{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T05:21:05Z","timestamp":1774243265949,"version":"3.50.1"},"reference-count":91,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["Ref.No:1137\/(CSIR-UGC NET DEC. 2018"],"award-info":[{"award-number":["Ref.No:1137\/(CSIR-UGC NET DEC. 2018"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008789","name":"Department of Science and Technology, Government of West Bengal","doi-asserted-by":"publisher","award":["429 (Sanc.)\/ST\/P\/S&T\/16G-23\/2018"],"award-info":[{"award-number":["429 (Sanc.)\/ST\/P\/S&T\/16G-23\/2018"]}],"id":[{"id":"10.13039\/501100008789","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Evolving Systems"],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s12530-025-09657-1","type":"journal-article","created":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T05:25:38Z","timestamp":1738819538000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Impact of displayed inventory level in a two-warehouse system for deteriorating item with discount facilities via different metaheuristic algorithms"],"prefix":"10.1007","volume":"16","author":[{"given":"Partha","family":"Halder","sequence":"first","affiliation":[]},{"given":"Goutam","family":"Mandal","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0072-5194","authenticated-orcid":false,"given":"Rajan","family":"Mondal","sequence":"additional","affiliation":[]},{"given":"Asoke Kumar","family":"Bhunia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,6]]},"reference":[{"key":"9657_CR1","doi-asserted-by":"crossref","unstructured":"Abualigah L, Sheikhan A, Ikotun AM, Zitar RA, Alsoud AR, Al-Shourbaji I, Jia H (2024) Particle swarm optimization algorithm: review and applications. Metaheuristic Optimization Algorithms, pp 1\u201314","DOI":"10.1016\/B978-0-443-13925-3.00019-4"},{"issue":"3","key":"9657_CR2","doi-asserted-by":"publisher","first-page":"2028","DOI":"10.29020\/nybg.ejpam.v17i3.5257","volume":"17","author":"A Ahmed","year":"2024","unstructured":"Ahmed A, Kummari K, Bandaru R, Shukla R (2024) Two-warehouse inventory model: interval valued costs, advanced payment, stock-dependent demand, and partial backlogging. Eur J Pure Appl Math 17(3):2028\u20132054","journal-title":"Eur J Pure Appl Math"},{"issue":"1","key":"9657_CR3","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1007\/s44196-023-00279-6","volume":"16","author":"I Al-Shourbaji","year":"2023","unstructured":"Al-Shourbaji I, Kachare P, Fadlelseed S, Jabbari A, Hussien AG, Al-Saqqar F, Alameen A (2023) Artificial ecosystem-based optimization with dwarf mongoose optimization for feature selection and global optimization problems. Int J Comput Intell Syst 16(1):102","journal-title":"Int J Comput Intell Syst"},{"issue":"3","key":"9657_CR4","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1504\/IJOR.2022.127140","volume":"45","author":"M Akhtar","year":"2022","unstructured":"Akhtar M, Manna AK, Duary A, Bhunia AK (2022) A hybrid tournament differential evolution algorithm for solving optimisation problems and applications. Int J Oper Res 45(3):300\u2013343","journal-title":"Int J Oper Res"},{"issue":"6","key":"9657_CR5","doi-asserted-by":"publisher","first-page":"715","DOI":"10.3846\/13926292.2015.1108936","volume":"20","author":"HK Alfares","year":"2015","unstructured":"Alfares HK (2015) Maximum-profit inventory model with stock-dependent demand, time-dependent holding cost, and all-units quantity discounts. Math Model Anal 20(6):715\u2013736","journal-title":"Math Model Anal"},{"issue":"7","key":"9657_CR6","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1287\/mnsc.16.7.413","volume":"16","author":"WJ Baumol","year":"1970","unstructured":"Baumol WJ, Vinod HD (1970) An inventory theoretic model of freight transport demand. Manag Sci 16(7):413\u2013421","journal-title":"Manag Sci"},{"issue":"1","key":"9657_CR7","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.ijpe.2009.01.010","volume":"119","author":"AK Bhunia","year":"2009","unstructured":"Bhunia AK, Kundu S, Sannigrahi T, Goyal SK (2009) An application of tournament genetic algorithm in a marketing oriented economic production lot-size model for deteriorating items. Int J Prod Econ 119(1):112\u2013121","journal-title":"Int J Prod Econ"},{"issue":"3","key":"9657_CR8","first-page":"164","volume":"1","author":"AK Bhunia","year":"2014","unstructured":"Bhunia AK, Mahato SK, Shaikh AA, Jaggi CK (2014) A deteriorating inventory model with displayed stock-level-dependent demand and partially backlogged shortages with all unit discount facilities via particle swarm optimisation. Int J Syst Sci Oper Logist 1(3):164\u2013180","journal-title":"Int J Syst Sci Oper Logist"},{"key":"9657_CR9","doi-asserted-by":"crossref","unstructured":"Biswas N, Priyadarshi S, Prakash O (2024) Exploring the dependency of order size in integrated inventory model under partial trade credit and all unit discounts with capacity constraints. In: Operations research forum, (Vol. 5) Springer International Publishing, Cham, p 106","DOI":"10.1007\/s43069-024-00387-9"},{"issue":"2","key":"9657_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40819-018-0490-1","volume":"4","author":"R Chakrabarty","year":"2018","unstructured":"Chakrabarty R, Roy T, Chaudhuri KS (2018) A two-warehouse inventory model for deteriorating items with capacity constraints and back-ordering under financial considerations. Int J Appl Comput Math 4(2):1\u201316","journal-title":"Int J Appl Comput Math"},{"key":"9657_CR11","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s40819-014-0011-9","volume":"1","author":"RR Chowdhury","year":"2015","unstructured":"Chowdhury RR, Ghosh SK, Chaudhuri KS (2015) An inventory model for deteriorating items with stock and price sensitive demand. Int J Appl Comput Math 1:187\u2013201","journal-title":"Int J Appl Comput Math"},{"issue":"4","key":"9657_CR12","first-page":"295","volume":"5","author":"I Darma Wangsa","year":"2018","unstructured":"Darma Wangsa I, Wee HM (2018) An integrated vendor\u2013buyer inventory model with transportation cost and stochastic demand. Int J Syst Sci Oper Logist 5(4):295\u2013309","journal-title":"Int J Syst Sci Oper Logist"},{"issue":"4","key":"9657_CR13","doi-asserted-by":"publisher","first-page":"3075","DOI":"10.21917\/ijsc.2023.0433","volume":"13","author":"D Das","year":"2023","unstructured":"Das D (2023) A two-warehouses production inventory model for deteriorating items with stock-dependent demand under preservation technology using modified genetic algorithm. ICTACT J Soft Comput 13(4):3075","journal-title":"ICTACT J Soft Comput"},{"issue":"5","key":"9657_CR14","doi-asserted-by":"publisher","first-page":"1925","DOI":"10.1016\/j.jfranklin.2022.01.035","volume":"359","author":"S Das","year":"2022","unstructured":"Das S, Mondal R, Shaikh AA, Bhunia AK (2022) An application of control theory for imperfect production problem with carbon emission investment policy in interval environment. J Franklin Inst 359(5):1925\u20131970","journal-title":"J Franklin Inst"},{"issue":"2","key":"9657_CR15","first-page":"151","volume":"31","author":"BK Debnath","year":"2018","unstructured":"Debnath BK, Majumder P, Bera UK (2018) Two warehouse inventory models of breakable items with stock dependent demand under trade credit policy with respect to both supplier and retailer. Int J Logist Syst Manag 31(2):151\u2013166","journal-title":"Int J Logist Syst Manag"},{"issue":"8","key":"9657_CR16","doi-asserted-by":"publisher","first-page":"5486","DOI":"10.3934\/jimo.2022182","volume":"19","author":"M Dolai","year":"2023","unstructured":"Dolai M, Banu A, Mondal SK (2023) Analyzing an imperfect production inventory model for green products considering learning effect on screening process under advertisement dependent credit period. J Ind Manag Optim 19(8):5486\u20135514","journal-title":"J Ind Manag Optim"},{"issue":"3","key":"9657_CR17","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1016\/j.ejor.2018.07.031","volume":"272","author":"L Duan","year":"2019","unstructured":"Duan L, Ventura JA (2019) A dynamic supplier selection and inventory management model for a serial supply chain with a novel supplier price break scheme and flexible time periods. Eur J Oper Res 272(3):979\u2013998","journal-title":"Eur J Oper Res"},{"issue":"2","key":"9657_CR18","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1016\/j.aej.2021.06.070","volume":"61","author":"A Duary","year":"2022","unstructured":"Duary A, Das S, Arif MG, Abualnaja KM, Khan MAA, Zakarya M, Shaikh AA (2022) Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially backlogged shortages. Alex Eng J 61(2):1735\u20131745","journal-title":"Alex Eng J"},{"issue":"1","key":"9657_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2018.11.067","volume":"279","author":"E Engebrethsen","year":"2019","unstructured":"Engebrethsen E, Dauz\u00e8re-P\u00e9r\u00e8s S (2019) Transportation mode selection in inventory models: a literature review. Eur J Oper Res 279(1):1\u201325","journal-title":"Eur J Oper Res"},{"issue":"2","key":"9657_CR500","first-page":"238","volume":"14","author":"PM Ghare","year":"1963","unstructured":"Ghare PM, Schrader GF (1963) An inventory model for exponentially deteriorating items. J Ind Eng 14(2):238\u2013243","journal-title":"J Ind Eng"},{"key":"9657_CR20","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/j.apm.2020.01.046","volume":"82","author":"Y Ghiami","year":"2020","unstructured":"Ghiami Y, Beullens P (2020) The continuous resupply policy for deteriorating items with stock-dependent observable demand in a two-warehouse and two-echelon supply chain. Appl Math Model 82:271\u2013292","journal-title":"Appl Math Model"},{"issue":"4","key":"9657_CR21","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1016\/0360-8352(95)00016-T","volume":"28","author":"SK Goyal","year":"1995","unstructured":"Goyal SK, Gunasekaran A (1995) An integrated production-inventory-marketing model for deteriorating items. Comput Ind Eng 28(4):755\u2013762","journal-title":"Comput Ind Eng"},{"key":"9657_CR22","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10479-020-03673-x","volume":"295","author":"M Gupta","year":"2020","unstructured":"Gupta M, Tiwari S, Jaggi CK (2020) Retailer\u2019s ordering policies for time-varying deteriorating items with partial backlogging and permissible delay in payments in a two-warehouse environment. Ann Oper Res 295:139\u2013161","journal-title":"Ann Oper Res"},{"key":"9657_CR23","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1142\/S0219686723500397","volume":"22","author":"P Hajialirezaei","year":"2023","unstructured":"Hajialirezaei P, Reza Pasandideh SH (2023) A two-warehouse lot sizing problem for defective items with a completely backlogged shortage under limited storage capacity for rented warehouses. J Adv Manuf Syst 22:894","journal-title":"J Adv Manuf Syst"},{"key":"9657_CR24","unstructured":"Harahap AZMK, Rahim MKIA (2023) Saving concepts in supply chain management: a study on inventory and transportation costs"},{"key":"9657_CR25","first-page":"315","volume-title":"Operations research: a managerial emphasis","author":"RV Hartley","year":"1976","unstructured":"Hartley RV (1976) Operations research: a managerial emphasis. GoodyearPublishing Company, California, pp 315\u2013317"},{"issue":"4","key":"9657_CR26","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s40819-022-01410-5","volume":"8","author":"A Hatibaruah","year":"2022","unstructured":"Hatibaruah A, Saha S (2022) A production inventory model for ameliorating and deteriorating items with price, time and advertisement frequency dependent demand under the effect of inflation. Int J Appl Comput Math 8(4):201","journal-title":"Int J Appl Comput Math"},{"key":"9657_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12597-024-00751-7","volume":"61","author":"MA Hoque","year":"2024","unstructured":"Hoque MA, Juman ZAMS (2024) Decreased minimum total transportation\u2013inventory cost bounds assuming variability in supplies and demands. OPSEARCH 61:1\u201318","journal-title":"OPSEARCH"},{"issue":"1","key":"9657_CR28","first-page":"69","volume":"18","author":"MA Hossen","year":"2022","unstructured":"Hossen MA (2022) Impact of inflation and advertisement dependent demand in an inventory system. J Calcutta Math Soc 18(1):69\u201378","journal-title":"J Calcutta Math Soc"},{"key":"9657_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.122005","volume":"238","author":"H Hu","year":"2024","unstructured":"Hu H, Guo S, Zhen L, Wang S, Bian Y (2024) A multi-product and multi-period supply chain network design problem with price-sensitive demand and incremental quantity discount. Expert Syst Appl 238:122005","journal-title":"Expert Syst Appl"},{"issue":"4","key":"9657_CR30","first-page":"503","volume":"30","author":"CK Jaggi","year":"2018","unstructured":"Jaggi CK, Tiwari S, Gupta M (2018) Impact of trade credit on inventory models for Weibull distribution deteriorating items with partial backlogging in two-warehouse environment. Int J Logist Syst Manag 30(4):503\u2013520","journal-title":"Int J Logist Syst Manag"},{"issue":"4","key":"9657_CR31","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1504\/IJOR.2019.101459","volume":"35","author":"CK Jaggi","year":"2019","unstructured":"Jaggi CK, Gupta M, Tiwari S (2019) Credit financing in economic ordering policies for deteriorating items with stochastic demand and promotional efforts in two-warehouse environment. Int J Oper Res 35(4):529\u2013550","journal-title":"Int J Oper Res"},{"key":"9657_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10479-020-03568-x","volume":"289","author":"MAA Khan","year":"2020","unstructured":"Khan MAA, Shaikh AA, Panda GC, Bhunia AK, Konstantaras I (2020a) Non-instantaneous deterioration effect in ordering decisions for a two-warehouse inventory system under advance payment and backlogging. Ann Oper Res 289:1\u201333","journal-title":"Ann Oper Res"},{"key":"9657_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2020.107804","volume":"230","author":"MAA Khan","year":"2020","unstructured":"Khan MAA, Shaikh AA, Konstantaras I, Bhunia AK, C\u00e1rdenas-Barr\u00f3n LE (2020b) Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price. Int J Prod Econ 230:107804","journal-title":"Int J Prod Econ"},{"key":"9657_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2021.102418","volume":"103","author":"MAA Khan","year":"2021","unstructured":"Khan MAA, Shaikh AA, C\u00e1rdenas-Barr\u00f3n LE (2021) An inventory model under linked-to-order hybrid partial advance payment, partial credit policy, all-units discount and partial backlogging with capacity constraint. Omega 103:102418","journal-title":"Omega"},{"key":"9657_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.119247","volume":"213","author":"MAA Khan","year":"2023","unstructured":"Khan MAA, C\u00e1rdenas-Barr\u00f3n LE, Trevi\u00f1o-Garza G, C\u00e9spedes-Mota A (2023) A prepayment installment decision support framework in an inventory system with all-units discount against link-to-order prepayment under power demand pattern. Expert Syst Appl 213:119247","journal-title":"Expert Syst Appl"},{"issue":"4","key":"9657_CR36","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1007\/s40819-021-00991-x","volume":"7","author":"S Kumar","year":"2021","unstructured":"Kumar S (2021) An inventory model for decaying items under preservation technological effect with advertisement dependent demand and trade credit. Int J Appl Comput Math 7(4):128","journal-title":"Int J Appl Comput Math"},{"key":"9657_CR37","doi-asserted-by":"crossref","unstructured":"Kumar N, Dahiya S, Kumar S (2022) Two warehouse inventory model for deteriorating items with fixed shelf-life stock-dependent demand and partial backlogging. J Math Comput Sci 12","DOI":"10.22214\/ijraset.2021.39265"},{"issue":"3","key":"9657_CR38","doi-asserted-by":"publisher","first-page":"896","DOI":"10.1007\/s10696-022-09456-9","volume":"35","author":"C Mahato","year":"2023","unstructured":"Mahato C, Mahata GC (2023) Sustainable partial backordering inventory model under linked-to-order credit policy and all-units discount with capacity constraint and carbon emissions. Flex Serv Manuf J 35(3):896\u2013944","journal-title":"Flex Serv Manuf J"},{"issue":"6","key":"9657_CR39","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1007\/s12530-023-09485-1","volume":"14","author":"G Mandal","year":"2023","unstructured":"Mandal G, Kumar N, Duary A, Shaikh AA, Bhunia AK (2023) A league-knock-out tournament quantum particle swarm optimization algorithm for nonlinear constrained optimization problems and applications. Evol Syst 14(6):1117\u20131143","journal-title":"Evol Syst"},{"key":"9657_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/s12597-024-00869-8","author":"G Mandal","year":"2024","unstructured":"Mandal G, Akhtar M, Bhunia AK, Shaikh AA (2024) Applications of a league-then-knockout tournament based hybrid algorithm for engineering problems. OPSEARCH. https:\/\/doi.org\/10.1007\/s12597-024-00869-8","journal-title":"OPSEARCH"},{"key":"9657_CR41","doi-asserted-by":"publisher","first-page":"S1069","DOI":"10.1051\/ro\/2020106","volume":"55","author":"AHM Mashud","year":"2021","unstructured":"Mashud AHM, Roy D, Daryanto Y, Wee HM (2021) Joint pricing deteriorating inventory model considering product life cycle and advance payment with a discount facility. RAIRO-Oper Res 55:S1069\u2013S1088","journal-title":"RAIRO-Oper Res"},{"key":"9657_CR42","unstructured":"Medina-Santana AA, C\u00e1rdenas-Barr\u00f3n LE (2020) A sustainable inventory model considering a discontinuous transportation cost function and different sources of pollution.\u00a0arXiv preprint arXiv:2005.03781"},{"issue":"3","key":"9657_CR43","doi-asserted-by":"publisher","first-page":"169","DOI":"10.5267\/j.uscm.2017.1.004","volume":"5","author":"P Mishra","year":"2017","unstructured":"Mishra P, Shaikh A (2017) Optimal ordering policy for an integrated inventory model with stock dependent demand and order linked trade credits for twin ware house system. Uncertain Supply Chain Manag 5(3):169\u2013186","journal-title":"Uncertain Supply Chain Manag"},{"issue":"8","key":"9657_CR44","first-page":"516","volume":"33","author":"DJ Mohanty","year":"2016","unstructured":"Mohanty DJ, Kumar RS, Goswami A (2016) A two-warehouse inventory model for non-instantaneous deteriorating items over stochastic planning horizon. J Ind Prod Eng 33(8):516\u2013532","journal-title":"J Ind Prod Eng"},{"issue":"5","key":"9657_CR45","doi-asserted-by":"publisher","first-page":"235","DOI":"10.3390\/systems11050235","volume":"11","author":"AF Momena","year":"2023","unstructured":"Momena AF, Rahaman M, Haque R, Alam S, Mondal SP (2023) A learning-based optimal decision scenario for an inventory problem under a price discount policy. Systems 11(5):235","journal-title":"Systems"},{"issue":"6","key":"9657_CR46","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1080\/13873954.2019.1692226","volume":"25","author":"R Mondal","year":"2019","unstructured":"Mondal R, Shaikh AA, Bhunia AK (2019) Crisp and interval inventory models for ameliorating item with Weibull distributed amelioration and deterioration via different variants of quantum behaved particle swarm optimization-based techniques. Math Comput Model Dyn Syst 25(6):602\u2013626","journal-title":"Math Comput Model Dyn Syst"},{"issue":"1","key":"9657_CR47","doi-asserted-by":"publisher","first-page":"78","DOI":"10.3390\/math10010078","volume":"10","author":"R Mondal","year":"2021","unstructured":"Mondal R, Shaikh AA, Bhunia AK, Hezam IM, Chakrabortty RK (2021) Impact of trapezoidal demand and deteriorating preventing technology in an inventory model in interval uncertainty under backlogging situation. Mathematics 10(1):78","journal-title":"Mathematics"},{"issue":"1","key":"9657_CR48","first-page":"2070296","volume":"10","author":"R Mondal","year":"2023","unstructured":"Mondal R, Das S, Das SC, Shaikh AA, Bhunia AK (2023) Pricing strategies and advance payment-based inventory model with partially backlogged shortages under interval uncertainty. Int J Syst Sci Oper Logist 10(1):2070296","journal-title":"Int J Syst Sci Oper Logist"},{"key":"9657_CR49","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s13198-024-02341-8","volume":"15","author":"R Mondal","year":"2024","unstructured":"Mondal R, Das S, Akhtar M, Shaikh AA, Bhunia AK (2024) A two-warehouse inventory model for deteriorating items with partially backlogged demand rate under trade credit policies. Int J Syst Assur Eng Manag 15:1\u201318","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"1","key":"9657_CR50","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1007\/s12063-022-00266-8","volume":"16","author":"V Murmu","year":"2023","unstructured":"Murmu V, Kumar D, Jha AK (2023) Quality and selling price dependent sustainable perishable inventory policy: lessons from Covid-19 pandemic. Oper Manag Res 16(1):408\u2013432","journal-title":"Oper Manag Res"},{"issue":"1","key":"9657_CR51","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1504\/IJMOR.2023.128645","volume":"24","author":"P Narang","year":"2023","unstructured":"Narang P, De PK (2023) An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm. Int J Math Oper Res 24(1):53\u201377","journal-title":"Int J Math Oper Res"},{"issue":"2","key":"9657_CR52","doi-asserted-by":"publisher","first-page":"37","DOI":"10.9734\/arjom\/2024\/v20i2785","volume":"20","author":"SV Padiyar","year":"2024","unstructured":"Padiyar SV, Jain K, Makholia D, Mishra R (2024) Integrated inventory model with inflation for deteriorating items. Asian Res J Math 20(2):37\u201347","journal-title":"Asian Res J Math"},{"issue":"1","key":"9657_CR53","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s40092-018-0269-3","volume":"15","author":"GC Panda","year":"2019","unstructured":"Panda GC, Khan MAA, Shaikh AA (2019) A credit policy approach in a two-warehouse inventory model for deteriorating items with price-and stock-dependent demand under partial backlogging. J Ind Eng Int 15(1):147\u2013170","journal-title":"J Ind Eng Int"},{"issue":"2","key":"9657_CR54","doi-asserted-by":"publisher","first-page":"446","DOI":"10.18280\/mmep.110216","volume":"11","author":"K Pathak","year":"2024","unstructured":"Pathak K, Yadav AS, Agarwal P (2024) Optimizing two-warehouse inventory for shelf-life stock with time-varying bi-quadratic demand under shortages and inflation. Math Modell Eng Probl 11(2):446","journal-title":"Math Modell Eng Probl"},{"key":"9657_CR55","doi-asserted-by":"crossref","unstructured":"Patro RR, Patro R, Giri PK, Pati B (2024) A PSO approach for two warehouse inventory problem with imperfect quality items and variable discount. In: International Conference on Machine Intelligence, Tools, and Applications. Springer Nature Switzerland, Cham, pp. 116\u2013127","DOI":"10.1007\/978-3-031-65392-6_11"},{"issue":"1","key":"9657_CR56","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1051\/ro\/2023005","volume":"57","author":"M Pervin","year":"2023","unstructured":"Pervin M, Roy SK, Sannyashi P, Weber GW (2023) Sustainable inventory model with environmental impact for non-instantaneous deteriorating items with composite demand. RAIRO-Oper Res 57(1):237\u2013261","journal-title":"RAIRO-Oper Res"},{"key":"9657_CR57","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1016\/j.apm.2016.11.003","volume":"57","author":"MA Rad","year":"2018","unstructured":"Rad MA, Khoshalhan F, Glock CH (2018) Optimal production and distribution policies for a two-stage supply chain with imperfect items and price-and advertisement-sensitive demand: a note. Appl Math Model 57:625\u2013632","journal-title":"Appl Math Model"},{"issue":"3","key":"9657_CR58","first-page":"332","volume":"41","author":"MS Rahman","year":"2022","unstructured":"Rahman MS, Hasan SN, Banerjee T, Mondal R, Shaikh AA (2022) An EOQ model for deteriorating item with time-dependent demand and partial backlogging: advance payment policy. Int J Logist Syst Manag 41(3):332\u2013348","journal-title":"Int J Logist Syst Manag"},{"key":"9657_CR59","doi-asserted-by":"crossref","unstructured":"Rana RS, Kumar D, Prasad K (2021) Two warehouse dispatching policies for perishable items with freshness efforts, inflationary conditions and partial backlogging.\u00a0In: Operations Management Research, pp 1\u201318","DOI":"10.1007\/s12063-020-00168-7"},{"key":"9657_CR60","doi-asserted-by":"crossref","unstructured":"Rana RS, Kumar D, Prasad K, Mathiyazhagan K (2023) Mitigating the impact of demand disruption on perishable inventory in a two-warehouse system.\u00a0In: Operations Management Research, pp 1\u201336","DOI":"10.1007\/s12063-023-00418-4"},{"issue":"1","key":"9657_CR61","first-page":"23","volume":"13","author":"H Rasay","year":"2020","unstructured":"Rasay H, Golmohammadi AM (2020) Modeling and analyzing incremental quantity discounts in transportation costs for a joint economic lot sizing problem. Interdiscip J Manag Stud (Formerly Known as Iran J Manag Stud) 13(1):23\u201349","journal-title":"Interdiscip J Manag Stud (Formerly Known as Iran J Manag Stud)"},{"issue":"1","key":"9657_CR62","doi-asserted-by":"publisher","first-page":"012130","DOI":"10.1088\/1742-6596\/1913\/1\/012130","volume":"1913","author":"M Rizwanullah","year":"2021","unstructured":"Rizwanullah M, Verma SK, Junnaidi MH (2021) Supply-chain two-warehouse inventory model for deteriorating items on exponential time function with shortage and partial backlogging in inflationary environment. J Phys Conf Ser 1913(1):012130","journal-title":"J Phys Conf Ser"},{"key":"9657_CR63","doi-asserted-by":"crossref","unstructured":"Sahoo AK, Indrajitsingha SK, Samanta PN, Misra UK (2021) A fuzzy two-warehouse inventory model of deteriorating items with exponentially demand and backlogged condition. In:\u00a0New Trends in Applied Analysis and Computational Mathematics: Proceedings of the International Conference on Advances in Mathematics and Computing (ICAMC 2020). Springer Singapore, Singapore, pp 1\u201315","DOI":"10.1007\/978-981-16-1402-6_1"},{"key":"9657_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2020.105169","volume":"128","author":"LA San-Jos\u00e9","year":"2021","unstructured":"San-Jos\u00e9 LA, Sicilia J, Abdul-Jalbar B (2021) Optimal policy for an inventory system with demand dependent on price, time and frequency of advertisement. Comput Oper Res 128:105169","journal-title":"Comput Oper Res"},{"key":"9657_CR65","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2023.109098","volume":"268","author":"LA San-Jos\u00e9","year":"2024","unstructured":"San-Jos\u00e9 LA, Sicilia J, C\u00e1rdenas-Barr\u00f3n LE, Gonz\u00e1lez-de-la-Rosa M (2024) A sustainable inventory model for deteriorating items with power demand and full backlogging under a carbon emission tax. Int J Prod Econ 268:109098","journal-title":"Int J Prod Econ"},{"key":"9657_CR66","doi-asserted-by":"crossref","unstructured":"Santhi G, Karthikeyan K (2021) Two-warehouse inventory model for instantaneous deteriorating items with price and time dependent demand, complete backlogging.\u00a0Ital J Pure Appl Math 24","DOI":"10.1007\/s40819-021-01070-x"},{"issue":"1","key":"9657_CR67","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TLA.2017.7827916","volume":"15","author":"MDA Serna","year":"2017","unstructured":"Serna MDA, Cortes JAZ (2017) Multiobjective model for the simultaneous optimization of transportation costs, inventory costs and service level in goods distribution. IEEE Lat Am Trans 15(1):129\u2013136","journal-title":"IEEE Lat Am Trans"},{"issue":"1","key":"9657_CR68","first-page":"34","volume":"7","author":"NH Shah","year":"2020","unstructured":"Shah NH, Chaudhari U, C\u00e1rdenas-Barr\u00f3n LE (2020) Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three echelon supply chain. Int J Syst Sci Oper Logist 7(1):34\u201345","journal-title":"Int J Syst Sci Oper Logist"},{"issue":"3","key":"9657_CR69","first-page":"221","volume":"54","author":"AA Shaikh","year":"2020","unstructured":"Shaikh AA, Mondal R, Bhattacharyya AN, Kumar N, Mandal G (2020) Analysis of a two-storage system for advance payment policies with the partial backlogged shortage. Adv Ind Eng 54(3):221\u2013242","journal-title":"Adv Ind Eng"},{"issue":"SI 2 (64)","key":"9657_CR70","first-page":"213","volume":"16","author":"S Sharma","year":"2021","unstructured":"Sharma S, Kumar V, Tyagi A (2021) A production inventory model for deteriorating items with effect of price discount under the stock dependent demand. Reliabil Theory Appl 16(SI 2 (64)):213\u2013224","journal-title":"Reliabil Theory Appl"},{"key":"9657_CR71","doi-asserted-by":"crossref","unstructured":"Sharma A, Kumar V, Kumar A, Gupta CB (2022) An EOQ model for non-instantaneously deteriorating items under permissible delay in payments and inflation. In: AIP Conference Proceedings\u00a0(Vol. 2597). AIP Publishing","DOI":"10.1063\/5.0115333"},{"issue":"2","key":"9657_CR72","first-page":"274","volume":"19","author":"A Sharma","year":"2024","unstructured":"Sharma A, Kumar V, Singh SR, Gupta CB (2024) Green inventory model with two-warehouse system considering variable holding cost, time dependent demand, carbon emissions and energy consumption. Int J Procur Manag 19(2):274\u2013296","journal-title":"Int J Procur Manag"},{"issue":"2","key":"9657_CR73","doi-asserted-by":"publisher","first-page":"195","DOI":"10.5267\/j.uscm.2017.7.002","volume":"6","author":"D Sharmila","year":"2018","unstructured":"Sharmila D, Uthayakumar R (2018) A two warehouse deterministic inventory model for deteriorating items with power demand, time varying holding costs and trade credit in a supply chain system. Uncertain Supply Chain Manag 6(2):195\u2013212","journal-title":"Uncertain Supply Chain Manag"},{"key":"9657_CR74","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-024-06175-2","author":"C Shekhar","year":"2024","unstructured":"Shekhar C, Yadav V, Saurav A (2024) Optimal analysis of time-price discount-advertisement dependent demand with credit policy for inventory models. Ann Oper Res. https:\/\/doi.org\/10.1007\/s10479-024-06175-2","journal-title":"Ann Oper Res"},{"key":"9657_CR75","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2020.125434","volume":"287","author":"SU Sherif","year":"2021","unstructured":"Sherif SU, Asokan P, Sasikumar P, Mathiyazhagan K, Jerald J (2021) Integrated optimization of transportation, inventory and vehicle routing with simultaneous pickup and delivery in two-echelon green supply chain network. J Clean Prod 287:125434","journal-title":"J Clean Prod"},{"key":"9657_CR76","doi-asserted-by":"crossref","unstructured":"Singh D, Sharma KC (2024) A deterministic inventory model for deteriorating products with replenishment rate dependent on inventory level. Int J Math Trends Technol IJMTT,\u00a070","DOI":"10.14445\/22315373\/IJMTT-V70I10P103"},{"issue":"4","key":"9657_CR77","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution\u2013a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341\u2013359","journal-title":"J Global Optim"},{"key":"9657_CR78","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2024.109922","volume":"188","author":"I Suemitsu","year":"2024","unstructured":"Suemitsu I, Miyashita N, Hosoda J, Shimazu Y, Nishikawa T, Izui K (2024) Integration of sales, inventory, and transportation resource planning by dynamic-demand joint replenishment problem with time-varying costs. Comput Ind Eng 188:109922","journal-title":"Comput Ind Eng"},{"key":"9657_CR79","doi-asserted-by":"crossref","unstructured":"Sunita, Kumar G (2022) An inflationary demand scheme with pareto deterioration in two warehouses. In: Advances in mathematical modelling, applied analysis and computation: proceedings of ICMMAAC 2021. Springer Nature Singapore, Singapore, pp. 227\u2013245","DOI":"10.1007\/978-981-19-0179-9_13"},{"key":"9657_CR80","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.cie.2018.11.003","volume":"127","author":"M Tamannaei","year":"2019","unstructured":"Tamannaei M, Rasti-Barzoki M (2019) Mathematical programming and solution approaches for minimizing tardiness and transportation costs in the supply chain scheduling problem. Comput Ind Eng 127:643\u2013656","journal-title":"Comput Ind Eng"},{"issue":"4","key":"9657_CR81","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1504\/IJPMB.2019.103427","volume":"9","author":"S Tayal","year":"2019","unstructured":"Tayal S, Singh SR, Attri AK (2019) Two levels of storage model for deteriorating items, stock dependent demand and partial backlogging with both rented warehouses. Int J Process Manag Benchmark 9(4):485\u2013498","journal-title":"Int J Process Manag Benchmark"},{"key":"9657_CR82","doi-asserted-by":"publisher","first-page":"160324","DOI":"10.1109\/ACCESS.2019.2950036","volume":"7","author":"L Teng","year":"2019","unstructured":"Teng L, Zhang Z, Li P, Gong D (2019) Integrated inventory-transportation problem in vendor-managed inventory system. IEEE Access 7:160324\u2013160333","journal-title":"IEEE Access"},{"key":"9657_CR83","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-023-05643-5","author":"V Tunuguntla","year":"2024","unstructured":"Tunuguntla V, Basu P, Rakshit K, Papadopoulos T (2024) Sponsored search advertising and inventory replenishment: a decision support framework for an online retailer. Ann Oper Res. https:\/\/doi.org\/10.1007\/s10479-023-05643-5","journal-title":"Ann Oper Res"},{"key":"9657_CR84","doi-asserted-by":"crossref","unstructured":"Vandana, Das AK (2022) Two-warehouse supply chain model under preservation technology and stochastic demand with shortages. OPSEARCH 59(4):1587\u20131612","DOI":"10.1007\/s12597-022-00600-5"},{"key":"9657_CR85","unstructured":"Verma M (2024) Inventory models for deteriorating items under trade credit period. J Inf Educ Res, 4(2)"},{"key":"9657_CR86","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2020.122120","volume":"271","author":"ID Wangsa","year":"2020","unstructured":"Wangsa ID, Tiwari S, Wee HM, Reong S (2020) A sustainable vendor-buyer inventory system considering transportation, loading and unloading activities. J Clean Prod 271:122120","journal-title":"J Clean Prod"},{"key":"9657_CR87","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1016\/j.matpr.2021.06.307","volume":"51","author":"AS Yadav","year":"2022","unstructured":"Yadav AS, Pandey G, Arora TK, Chaubey PK (2022) Block-chain application based economic impact of coronavirus pandemic on medicine industry inventory system for deteriorating objects with two-warehouse and wastewater treatment using PSO. Mater Today Proc 51:939\u2013946","journal-title":"Mater Today Proc"},{"key":"9657_CR88","doi-asserted-by":"publisher","DOI":"10.1007\/s12008-023-01689-8","author":"AS Yadav","year":"2023","unstructured":"Yadav AS, Kumar A, Yadav KK, Rathee S (2023) Optimization of an inventory model for deteriorating items with both selling price and time-sensitive demand and carbon emission under green technology investment. Int J Interact Des Manuf (IJIDeM). https:\/\/doi.org\/10.1007\/s12008-023-01689-8","journal-title":"Int J Interact Des Manuf (IJIDeM)"},{"key":"9657_CR89","doi-asserted-by":"publisher","DOI":"10.1007\/s12008-023-01672-3","author":"KK Yadav","year":"2024","unstructured":"Yadav KK, Yadav AS, Bansal S (2024) Interval number approach for two-warehouse inventory management of deteriorating items with preservation technology investment using analytical optimization methods. Int J Interact Des Manuf (IJIDeM). https:\/\/doi.org\/10.1007\/s12008-023-01672-3","journal-title":"Int J Interact Des Manuf (IJIDeM)"},{"key":"9657_CR90","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2024.103462","volume":"184","author":"L Yang","year":"2024","unstructured":"Yang L, Liu K, Zhang J, Zelbst PJ (2024) Inventory management with actual palletized transportation costs and lost sales. Transp Res Part e Logist Transp Rev 184:103462","journal-title":"Transp Res Part e Logist Transp Rev"}],"container-title":["Evolving Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12530-025-09657-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12530-025-09657-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12530-025-09657-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T08:49:04Z","timestamp":1743670144000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12530-025-09657-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2]]},"references-count":91,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["9657"],"URL":"https:\/\/doi.org\/10.1007\/s12530-025-09657-1","relation":{},"ISSN":["1868-6478","1868-6486"],"issn-type":[{"value":"1868-6478","type":"print"},{"value":"1868-6486","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2]]},"assertion":[{"value":"18 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 February 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No potential conflict of interest is reported by the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"No participation of humans takes place in this implementation process.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"No violation of human and animal rights is involved.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human or animal rights"}}],"article-number":"31"}}