{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T04:40:47Z","timestamp":1769834447254,"version":"3.49.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s00500-025-10920-5","type":"journal-article","created":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T08:19:38Z","timestamp":1764058778000},"page":"263-287","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhancing sustainability and operational resilience: Robust optimization for mitigating lost sales through fuzzy shortage and energy efficiency in supply chains"],"prefix":"10.1007","volume":"30","author":[{"given":"B.","family":"Karthick","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"issue":"3","key":"10920_CR1","doi-asserted-by":"publisher","first-page":"250","DOI":"10.2307\/1906813","volume":"19","author":"KJ Arrow","year":"1951","unstructured":"Arrow KJ, Harris TE, Marschak J (1951) Optimal inventory policy. Econometrica: Journal of the Econometric Society 19(3):250\u2013272","journal-title":"Econometrica: Journal of the Econometric Society"},{"issue":"17","key":"10920_CR2","doi-asserted-by":"publisher","first-page":"5131","DOI":"10.1016\/j.apm.2015.03.044","volume":"39","author":"E Bazan","year":"2015","unstructured":"Bazan E, Jaber MY, Zanoni S (2015) Supply chain models with greenhouse gases emissions, energy usage and different coordination decisions. Appl Math Model 39(17):5131\u20135151","journal-title":"Appl Math Model"},{"issue":"3","key":"10920_CR3","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1016\/j.ijar.2008.10.001","volume":"50","author":"KM Bj\u00f6rk","year":"2009","unstructured":"Bj\u00f6rk KM (2009) An analytical solution to a fuzzy economic order quantity problem. Int J Approx Reason 50(3):485\u2013493","journal-title":"Int J Approx Reason"},{"issue":"4","key":"10920_CR4","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1287\/mnsc.6.4.475","volume":"6","author":"CE Clark","year":"1960","unstructured":"Clark CE, Scarf H (1960) Optimal policies for a multi-echelon inventory problem. Manage Sci 6(4):475\u2013490","journal-title":"Manage Sci"},{"issue":"21","key":"10920_CR5","doi-asserted-by":"publisher","first-page":"15817","DOI":"10.1007\/s00500-023-08824-3","volume":"27","author":"S Das","year":"2023","unstructured":"Das S, Choudhury M, Mahato C, Mahata GC (2023) Dual-channel supply chain inventory model under two-warehouse setting with order volume-linked trade credit, all-units discount and partial backordering. Soft Comput 27(21):15817\u201315852","journal-title":"Soft Comput"},{"issue":"1","key":"10920_CR6","first-page":"59","volume":"3","author":"PK De","year":"2011","unstructured":"De PK, Rawat A (2011) A fuzzy inventory model without shortages using triangular fuzzy number. FIE 3(1):59\u201368","journal-title":"FIE"},{"issue":"6","key":"10920_CR7","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1016\/j.envsoft.2004.10.002","volume":"20","author":"JQ Guo","year":"2005","unstructured":"Guo JQ, Zheng L (2005) A modified simulated annealing algorithm for estimating solute transport parameters in streams from tracer experiment data. Environ Model Softw 20(6):811\u2013815","journal-title":"Environ Model Softw"},{"issue":"8","key":"10920_CR8","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1057\/jors.1993.141","volume":"44","author":"G Gallego","year":"1993","unstructured":"Gallego G, Moon I (1993) The distribution free newsboy problem: review and extensions. J Oper Res Soc 44(8):825\u2013834","journal-title":"J Oper Res Soc"},{"issue":"12","key":"10920_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/s10668-022-02631-w","volume":"25","author":"B Karthick","year":"2022","unstructured":"Karthick B, Uthayakumar R (2022) A closed-loop supply chain model with carbon emission and pricing decisions under an intuitionistic fuzzy environment. Environ Dev Sustain 25(12):49. https:\/\/doi.org\/10.1007\/s10668-022-02631-w","journal-title":"Environ Dev Sustain"},{"issue":"16","key":"10920_CR10","doi-asserted-by":"publisher","first-page":"11431","DOI":"10.1007\/s00500-023-08290-x","volume":"27","author":"B Karthick","year":"2023","unstructured":"Karthick B, Uthayakumar R (2023) An optimal strategy for forecasting demand in a three-echelon supply chain system via metaheuristic optimization. Soft Comput 27(16):11431\u201311450","journal-title":"Soft Comput"},{"issue":"4","key":"10920_CR11","first-page":"649","volume":"10","author":"B Karthick","year":"2023","unstructured":"Karthick B (2023) An inventory analysis in a multi-echelon supply chain system under asymmetry fuzzy demand: a fmincon optimization. J Manage Anal 10(4):649\u2013675","journal-title":"J Manage Anal"},{"issue":"1","key":"10920_CR12","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s13198-019-00941-3","volume":"11","author":"PS Kumar","year":"2020","unstructured":"Kumar PS (2020) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11(1):189\u2013222","journal-title":"Int J Syst Assur Eng Manag"},{"key":"10920_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.envsoft.2021.105198","volume":"145","author":"AS Leon","year":"2021","unstructured":"Leon AS, Bian L, Tang Y (2021) Comparison of the genetic algorithm and pattern search methods for forecasting optimal flow releases in a multi-storage system for flood control. Environ Model Softw 145:105198","journal-title":"Environ Model Softw"},{"issue":"3","key":"10920_CR14","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1016\/j.cie.2007.10.002","volume":"54","author":"YJ Lin","year":"2008","unstructured":"Lin YJ (2008) A periodic review inventory model involving fuzzy expected demand short and fuzzy backorder rate. Comput Ind Eng 54(3):666\u2013676","journal-title":"Comput Ind Eng"},{"issue":"6","key":"10920_CR15","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.1016\/j.jom.2007.01.012","volume":"25","author":"JD Linton","year":"2007","unstructured":"Linton JD, Klassen R, Jayaraman V (2007) Sustainable supply chains: an introduction. J Oper Manag 25(6):1075\u20131082","journal-title":"J Oper Manag"},{"issue":"11","key":"10920_CR16","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1016\/S0305-0548(97)00103-2","volume":"25","author":"I Moon","year":"1998","unstructured":"Moon I, Choi S (1998) Technical notea note on lead time and distributional assumptions in continuous review inventory models. Comput Oper Res 25(11):1007\u20131012","journal-title":"Comput Oper Res"},{"key":"10920_CR17","first-page":"1","volume":"28","author":"R Pakhira","year":"2023","unstructured":"Pakhira R, Mondal B, Ghosh U, Sarkar S (2023) An EOQ model with fractional order rate of change of inventory level and time-varying holding cost. Soft Comput 28:1\u201319","journal-title":"Soft Comput"},{"issue":"2","key":"10920_CR18","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1111\/j.1745-493X.2009.03162.x","volume":"45","author":"M Pagell","year":"2009","unstructured":"Pagell M, Wu Z (2009) Building a more complete theory of sustainable supply chain management using case studies of 10 exemplars. J Supply Chain Manag 45(2):37\u201356","journal-title":"J Supply Chain Manag"},{"issue":"1","key":"10920_CR19","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1287\/opre.34.1.137","volume":"34","author":"EL Porteus","year":"1986","unstructured":"Porteus EL (1986) Optimal lot sizing, process quality improvement and setup cost reduction. Oper Res 34(1):137\u2013144","journal-title":"Oper Res"},{"key":"10920_CR20","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s12597-016-0267-4","volume":"54","author":"S Priyan","year":"2017","unstructured":"Priyan S, Manivannan P (2017) Optimal inventory modeling of supply chain system involving quality inspection errors and fuzzy defective rate. Opsearch 54:21\u201343","journal-title":"Opsearch"},{"key":"10920_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40815-023-01559-1","volume":"25","author":"J Qi","year":"2023","unstructured":"Qi J, Hu J, Peng Y (2023) Conceptual design evaluation using interval intuitionistic fuzzy-Z-number for multiple uncertain information from decision-maker. Int J Fuzzy Syst 25:1\u201325","journal-title":"Int J Fuzzy Syst"},{"issue":"15","key":"10920_CR22","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1016\/j.jclepro.2008.04.020","volume":"16","author":"S Seuring","year":"2008","unstructured":"Seuring S, M\u00fcller M (2008) From a literature review to a conceptual framework for sustainable supply chain management. J Clean Prod 16(15):1699\u20131710","journal-title":"J Clean Prod"},{"issue":"2","key":"10920_CR23","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1108\/13598541211212924","volume":"17","author":"J Sarkis","year":"2012","unstructured":"Sarkis J (2012) A boundaries and flows perspective of green supply chain management. Supply Chain Manag Int J 17(2):202\u2013216","journal-title":"Supply Chain Manag Int J"},{"issue":"3","key":"10920_CR24","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1051\/ro\/2016075","volume":"52","author":"HN Soni","year":"2018","unstructured":"Soni HN, Sarkar B, Mahapatra AS, Mazumder SK (2018) Lost sales reduction and quality improvement with variable lead time and fuzzy costs in an imperfect production system. RAIRO-Operations Research 52(3):819\u2013837","journal-title":"RAIRO-Operations Research"},{"issue":"6","key":"10920_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/s40819-021-01149-5","volume":"7","author":"P Supakar","year":"2021","unstructured":"Supakar P, Mahato SK, Pal P (2021) Intuitionistic fuzzy inventory model with deterioration incorporating advance payment with time-dependent demand. Int J Appl Comput Math 7(6):228","journal-title":"Int J Appl Comput Math"},{"issue":"1","key":"10920_CR26","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s12597-022-00610-3","volume":"60","author":"R Uthayakumar","year":"2023","unstructured":"Uthayakumar R, Karthick B (2023) Analysis of several reduction strategies on a two-echelon sustainable supply chain model with triangular fuzzy demand. Opsearch 60(1):393\u2013419","journal-title":"Opsearch"},{"issue":"2","key":"10920_CR27","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1016\/S0377-2217(03)00221-2","volume":"157","author":"HL Yang","year":"2004","unstructured":"Yang HL (2004) Two-warehouse inventory models for deteriorating items with shortages under inflation. Eur J Oper Res 157(2):344\u2013356","journal-title":"Eur J Oper Res"},{"issue":"3","key":"10920_CR28","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1016\/j.ejor.2012.02.015","volume":"220","author":"RQ Zhang","year":"2012","unstructured":"Zhang RQ (2012) An extension of partial backordering eoq with correlated demand caused by cross-selling considering multiple minor items. Eur J Oper Res 220(3):876\u2013881","journal-title":"Eur J Oper Res"},{"issue":"18\u201319","key":"10920_CR29","doi-asserted-by":"publisher","first-page":"4333","DOI":"10.1080\/00207540701440345","volume":"45","author":"Q Zhu","year":"2007","unstructured":"Zhu Q, Sarkis J (2007) The moderating effects of institutional pressures on emergent green supply chain practices and performance. Int J Prod Res 45(18\u201319):4333\u20134355","journal-title":"Int J Prod Res"},{"issue":"9","key":"10920_CR30","doi-asserted-by":"publisher","first-page":"3765","DOI":"10.1016\/j.jbusres.2015.12.068","volume":"69","author":"P Zou","year":"2016","unstructured":"Zou P, Li G (2016) How emerging market investors\u2019 value competitors\u2019 customer equity: brand crisis spillover in China. J Bus Res 69(9):3765\u20133771","journal-title":"J Bus Res"},{"issue":"3","key":"10920_CR31","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1287\/moor.9.3.402","volume":"9","author":"P Zipkin","year":"1984","unstructured":"Zipkin P (1984) On the imbalance of inventories in multi-echelon systems. Math Oper Res 9(3):402\u2013423","journal-title":"Math Oper Res"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-025-10920-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-025-10920-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-025-10920-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T15:55:01Z","timestamp":1769788501000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-025-10920-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,25]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["10920"],"URL":"https:\/\/doi.org\/10.1007\/s00500-025-10920-5","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,25]]},"assertion":[{"value":"16 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 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":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"No animal studies were conducted by the author in this article.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"It was obtained from the author of this study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}