{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T04:08:34Z","timestamp":1768450114179,"version":"3.49.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s12351-021-00634-5","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T19:02:52Z","timestamp":1616612572000},"page":"2803-2829","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A production-repairing inventory model considering demand and the proportion of defective items as rough intervals"],"prefix":"10.1007","volume":"22","author":[{"given":"Subhendu","family":"Ruidas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4746-5369","authenticated-orcid":false,"given":"Mijanur Rahaman","family":"Seikh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prasun Kumar","family":"Nayak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"issue":"2","key":"634_CR1","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s12351-017-0302-0","volume":"19","author":"S Bardhan","year":"2019","unstructured":"Bardhan S, Pal H, Giri BC (2019) Optimal replenishment policy and preservation technology investment for a non-instantaneous deteriorating item with stock-dependent demand. Oper Res Int J 19(2):347\u2013368","journal-title":"Oper Res Int J"},{"key":"634_CR2","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1016\/j.asoc.2017.02.012","volume":"55","author":"AK Bhunia","year":"2017","unstructured":"Bhunia AK, Shaikh AA, C\u00e1rdenas-Barr\u00f3n LE (2017) A partially integrated production-inventory model with intervalvalued inventory costs, variable demand and flexible reliability. Appl Soft Comp 55:491\u2013502","journal-title":"Appl Soft Comp"},{"issue":"12","key":"634_CR3","doi-asserted-by":"publisher","first-page":"2079","DOI":"10.1016\/S0305-0548(03)00166-7","volume":"31","author":"HC Chang","year":"2004","unstructured":"Chang HC (2004) An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput Oper Res 31(12):2079\u20132092","journal-title":"Comput Oper Res"},{"issue":"2","key":"634_CR4","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/s10479-017-2511-6","volume":"271","author":"N Cheikhrouhou","year":"2018","unstructured":"Cheikhrouhou N, Sarkar B, Ganguly B, Malik AI, Batista R, Lee YH (2018) Optimization of sample size and order size in an inventory model with quality inspection and return of defective items. Annals Oper Res 271(2):445\u2013467","journal-title":"Annals Oper Res"},{"issue":"1","key":"634_CR5","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s12351-016-0227-z","volume":"17","author":"TK Datta","year":"2017","unstructured":"Datta TK (2017) Inventory system with defective products and investment opportunity for reducing defective proportion. Oper Res Int J 17(1):297\u2013312","journal-title":"Oper Res Int J"},{"issue":"1","key":"634_CR6","first-page":"1043","volume":"19","author":"TK Datta","year":"1988","unstructured":"Datta TK, Pal AK (1988) Order-level inventory system with power demand pattern for items with variable rate of deterioration. Indian J Pure Appl Math 19(1):1043\u20131053","journal-title":"Indian J Pure Appl Math"},{"key":"634_CR7","doi-asserted-by":"crossref","unstructured":"Garai T, Chakraborty D, Roy TK (2019) A fuzzy rough multi-objective multi-item inventory model with both stock-dependent demand and holding cost rate. Granul Comput 4(1):71\u201388","DOI":"10.1007\/s41066-018-0085-6"},{"issue":"1","key":"634_CR8","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1142\/S0219686718500051","volume":"17","author":"PK Ghosh","year":"2018","unstructured":"Ghosh PK, Hazari S, Dey JK, Kar S (2018) Three-layer supply chain production\/by-production inventory model under fuzzy rough environment. J Adv Manuf Syst 17(1):61\u201388","journal-title":"J Adv Manuf Syst"},{"issue":"1","key":"634_CR9","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s12351-015-0184-y","volume":"16","author":"BC Giri","year":"2016","unstructured":"Giri BC, Sharma S (2016) Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing. Oper Res Int J 16(1):25\u201350","journal-title":"Oper Res Int J"},{"key":"634_CR10","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.3233\/IFS-130804","volume":"26","author":"A Hamzehea","year":"2004","unstructured":"Hamzehea A, Yaghoobia MA, Mashineh M (2004) Linear programming with rough interval coefficients. J Intel Fuzzy syst 26:1179\u20131189","journal-title":"J Intel Fuzzy syst"},{"key":"634_CR11","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.ijpe.2008.05.007","volume":"115","author":"MY Jaber","year":"2008","unstructured":"Jaber MY, Goyal SK, Imran M (2008) Economic production quantity model for items with imperfect quality subject to learning effects. Int J Prod Econ 115:143\u2013150","journal-title":"Int J Prod Econ"},{"issue":"4","key":"634_CR12","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s12597-013-0122-9","volume":"50","author":"DK Jana","year":"2013","unstructured":"Jana DK, Maity K, Roy TK (2013) Multi-item production inventory model with fuzzy rough coefficients via geometric programming approach. OPSEARCH 50(4):475\u2013490","journal-title":"OPSEARCH"},{"key":"634_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1781-2","volume-title":"Theory and Practice of Uncertain Programming","author":"B Liu","year":"2002","unstructured":"Liu B (2002) Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg"},{"key":"634_CR14","first-page":"183","volume":"2","author":"NK Mahapatra","year":"2012","unstructured":"Mahapatra NK, Bera UK, Maiti M (2012) A Production inventory model with shortages, fuzzy preparation time and variable production and demand. Am J Oper Res 2:183\u2013192","journal-title":"Am J Oper Res"},{"issue":"4","key":"634_CR15","first-page":"466","volume":"14","author":"GC Mahata","year":"2013","unstructured":"Mahata GC (2013) Application of fuzzy sets theory in an EOQ model for items with imperfect quality and shortage backordering. Int J Serv Oper Manag 14(4):466\u2013490","journal-title":"Int J Serv Oper Manag"},{"key":"634_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2020.106814","author":"AI Malik","year":"2020","unstructured":"Malik AI, Kim BS (2020) A multi-constrained supply chain model with optimal production rate in relation to quality of products under stochastic fuzzy demand. Comput Ind Eng. https:\/\/doi.org\/10.1016\/j.cie.2020.106814","journal-title":"Comput Ind Eng"},{"issue":"2","key":"634_CR17","doi-asserted-by":"publisher","first-page":"275","DOI":"10.3390\/math8020275","volume":"8","author":"AI Malik","year":"2020","unstructured":"Malik AI, Kim BS (2020) A constrained production system involving production flexibility and carbon emissions. Mathematics 8(2):275. https:\/\/doi.org\/10.3390\/math8020275","journal-title":"Mathematics"},{"key":"634_CR18","doi-asserted-by":"publisher","first-page":"36176","DOI":"10.1109\/ACCESS.2018.2849694","volume":"6","author":"AI Malik","year":"2018","unstructured":"Malik AI, Sarkar B (2018) Optimizing a multi-product continuous-review inventory model with uncertain demand, quality improvement, setup cost reduction, and variation control in lead time. IEEE Access 6:36176\u201336187","journal-title":"IEEE Access"},{"issue":"5","key":"634_CR19","doi-asserted-by":"publisher","first-page":"480","DOI":"10.3390\/math7050480","volume":"7","author":"AI Malik","year":"2019","unstructured":"Malik AI, Sarkar B (2019) Coordinating supply-chain management under stochastic fuzzy environment and lead-time reduction. Mathematics 7(5):480. https:\/\/doi.org\/10.3390\/math7050480","journal-title":"Mathematics"},{"issue":"5","key":"634_CR20","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1057\/jors.1989.75","volume":"40","author":"BN Mandal","year":"1989","unstructured":"Mandal BN, Phaujdar S (1989) An inventory model for deteriorating items and stock-dependent consumption rate. J Oper Res Soc 40(5):483\u2013488","journal-title":"J Oper Res Soc"},{"key":"634_CR21","doi-asserted-by":"publisher","first-page":"3200","DOI":"10.1016\/j.apm.2012.07.024","volume":"37","author":"M Mondal","year":"2013","unstructured":"Mondal M, Maity AK, Maiti MK, Maiti M (2013) A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money. Appl Math Model 37:3200\u20133215","journal-title":"Appl Math Model"},{"issue":"1","key":"634_CR22","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s12351-017-0318-5","volume":"20","author":"M Nagare","year":"2020","unstructured":"Nagare M, Dutta P, Suryawanshi P (2020) Optimal procurement and discount pricing for single period non-instantaneous deteriorating products with promotional efforts. Oper Res Int J 20(1):89\u2013117","journal-title":"Oper Res Int J"},{"issue":"2","key":"634_CR23","first-page":"197","volume":"1","author":"M Palanivel","year":"2014","unstructured":"Palanivel M, Uthayakumar R (2014) A production-inventory model with variable production cost and probabilistic deterioration. Asia Pacific J Math 1(2):197\u2013212","journal-title":"Asia Pacific J Math"},{"issue":"1","key":"634_CR24","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s12597-018-00352-1","volume":"56","author":"R Patro","year":"2019","unstructured":"Patro R, Nayak MM, Acharya M (2019) An EOQ model for fuzzy defective rate with allowable proportionate discount. OPSEARCH 56(1):191\u2013215","journal-title":"OPSEARCH"},{"issue":"5","key":"634_CR25","first-page":"341","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak Z (1982) Rough Stes. Int J Parallel Progr 11(5):341\u2013356","journal-title":"Int J Parallel Progr"},{"issue":"1","key":"634_CR26","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":"634_CR27","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1016\/j.artint.2006.02.004","volume":"170","author":"M Rebolledo","year":"2006","unstructured":"Rebolledo M (2006) Rough intervals-enhancing intervals for qualitative modeling of technical systems. Artif Intel 170:667\u2013685","journal-title":"Artif Intel"},{"issue":"1","key":"634_CR28","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1080\/07408178608975329","volume":"18","author":"MJ Rosenblatt","year":"1986","unstructured":"Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production process. IIE Trans 18(1):48\u201355","journal-title":"IIE Trans"},{"issue":"2","key":"634_CR29","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s13198-019-00867-w","volume":"11","author":"S Ruidas","year":"2020","unstructured":"Ruidas S, Seikh MR, Nayak PK (2020) An EPQ model with stock and selling price dependent demand and variable production rate in interval environment. Int J Syst Assur Eng Manag 11(2):385\u2013399","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"6","key":"634_CR30","first-page":"1059","volume":"21","author":"S Ruidas","year":"2018","unstructured":"Ruidas S, Seikh MR, Nayak PK, Pal M (2018) Interval valued EOQ model with two types of defective items. J Stat Manag Syst 21(6):1059\u20131082","journal-title":"J Stat Manag Syst"},{"key":"634_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/s40819-018-0591-x","author":"S Ruidas","year":"2019","unstructured":"Ruidas S, Seikh MR, Nayak PK, Sarkar B (2019) A single period production inventory model in interval environment with price revision. Int J Appl Comput Mat. https:\/\/doi.org\/10.1007\/s40819-018-0591-x","journal-title":"Int J Appl Comput Mat"},{"issue":"1\u20133","key":"634_CR32","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/S0925-5273(99)00044-4","volume":"64","author":"M Salameh","year":"2000","unstructured":"Salameh M, Jaber M (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64(1\u20133):59\u201364","journal-title":"Int J Prod Econ"},{"key":"634_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2020.106861","author":"B Sarkar","year":"2020","unstructured":"Sarkar B, Dey BK, Pareek S, Sarkar M (2020) A single-stage cleaner production system with random defective rate and remanufacturing. Comput Ind Eng. https:\/\/doi.org\/10.1016\/j.cie.2020.106861","journal-title":"Comput Ind Eng"},{"key":"634_CR34","doi-asserted-by":"crossref","first-page":"6159","DOI":"10.1016\/j.amc.2010.12.098","volume":"217","author":"B Sarkar","year":"2011","unstructured":"Sarkar B, Moon I (2011) An EPQ model with inflation in an imperfect production system. Appl Math Comput 217:6159\u20136167","journal-title":"Appl Math Comput"},{"issue":"2","key":"634_CR35","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s12351-016-0267-4","volume":"18","author":"NH Shah","year":"2018","unstructured":"Shah NH, Patel DG, Shah DB (2018) EPQ model for returned\/reworked inventories during imperfect production process under price-sensitive stock-dependent demand. Oper Res Int J 18(2):343\u2013359","journal-title":"Oper Res Int J"},{"issue":"6","key":"634_CR36","doi-asserted-by":"publisher","first-page":"1931","DOI":"10.1007\/s00521-017-3168-4","volume":"31","author":"AA Shaikh","year":"2019","unstructured":"Shaikh AA, LE C-B, Tiwari S (2019) A two-warehouse inventory model for non-instantaneous deteriorating items with interval-valued inventory costs and stock-dependent demand under inflationary conditions. Neural Comput Appl 31(6):1931\u20131948","journal-title":"Neural Comput Appl"},{"issue":"5\u20136","key":"634_CR37","doi-asserted-by":"publisher","first-page":"1466","DOI":"10.1016\/j.mcm.2012.12.008","volume":"57","author":"AA Taleizadeh","year":"2013","unstructured":"Taleizadeh AA, Wee HM, Jolai F (2013) Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math Comput Model 57(5\u20136):1466\u20131479","journal-title":"Math Comput Model"},{"key":"634_CR38","doi-asserted-by":"publisher","first-page":"2107","DOI":"10.1016\/j.camwa.2008.03.040","volume":"56","author":"J Xu","year":"2008","unstructured":"Xu J, Zhao L (2008) A class of fuzzy rough expected value multi-objective decision making model and its application to inventory problems. Comput Math Appl 56:2107\u20132119","journal-title":"Comput Math Appl"},{"key":"634_CR39","unstructured":"Xu J, Tao Z (2012) Rough multiple objective decision making. CRC Press, pp22-28"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-021-00634-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12351-021-00634-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-021-00634-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T00:29:09Z","timestamp":1698798549000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12351-021-00634-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,24]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["634"],"URL":"https:\/\/doi.org\/10.1007\/s12351-021-00634-5","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,24]]},"assertion":[{"value":"6 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}