study analyses measles transmission vertically with vaccination failure and delay of vaccination. The effect of infected newborns as a time delay is analysed. Time delay is considered as a loss of maternal immunity amongst newborns. The system of non-linear differential equations for the proposed problem is formulated. The next generation matrix method is used to find the reproduction number, and to obtain the stability of the infection free as well as the endemic equilibrium. Effect of time delay in vaccination has been studied for disease-free equilibrium. The local and global stability of the system is analysed. Sensitivity of the key parameters is measured using numerical simulation and observed that it supports the analytical results.

Mathematical Model for Hereditary Transmission of Culture

Journal

Journal NameInternational Journal of Computer Applications

Title of PaperMathematical Model for Hereditary Transmission of Culture

Volume Number975

Published YearMarch 2017

ISSN/ISBN No 0975 - 8887

Indexed INEBSCO, UGC List

Abstract

Culture is the complex set of knowledge, beliefs, art, morals, customs and many more habits acquired by a human being a part of society or from hereditary. It defines the quality in a person. It is based on nurturing mind by education or training. In this paper, a mathematical model of a culture which gets transmitted directly from one generation to another also called vertical transmission as well as among the generation through concepts with society is formulated. Local and global stability is established and inheritance of the culture is discussed.

Dhiren Pandit

PCA + LDA Fuzzy Based Model for Emotional Nature Recognition of Human Video

Journal

Journal NameInternational Journal of Recent Technology and Engineering

Title of Paper PCA + LDA Fuzzy Based Model for Emotional Nature Recognition of Human Video

PublisherBlue Eyes Intelligence Engineering & Sciences Publication

Volume Number8

Page Number242 - 246

Published YearSeptember 2019

ISSN/ISBN No2277-3878

Indexed INScopus

Abstract

Human expresses their emotions by means of verbal and nonverbal communication. Nonverbal communications are done mainly using facial expression. This paper aims to recognize human emotion using nonverbal communication of human facial expressions. Different mathematical techniques like: principle component analysis (PCA), linear discriminate analysis (LDA) and independent component analysis (ICA) are widely used for human facial expression recognition. This paper applied fusion of PCA and LDA based model for facial video emotion recognition with neural network (NN), fuzzy approach and Ekman’s proposed concept of action units of faces. Moreover, results obtained in linguistic form using action units with fuzzy approach on unknown individual persons for identification of nature of input video and compare with the actual data to validate the model. This paper concludes that developed approach provides 99% accuracy for human facial expression recognition and identification of nature of input video.

Dr. Ekta Patel

Vendor-Buyer Pollution Sensitive Inventory System for Deteriorating Items

Journal

Journal NameProcess Integration and Optimization for Sustainability

Title of PaperVendor-Buyer Pollution Sensitive Inventory System for Deteriorating Items

Volume Number6

Page Number285-293

Published YearJanuary 2022

ISSN/ISBN No2509-4238

Indexed INScopus

Investigation of Carbon Emissions due to COVID-19 Vaccine Inventory

Journal

Journal NameInternational Journal of System Assurance Engineering and Management

Title of PaperInvestigation of Carbon Emissions due to COVID-19 Vaccine Inventory

Volume Number13

Page Number409-420

Published YearJanuary 2022

ISSN/ISBN No0975-6809

Indexed INScopus, Web of Science

EPQ Model to Price-Sensitive Stock-Dependent Demand with Carbon Emission under Green and Preservation Technology Investment

Journal

Journal NameEconomic Computation & Economic Cybernetics Studies & Research

Title of PaperEPQ Model to Price-Sensitive Stock-Dependent Demand with Carbon Emission under Green and Preservation Technology Investment

Volume Number56

Page Number209-222

Published YearJanuary 2022

ISSN/ISBN No1842-3264

Indexed INScopus, Others

Gayatri Pany

Coercive and Noncoercive Mixed Generalized Complementarity Problems

Journal

Journal NameAxioms

Title of Paper Coercive and Noncoercive Mixed Generalized Complementarity Problems

Volume Number13

Page Number328-347

Published YearJanuary 2024

Indexed INScopus

A study on vector variational like inequalities using convexificators and application to its bi-level form

Journal

Journal Name Journal of Industrial and Management Optimization

Title of PaperA study on vector variational like inequalities using convexificators and application to its bi-level form

PublisherAmerican Institute of Mathematical Sciences

Volume Number18

Page Number4333-4350

Published YearJanuary 2022

Indexed INScopus, ABDC

Densely Relaxed Pseudomonotone and Quasimonotone Generalized Variational like Inequalities

Journal

Journal NameOptimization

Title of PaperDensely Relaxed Pseudomonotone and Quasimonotone Generalized Variational like Inequalities

PublisherTaylor & Francis Online

Volume Number70

Page Number413-435

Published YearJanuary 2021

Indexed INScopus, ABDC

Existence and iterative approximation method for solving mixed equilibrium problem under generalized monotonicity in Banach spaces

Journal

Journal NameNumerical Algebra, Control and Optimization

Title of PaperExistence and iterative approximation method for solving mixed equilibrium problem under generalized monotonicity in Banach spaces

Volume Number10

Page Number75-92

Published YearJanuary 2020

Indexed INScopus

Generalized monotone mixed equilibrium problems in FC spaces: Existence and approximation

Journal

Journal NameJournal of Applied and Numerical Optimization

Title of PaperGeneralized monotone mixed equilibrium problems in FC spaces: Existence and approximation

Volume Number1

Page Number183-199

Published YearJanuary 2019

Indexed INScopus

Solution of a class of equilibrium problems and variational inequalities in FC spaces

Journal

Journal NameAnnals of Operations Research

Title of PaperSolution of a class of equilibrium problems and variational inequalities in FC spaces

PublisherSpringer International Publishing

Volume Number269

Page Number565-582

Published YearJanuary 2018

Indexed INScopus, ABDC

Error analysis for a class of Nonlinear Quasi Variational Inequalities

Journal

Journal NameJournal of Dynamics of Continuous, Discrete and Impulsive Systems-A

Title of PaperError analysis for a class of Nonlinear Quasi Variational Inequalities

Volume Number24

Page Number147-157

Published YearJanuary 2017

Indexed INScopus

On Mixed Equilibrium Problems in Banach Spaces

Journal

Journal NamePanAmerican Mathematical Journal

Title of PaperOn Mixed Equilibrium Problems in Banach Spaces

Volume Number26

Page Number12-24

Published YearJanuary 2016

Indexed INScopus

A Class of Mixed Variational like Inequalities and Equilibrium Problems in Banach Spaces

Journal

Journal NameJournal of Inequalities and Special Functions

Title of PaperA Class of Mixed Variational like Inequalities and Equilibrium Problems in Banach Spaces

Volume Number7

Page Number241-252

Published YearJanuary 2016

Indexed INScopus

Kunal Pathak

Finite element model to study two dimensional unsteady state calcium distriution in cardiac myocytes

Journal

Journal NameAlexandria Journal of Medicine

Title of PaperFinite element model to study two dimensional unsteady state calcium distriution in cardiac myocytes

PublisherELSEVIER

Volume Number52

Page Number261-268

Published YearSeptember 2016

ISSN/ISBN No2090-5068

Indexed INIndian citation Index, UGC List

Abstract

The calcium signaling plays a crucial role in expansion and contraction of cardiac myocytes. This calcium signaling is achieved by calcium diffusion, buffering mechanisms and influx in cardiac myocytes. The various calcium distribution patterns required for achieving calcium signaling in myocytes are still not well understood. In this paper an attempt has been made to develop a model of calcium di

Finite Element Model to Study Calcium Singalling in cardiac myocytes involving pump, leak and excess buffer.

Journal

Journal NameJournal of Medical Imaging and Health Informatics

Title of PaperFinite Element Model to Study Calcium Singalling in cardiac myocytes involving pump, leak and excess buffer.

PublisherAmerican Scientific Publication

Volume Number5

Page Number1-6

Published YearAugust 2015

ISSN/ISBN No2156-7026

Indexed INScopus, UGC List

Abstract

The calcium signaling plays an important role in expansion and contraction of myocytes. This calcium signaling is achieved by diffusion of calcium, out ﬂux of calcium through pumps, in ﬂow of calcium through leak and buffering mechanisms in cardiac myocytes. In this paper an attempt has been made to develop a model of calcium signaling in myocytes incorporating diffusion of calcium, pump, leak and

Finite Element model to study one dimensional calcium dynamics in cardiac myocytes

Journal

Journal NameJournal of Multiscale Modeling

Title of PaperFinite Element model to study one dimensional calcium dynamics in cardiac myocytes

PublisherImperial College Press

Volume Number6

Page Number1-12

Published YearJuly 2015

ISSN/ISBN No1756-9745

Indexed INEBSCO

Abstract

The multi physical process involving calcium ions regulate expansion and contraction of cardiac myocytes. This mechanism of expansion and contraction of cardiac myocytes is responsible for contraction and expansion of heart for pumping of blood into arteries and receiving blood into heart from vein. Thus calcium dynamics in cardiac myocytes is responsible for the activities of the myocytes cells a

Two dimensional coaxial circular elements in finite element method to study calcium diffusion in cardiac myocytes

Conference

Title of PaperTwo dimensional coaxial circular elements in finite element method to study calcium diffusion in cardiac myocytes

Proceeding NameNirma University International Conference on Engineering

PublisherIEEE

OrganizationNirma University

Year , VenueNovember 2013 , Nirma University, Ahmedabad

Page Number1-6

ISSN/ISBN No2375-1282

Indexed INScopus, Web of Science

Abstract

The calcium signaling plays an important role in expansion and contraction of Myocytes. This calcium signaling is achieved by diffusion of calcium and buffering mechanisms in cardiac myocytes. In this paper an attempt has been made to develop model calcium signaling in myocytes incorporating diffusion of calcium and excess buffers. The model has been developed for a two dimensional steady state ca

Motilal Panigrahi

Effect of calcium chloride and gallic acid combination on the extension of postharvest life of Lagenaria siceraria, a vegetable with medicinal importance

Journal

Journal NameMedicinal Plants Indian Journals.com

Title of PaperEffect of calcium chloride and gallic acid combination on the extension of postharvest life of Lagenaria siceraria, a vegetable with medicinal importance

PublisherIndianJournals.com

Volume NumberVol. 13 (1)

Page Number110-119

Published YearMarch 2021

ISSN/ISBN NoMedicinal Plants IndianJournals.com

Indexed INScopus

Abstract

Lagenaria siceraria (Mol.) Standl. consists of all essential elements that are required for good and normal human health. Post harvest losses occur due to lack of proper packaging material, microbial spoilage, and improper handling during transport. Thus, this study deals with viability, sensory evaluation, antioxidant enzymatic activities of L. siceraria fruits by the treatment of a combination of calcium chloride and gallic acid (abbreviated as CG) for 21 days storage at room temperature. The solutions were prepared by the addition of CG in equal amount with different concentrations: 1:1 μM, 2:2 μM, 3:3 μM, and 4:4 μM. The untreated L. siceraria fruits survived for 14 days. However, all the coated L. siceraria fruits could sustain for 21 days, and the combination of 2:2 μM CG was superior in all aspects. The combination of calcium chloride and gallic acid showed beneficial effects by delaying the ripening process.

Convex Fuzzy Mapping with Differentiability and its Application in Fuzzy Optimization

Journal

Journal NameEuropean Journal of Operation Research

Title of PaperConvex Fuzzy Mapping with Differentiability and its Application in Fuzzy Optimization

Volume Number185(2008)

Page Number47-62

Published YearJanuary

ISSN/ISBN No0377-2217

Indexed INWeb of Science

Abstract

The concepts of differentiability, convexity, generalized convexity and minimization of a fuzzy mapping are known in the literature. The purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using Buckley–Feuring approach for fuzzy differentiation and derive Karush–Kuhn–Tucker condition for the constrained fuzzy minimization problem.

Generalized Ideals with a Triangular Norm

Journal

Journal NameJournal of Advanced Mathematical Studies

Title of PaperGeneralized Ideals with a Triangular Norm

PublisherFair Partners Publishers, Romania

Volume NumberVol. 6(2013), No. 1

Page Number116-126

Published YearJune 2013

ISSN/ISBN NoPrint Edition: ISSN 2065-3506, Online Edition: ISSN 2065-5851

Indexed INEBSCO, Others

Abstract

The notion of generalized ideal is redefined with respect to a triangular norm for a completely distributive complete lattice with a greatest element and least element and the new mathematical object is termed as a T-g-ideal. We have furnished examples of T-g-ideals with different t-norms and shown that a T-g-ideal with respect to one tnorm may not be a T-g-ideal with respect to another t-norm. Ne

Intuitionistic Fuzzy Relations over Intuitionistic Fuzzy Sets

Journal

Journal NameThe Journal of Fuzzy Mathematics

Title of PaperIntuitionistic Fuzzy Relations over Intuitionistic Fuzzy Sets

PublisherInternational Fuzzy Mathematics Institute, Los Angeles, Calif

Volume NumberVol 15, No3

Page Number675-688

Published YearSeptember 2007

ISSN/ISBN No1066-8950

Indexed INUGC List

Abstract

In this paper we have defined intuitionistic fuzzy relation from an intuitionistic fuzzy set to another intuitionistic fuzzy set. Defined some operations on these intuitinsitic fuzzy relations and studied some properties.

Equivalence Class in the set of Fuzzy Numbers and Its Application in Decision Making Problems

Journal

Journal NameInternational Journal of Mathematics and Mathematical Sciences

Title of PaperEquivalence Class in the set of Fuzzy Numbers and Its Application in Decision Making Problems

PublisherHindawi limited

Volume Number2006

Page Number1-19

Published YearJune 2006

ISSN/ISBN No0161-1712 (Print), 1687-0425 (Online)

Indexed INScopus, UGC List

Abstract

An equivalence relation is defined in the set of fuzzy numbers. In a particular equivalence class, arithmetic operations of fuzzy numbers are introduced. A fuzzy matrix with respect to a particular class and its associated crisp matrices are also introduced. The concept of equivalence class is applied in fuzzy decision-making problems and justified through a numerical example.

A Comparison between Intuitionistic Fuzzy Sets and Generalized Intuitionistic Fuzzy Sets

Journal

Journal NameThe Journal of Fuzzy Mathematics

Title of PaperA Comparison between Intuitionistic Fuzzy Sets and Generalized Intuitionistic Fuzzy Sets

Publisher International Fuzzy Mathematics Institute, Los Angeles, Calif

Volume Number14(2006), No. 2

Page Number407-421

Published YearJune 2006

ISSN/ISBN No1066-8950

Indexed INUGC List

Abstract

In this paper we have shown that some operations that are valid for intuitionistic fuzzy sets are not valid for generalized intuitionistic fuzzy sets. Also we have found that some results which appeared in the paper by Krassimir Atanassov are not correct and we have presented the correct version of the results. We have further introduced some new operations over generalized intuitionistic fuzzy se

Sandeep Malhotra

Transient Simulation of vapor liquid two phase flow inside single tube evaporator using quazi linearization approach

Book Chapter

Book NameAdvanced Engineering Research & Applications Vol III

PublisherResearch India Publication

Author NameHongseok Choi, Department of Mechanical Engineering, Clemson University, USA

Page Number1-16

Chapter TitleTransient Simulation of vapor liquid two phase flow inside single tube evaporator using quazi linearization approach

Published YearOctober 2018

ISSN/ISBN No978-93-87374-54-6

Solution of Stiff Differential Equations & Dynamical Systems Using Neural Network Methods

Book Chapter

Book NameIntroduction of Computational and Applied Mathematics

PublisherResearch India Publication

Author NameProf. Kewan Zhao, Department of Mathematics, University of Qiongzhou, Hainan, P. R. China

Page Number27-34

Chapter TitleSolution of Stiff Differential Equations & Dynamical Systems Using Neural Network Methods

Published YearJune 2018

ISSN/ISBN No978-93-87374-35-5

Compressed Sensing and Applications by using Dictionaries in Image Processing

Book Chapter

Book NameIntroduction of Computational and Applied Mathematics

PublisherResearch India Publication

Author NameProf. Kewan Zhao, Department of Mathematics, University of Qiongzhou, Hainan, P. R. China

Page Number35-46

Chapter TitleCompressed Sensing and Applications by using Dictionaries in Image Processing

Published YearJune 2018

ISSN/ISBN No978-93-87374-35-5

Transient simulation of Vapor Liquid Two Phase Flow inside Single Tube Heat Exchanger using Finite Difference Method

Conference

Title of PaperTransient simulation of Vapor Liquid Two Phase Flow inside Single Tube Heat Exchanger using Finite Difference Method

OrganizationDepartment of Mathematics, IIT, Bombay

Year , VenueJune 2017 , Department of Mathematics, IIT, Bombay

Transient Simulation of vapor liquid two phase flow inside single tube condenser using quazi linearization approach

Book Chapter

Book NameAdvanced Mathematics: Theory & Applications, ISBN 978-93-84443-20-7 (2016), Chapter 27

PublisherResearch India Publication

Author NameProf. Taekyun Kim, Jangjeon Research Institute for Mathematical Science and Physics, South Korea

Page Number305-324

Chapter TitleTransient Simulation of vapor liquid two phase flow inside single tube condenser using quazi linearization approach

Published YearJanuary 2016

ISSN/ISBN No978-93-84443-20-7

Teaching of Mathematics in Engineering by Discussing the Different Conceptual Ideas

Conference

Title of PaperTeaching of Mathematics in Engineering by Discussing the Different Conceptual Ideas

Proceeding NameIEEE Digital Library

PublisherIEEE

OrganizationInstitute of Technology, Nirma University

Year , VenueNovember 2015 , Nirma University

ISSN/ISBN No978-1-4799-9991

Indexed INScopus

Derivation of European call option for financial market using Fourier Transform Method

Conference

Title of PaperDerivation of European call option for financial market using Fourier Transform Method

Proceeding NameInternational Science Congress Association E - Publications

OrganizationNational Conference on Advances in Technology & Applied Sciences

Year , VenueMarch 2014 , JIET School of Engineering & Technology, Jodhpur, Rajasthan

ISSN/ISBN NoISBN - 978-93-84648-10-7

Stiff Dynamical System & Simulation of Single tube Heat exchanger

Conference

Title of PaperStiff Dynamical System & Simulation of Single tube Heat exchanger

OrganizationDepartment of Mathematics, Central University of Rajasthan

Year , VenueMarch 2014 , Department of Mathematics, Central University of Rajasthan

Black-Scholes Merton Partial Differential Equations & Scientific Computations

Conference

Title of PaperBlack-Scholes Merton Partial Differential Equations & Scientific Computations

Author NameSandeep Malhotra, Jigna Panchal

OrganizationIndus University, Ahmadabad

Year , VenueJanuary 2014 , Indus University, Ahmadabad

Klein-Gordan Partial Differential Equations & Scientific Computations

Conference

Title of PaperKlein-Gordan Partial Differential Equations & Scientific Computations

Author NameSandeep Malhotra, Nutan Patel

OrganizationIndus University, Ahmadabad

Year , VenueJanuary 2014 , Indus University, Ahmadabad

Time Step calculation in Transient Simulation of Vapor-Liquid two Phase flow inside single tube condenser

Conference

Title of PaperTime Step calculation in Transient Simulation of Vapor-Liquid two Phase flow inside single tube condenser

OrganizationDepartment of Applied Mathematics and Humanities, SVNIT, Surat

Year , VenueDecember 2010 , Department of Applied Mathematics and Humanities, SVNIT, Surat

Siddhant Trivedi

Chapter 14 Vertex Magic Total Labeling of Tensor Product of Cycles

Book Chapter

Book NameRecent Advancements in Graph Theory

PublisherTaylor & Francis Group, CRC publishers

Author NameS T Trivedi, N P Shrimali

Page Number169-179

Chapter TitleChapter 14 Vertex Magic Total Labeling of Tensor Product of Cycles

Published YearNovember 2020

ISSN/ISBN No9781000210200

Indexed INScopus, Others

Abstract

A vertex magic total labeling of a graph assigns a set of labels from a specific set to all vertices and edges of the graph such that the sum of the vertex label and labels of all incident edges does not depend on the vertex. This chapter presents a construction of vertex magic total labeling of a specific tensor product. The construction is based on a vertex magic total labeling of a Cartesian product. In vertex magic total labeling, a bijective function exists if there is a constant. A vertex magic total graph is provided with a vertex magic total labeling. Graphs for odd natural number have the vertex magic total labeling. The chapter discusses the calculation of magic constant and cyclic grid form of tensor product.

(a,d)-total Neighborhood-ntimagic Labeling

Journal

Journal NameAdvances in Mathematics: Scientific Journal

Title of Paper(a,d)-total Neighborhood-ntimagic Labeling

Publisher the Union of researchers of Macedonia, Skopje, North Macedonia

Volume Number9 (7)

Page Number4673-4685

Published YearAugust 2020

ISSN/ISBN No1857-8365

Indexed INScopus, Others

Abstract

In this paper, we introduce a new variant of (a, d)-antimagic total labeling for a graph G = (V,E) called (a, d)-total neighborhood-antimagic labeling (TNAL). A total labeling is said to be an (a, d)-total neighborhoodantimagic labeling if the set of total weights of vertices form an arithmetic progression with initial value a and difference d. We give some necessary conditions for the existence of this labeling for a graph G. We investigate (a, d)-total neighborhood-antimagic labeling of cycle Cn. We also discuss the construction of dual labeling from the existing labeling.

Gaussian Neighborhood-prime Labeling of Graphs containing Hamiltonian cycle

Journal

Journal NameMathematical Journal of Interdisciplinary Sciences

Title of PaperGaussian Neighborhood-prime Labeling of Graphs containing Hamiltonian cycle

PublisherChitkara University Publications

Volume Number7 (2)

Page Number161-165

Published YearMarch 2019

ISSN/ISBN No2278-9561

Indexed INWeb of Science, Others

Abstract

In this paper, we examine Gaussian neighborhood-prime labeling of generalized Peterson graph and graphs which contain Hamiltonian cycle.

Gaussian Neighborhood-prime Labeling of Trees and some other Graphs

Journal

Journal NameJournal of Science and Computations

Title of PaperGaussian Neighborhood-prime Labeling of Trees and some other Graphs

PublisherJournal of Science and Computations

Volume Number6

Page Number1227-1235

Published YearMarch 2019

ISSN/ISBN No2278-9561

Indexed INWeb of Science, Others

Abstract

In this paper, we examine the Gaussian neighborhood-prime labeling of Triangular snake, Quadrilateral snake, Mobius ladder, Banana tree and Caterpillars.

Tapan Kumar Datta

A combined architecture of multivariate LSTM with Mahalanobis and Z-Score transformations for oil price forecasting

Journal

Journal NameEnergy

Title of PaperA combined architecture of multivariate LSTM with Mahalanobis and Z-Score transformations for oil price forecasting

PublisherELSEVIER

Volume Number231

Published YearSeptember 2021

Indexed INScopus, Web of Science, EBSCO

Abstract

Oil price plays a vital role in a country's economy. Oil price forecasting helps in making better economic planning and decisions. The fluctuation in the oil price occurs due to several factors that make oil price forecasting a challenging task. Deep learning models such as Recurrent Neural Networks (RNN) have emerged as a successful method in solving many nonlinear and complex problems. In this research, a combined architecture of Multivariate Long Short Term Memory (MLSTM) is proposed with Mahalanobis and Z-score transformations. These transformations improve the data to uncorrelated and standardized variance, thus making data more suitable for regression analysis. The available historical time-series data on the West Texas Intermediate (WTI) oil prices and the factors affecting the oil prices are collected to form the data set. The feature selection process using selectKBest and correlation analysis is carried out. We develop six variants of MLSTM models with different features, transformations, and outlier elimination. The MLSTM model with Z-score transformation on the selected features and outlier eliminated data gives an RMSE of 0.212 and an R2 score of 0.954. This indicates that our model performed well.

A multi-criteria decision-making approach to rank the sectoral stock indices of national stock exchange of India based on their performances

Journal

Journal NameNational Accounting Review

Title of PaperA multi-criteria decision-making approach to rank the sectoral stock indices of national stock exchange of India based on their performances

PublisherAIMS Press

Volume Number3

Page Number272-292

Published YearJuly 2021

ISSN/ISBN No2689-3010

Abstract

The ideal sector for an investment is a challenge for any capital market investor. This complexity is primarily attributed to the dynamic and volatile nature of public policies and macroeconomic factors that indirectly impact a sector’s growth. In recent years, India in particular, has witnessed dynamic policies being implemented by the Government, such as Demonetization and Goods and Services Tax (GST), which led to sudden changes in the market forces. Thus, it is imperative that researchers focus on developing new scientific techniques for selecting the ideal sector to invest in capital markets. Understanding and analyzing a sector’s behaviour is of prime importance to investors in any emerging capital market. This task appears to be complex as an investor needs to decide from a diverse set of sectors, where performance ranking can conflict with another for different variables. A volatile sector might be ranked higher on pure returns but would be ranked lower if risk-adjusted performance was considered. This is commonly referred to as a multiple criteria decision-making (MCDM) problem. In this paper, we consider the data of eleven Nifty sectoral indices from the National Stock Exchange (NSE) of India from January 2017 to December 2018. We apply three MCDM methods—COPRAS, SAW, and TOPSIS to rank the sectors and provide a holistic overview of their performance. Additionally, we propose a hybrid-ranking approach to solve the issue of divergent rankings from different MCDM.

An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment

Journal

Journal NameRAIRO-Oper. Res

Title of PaperAn integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment

Volume Number55

Page NumberS2727-S2746

Published YearMarch 2021

Indexed INScopus, Others

Abstract

Brand substitution is common observed phenomenon in daily life. It is the decision makers’ economic understanding and potential scheme for business-industries. Also, it provides the flexibility in management and increases the ability to control the production. This works proposes an integrated supplier–retailer inventory model for substitutable products. Two suppliers work not works with two different brand products with their corresponding demand are involved and one retailer sells each of the products. To nullify the complexities of the joint optimization problem, we first develop a deterministic model for three cases: no substitution, partial substitution and full substitution, then we go for its fuzzification. Keeping the financial constraint of each producer, we have studied over the elasticity of the cost parameters by means of triangular dense fuzzy lock set approach with its locking and unlocking property for final decision making. Finally, sensitivity analysis and graphical illustrations are made to justify the model.

A New Green Efficiency-Based Carbon Taxing Policy and Its Effects on a Production-Inventory System with Random Carbon Emissions and Green Investment

Journal

Journal NameAdvances in Operations Research

Title of PaperA New Green Efficiency-Based Carbon Taxing Policy and Its Effects on a Production-Inventory System with Random Carbon Emissions and Green Investment

PublisherHindawi

Volume Number2020

Published YearOctober 2020

Indexed INScopus, EBSCO

Abstract

In this study, the author proposes a new carbon taxing policy. This proposed carbon tax has two tax components. The first component is constant, and the second component depends on the green efficiency of production. The green efficiency of production is measured by the average amount of emissions per unit production in an assessment year. The green efficiency-based tax component can be reset every year. Lesser average emission rate indicates better green efficiency. The second component of this proposed carbon tax forces the firm to improve the green efficiency of production, which results in cleaner production. The author incorporates this new carbon tax policy in a production-inventory system with a price-sensitive demand rate. A rule is provided for the implementation of this new tax. Emissions during setup, production, and storage are considered as independent random variables. The firm has the opportunity of investing in green technologies to improve green efficiency. A profit maximization policy is adopted to solve the developed model. A solution algorithm is also provided. The model is illustrated by numerical examples with randomly generated model parameters. The results of numerical examples show the environmental benefits of the proposed carbon tax.

A hybrid carbon policy inventory model with emission source-based green investments

Journal

Journal NameOPSEARCH

Title of PaperA hybrid carbon policy inventory model with emission source-based green investments

PublisherSpringer

Volume Number57

Page Number202-220

Published YearMarch 2020

Indexed INScopus, EBSCO, Others

Abstract

The present study analyzes a production-inventory system with hybrid carbon regulation policy. This hybrid carbon policy is a combination of carbon tax and cap-and-trade policies. It considers a single item that can be produced in different qualities. Production cost, setup cost, amount of emissions and the demand rate depend on the quality. The demand rate for each quality is price sensitive. Emissions occur from three sources—setup, production process and stock holding. The firm can invest on green technologies in each emission source separately to reduce emissions. This model considers profit maximization policy. The managerial problem is to select the profit-maximizing quality for production, and to find the optimum values of the production run time, green investments and the selling price. An algorithm is provided to solve the model. The model is illustrated by a numerical example. Sensitivity analysis is also performed.

Effect of green technology investment on a production-inventory system with carbon tax

Journal

Journal NameAdvances in Operations Research

Title of PaperEffect of green technology investment on a production-inventory system with carbon tax

PublisherHindawi

Volume Number2017

Published YearJanuary 2017

Indexed INScopus, EBSCO, Others

Abstract

Carbon emissions play the central role in global warming. Manufacturing firms are significant contributors to carbon emissions. In many countries, regulatory authorities are taking actions to reduce emissions. Carbon taxation and cap-and-trade schemes are two mechanisms implemented in many countries. In the present paper, the author analyzes a production-inventory model under a carbon tax system. The production rate is assumed to be a decision variable and can be set at any level within machine limits. A proportion of items produced are defective, and this proportion depends on the production rate. Demand depends on the selling price. Unit price is a decreasing function of the production rate. Emissions can be reduced to some extent by capital investment on green technology, and this capital investment amount is a decision variable. Customers are categorized as retail customers and wholesale customers. A discount is offered to the wholesale customers on the regular selling price. The results are illustrated by a numerical example and a sensitivity analysis is performed.

Inventory system with defective products and investment opportunity for reducing defective proportion

Journal

Journal NameOperational Research

Title of PaperInventory system with defective products and investment opportunity for reducing defective proportion

PublisherSpringer

Volume Number17

Page Number297-312

Published YearJanuary 2016

Indexed INScopus, EBSCO, Others

Abstract

This paper proposes a production-inventory model with defective items. The model incorporates additional investment opportunity on quality improvement for reducing the proportion of defective products. Defective proportion depends upon production rate and the amount of this additional investment on quality improvement. Shortages are allowed and are fully backlogged. Only a random proportion of defective items can be resold at a highly discounted price and rest are to be disposed. Demand rate is assumed to be dependent on selling price. Unit cost is assumed to be a decreasing function of production rate. Profit maximization criterion is used to develop the model. The model jointly determines the optimum values of additional investment, selling price, production rate, production cycle, and production period. Concavity of the expected average net profit is proved. An iteration-based simple algorithm is provided to solve the developed model. The model is illustrated by a numerical example. A sensitivity analysis has been performed.

An inventory model for deteriorating items with stock-dependent demand, time-varying holding cost and shortages

Journal

Journal NameOPSEARCH

Title of PaperAn inventory model for deteriorating items with stock-dependent demand, time-varying holding cost and shortages

PublisherSpringer

Volume Number52

Page Number55-74

Published YearMarch 2015

Indexed INScopus, EBSCO, Others

Abstract

In this article, an inventory model for deteriorating items with two components demand and time-varying holding cost has been developed. Demand is assumed to be stock-dependent up to the level of available stock. After which the demand is considered as constant i.e. during stock-out period. Shortages are allowed and are fully backlogged. Profits are maximized in both the infinite and finite time horizon cases. Some special cases are also derived from the main models. Two numerical examples are provided for both finite and infinite time horizon. Sensitivity analysis performed has shown successful effects of various model parameters on net profit.

An inventory model with price and quality dependent demand where some items produced are defective

Journal

Journal NameAdvances in Operations Research

Title of PaperAn inventory model with price and quality dependent demand where some items produced are defective

PublisherHindawi

Volume Number2013

Published YearJanuary 2013

Indexed INScopus, Others

Abstract

This paper analyzes an inventory system for joint determination of product quality and selling price where a fraction of items produced are defective. It is assumed that only a fraction of defective items can be repaired/reworked. The demand rate depends upon both the quality and the selling price of the product. The production rate, unit price, and carrying cost depend upon the quality of the items produced. Quality index is used to determine the quality of the product. An algorithm is provided to solve the model with given values of model parameters. Sensitivity analysis has also been performed.

An inventory system with stock-dependent, price-sensitive demand rate

Journal

Journal NameProduction Planning & Control

Title of PaperAn inventory system with stock-dependent, price-sensitive demand rate

PublisherTaylor & Francis

Volume Number12

Page Number13-20

Published YearJanuary 2001

Indexed INScopus, EBSCO, Others

Abstract

This article analyses an inventory system where the demand rate is influenced by both displayed stock level and selling price. A finite period system has been considered under multi-replenishment scenario. Optimal selling price and the optimal order quantities have been treated as decision variables. An algorithmic solution procedure is provided on the basis of some observations and is illustrated by some numerical examples. A sensitivity analysis has been performed to study the effects of changes of the demand parameters on the net profit.

Demand promotion by upgradation under stock-dependent demand situation–a model

Journal

Journal NameInternational Journal of Production Economics

Title of PaperDemand promotion by upgradation under stock-dependent demand situation–a model

PublisherElsevier

Volume Number55

Page Number31-38

Published YearJune 1998

Abstract

The idea of demand promotion by upgrading the existing system of the selling centre has been modelled in this article. The consumption rate is assumed to be dependent on the stock level. The problem has been reduced to a maximizing problem. The algorithmic approach for solving this maximizing problem is also provided. Objective is to maximize the net profit over a prescribed time. An increasing convex upgradation cost is considered. Exponential upgradation cost has been considered for the numerical examples.

An inventory model with two-component demand rate and shortages

Journal

Journal NameJournal of the Operational Research Society

Title of PaperAn inventory model with two-component demand rate and shortages

PublisherTaylor & Francis online

Volume Number47

Page Number1029-2036

Published YearAugust 1996

Indexed INScopus, Web of Science, ABDC, Others

Abstract

The article investigates a deterministic inventory system with two-component demand rate. The demand rate is stock-dependent down to a certain level and then constant. Shortages are allowed and are fully backlogged. The storage space is assumed to be limited. A flowchart is provided to solve a general system. To study the effects of changes in the system parameters on the average net profit a sensitivity analysis has been performed.

A note on a replenishment policy for an inventory model with linear trend in demand and shortages

Journal

Journal NameJournal of the Operational Research Society

Title of PaperA note on a replenishment policy for an inventory model with linear trend in demand and shortages

Volume Number43

Page Number993-1001

Published YearOctober 1992

Indexed INScopus, Web of Science, ABDC, Others

Abstract

The present paper deals with an alternative approach for finding the optimal number of replenishments and optimal replenishment times for a finite-horizon inventory problem with linearly increasing demand allowing shortages which are fully backlogged. The method is developed by assuming that successive replenishment cycle lengths are in arithmetic progression. The corresponding results in the absence of shortage are also derived and finally some numerical examples are presented and compared with the existing methods to test the accuracy and effectiveness of the method. A sensitivity analysis has also been presented to study the effect of changes in the system parameters on the optimal cost.

Effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages

Journal

Journal NameEuropean Journal of Operational Research

Title of PaperEffects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages

PublisherNorth-Holland

Volume Number52

Page Number326-333

Published YearJune 1991

Abstract

In the present paper an attempt has been made to investigate the effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate. Shortages are allowed in this model. The model developed in this article is a finite-horizon (T, Si) policy inventory model. To the best of the authors knowledge, such type of inventory model has not been considered earlier. A numerical example has also been given to illustrate the developed model.