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- W4386043848 abstract "ABSTRACTAdvance payment for replenishment and the lifetime of an item are the most vital issues in the business sector. With the consideration of these issues, the formulation of a non-deterministic inventory model in the interval environment is of great importance. In this work, two different non-deterministic inventory models are formulated along with a variable holding cost, variable demand, and advertisement frequency under an advance payment policy in the interval environment. In the first inventory model, a no-shortage situation is discussed, whereas in the second model, a stock-out scenario is adopted by partially backordering during modelling. The modelling framework for both problems is accomplished based on interval differential equations. The interval optimization problems related to both models are obtained utilizing parametric approach and interval mathematics. Then, using interval order relations and different types of quantum particle swarm optimization, both interval optimization problems are solved. By means of two examples, the authentication of both models is examined and the benefits of the proposed approach are demonstrated. The impact of deviations of various parameters on optimality is studied graphically through the performance of sensitivity analyses, and the work is concluded by providing potential management insights and future scopes.KEYWORDS: Parametric approachinterval demandinventoryexpiry dateadvance paymentpartial backlogginginterval differential equation Nomenclature Symbol=Descriptionp=Selling price ($/unit)CoL,CoU=Ordering cost ($/order)CpL,CpU=Purchasing price ($/unit)CsL,CsU=Backordering cost ($/unit/unit time)ClsL,ClsU=Opportunity cost ($/unit)gL,gU=Fixed cost for keeping a unit product ($/unit/unit time)hL,hU=Holding cost ($/unit/(unit time)2)aL,aU=Fixed demand with aL>0 (units)bL,bU=Price sensitivity parameter of the demand where bL>0(units)θ(t)=Deterioration rate at time (0<θ(t)<<1)L=Time duration for the prepayment (unit time)E=Highest lifetime of the products (unit time)IcL,IcU=Interest charging rate for the loan where IcL>0(/$/unit time)n=Number of advanced payments in equal intervals during Lα=Fraction of the purchase cost for the multiple pre-payments where α∈(0,1)Φ(u)=Waiting time (u)-dependent backlogging rateδ=Parameter of the backlogging rate where δ∈(0,∞)SL,SU=Initial stock amount where SL>0 (units)RL,RU=Backlogged amount where RL>0 (units)QL,QU=Total order amount per inventory cycle where QL>0 (units)qL(t),qU(t)=Inventory level at any time tZL(p,T),ZU(p,T)=Average profit (in $)Decision variables for without shortage case p=Selling price ($/unit)T=Inventory cycle length (unit time)Decision variables for shortage case p=Selling price ($/unit)t1=Time period for non-negative inventory level (unit time)t2=Time period for accumulating shortages (unit time)AcknowledgmentsM.S Rahman would like to thank the University Grants Commission (UGC) of India for providing financial assistance under Maulana Azad National Fellowship (F.No.61/2019 (SA-III)) to carry out this research. A.A Shaikh would like to thank the UGC of India for providing financial assistance under UGC-BSR (Start-Up) research scheme (File number: F.30-425/2018 (BSR)). Finally, A.A Shaikh and A.K Bhunia would like to acknowledge the Department of Science and Technology, Government of India, for FIST support (SR/FST/MSII/2017/10 (C)).Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe work was supported by the Department of Science and Technology, Government of India [SR/FST/MSII/2017/10(C)]; University Grants Commission [F.No.61/2019 (SA-III)]; University Grants Commission [F.30-425/2018 (BSR)].Notes on contributorsMd Sadikur RahmanDr. Md Sadikur Rahman is working as an Assistant Professor in Mathematics at Supreme Knowledge Foundation Group of Institutions, Hooghly, West Bengal, India. He completed his Master degree in the year of 2017 from the University of Kalyani,Nadia, West Bengal, India. He qualified National Eligibility Test (NET) in Mathematical Sciences 5 times during the years of 2017 to 2020. He achieved his Ph. D. degree in 2022 from the University of Burdwan, Burdwan, West Bengal, India. More than 25 papers published in different national/international journals of repute are in his credit. The area of his research interests included: Non-linear Optimization, Interval/Type-2 Interval Analysis, Numerical Analysis, Differential Equation, Inventory Control, etc.Subhash Chandra DasDr. Subhash Chandra Das working as an Assistant Professor in Mathematics at Chandrapur College, West Bengal, India since 2006. He completed M. Sc. in 2003 with Mathematics. He qualified two times in NET eligibility test in 2003 and 2005. He completed his Ph. D. degree in 2021. Also, five articles published in the international journals. He is working in inventory, interval mathematics and PSO algorithm.Md. Al-Amin KhanMd. Al-Amin Khan is a PhD student at Tecnológico de Monterrey. He is also an Assistant Professor in the Department of Mathematics at Jahangirnagar University, Savar, Dhaka. Mr. Khan received an MS degree in Mathematics from Jahangirnagar University in Bangladesh. He joined the Department of Mathematics at Jahangirnagar University in Bangladesh in 2014. Moreover, he received SHARFUDDIN GOLD MEDAL for outstanding results in the Master’s examination and securing the highest marks among all faculties of Jahangirnagar University in the MS Examination 2012 from the Department of Mathematics. He is working on supply chain management, inventory control theory, computational optimization, soft computing, and interval mathematics. He has published articles in Omega, International Journal of Production Economics, Expert Systems With Applications, Knowledge-Based Systems, Computers & Operations Research, Computers & Industrial Engineering, Artificial Intelligence Review, International Journal of Systems Science: Operations and Logistics, Annals of Operations Research, International Transactions in Operational Research, Soft Computing, RAIRO-Operations Research, and others.Ali Akbar ShaikhDr. Ali Akbar Shaikh is an Assistant Professor of Mathematics at The University of Burdwan, West Bengal, India. Earlier, he was a Postdoctoral Fellow at the School of Engineering and Sciences of Tecnológico de Monterrey, México. He has obtained the award SNI of level 1 (out of 0–3) presented by the National System of Researchers of México from Government of México, in 2017. He obtained his PhD and MPhil in Mathematics from The University of Burdwan, and MSc in Applied Mathematics from University of Kalyani, India. He has published more than 110 research papers in different international journals of repute (like Omega, International Journal of Production Economics, Expert Systems With Applications, Knowledge-Based Systems, Computers & Operations Research, Computers & Industrial Engineering, Artificial Intelligence Review, International Journal of Systems Science: Operations and Logistics, Annals of Operations Research, International Transactions in Operational Research, Applied Soft Computing, Soft Computing etc.). His research interests include inventory control, interval optimisation, and particle swarm optimisation.Asoke Kumar BhuniaDr. Asoke Kumar Bhunia is a Professor at the Department of Mathematics, The University of Burdwan, West Bengal, India. He obtained his PhD in Mathematics and MSc in Applied Mathematics from Vidyasagar University, India. His research interests include computational optimisation, soft computing, interval mathematics, and interval ranking. He has published over 140 research papers in various national and international journals of repute. He is a reviewer of several SCI journals. He has guided 15 PhD and two MPhil students. He is an author of four research monographs and six book chapters. He has written two text/reference level books in the area of optimization and Operations Research. He is an INSA Visiting Fellow and former Associate Editor of the Springer’s journal, OPSEARCH." @default.
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- W4386043848 date "2023-08-20" @default.
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- W4386043848 title "Inventory model for perishable items for interval-valued price dependent demand and advance payment policy with parametric approach via particle swarm optimization" @default.
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- W4386043848 doi "https://doi.org/10.1080/02286203.2023.2246829" @default.
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