{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T07:58:18Z","timestamp":1773388698598,"version":"3.50.1"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100020970","name":"Rashtriya Uchchatar Shiksha Abhiyan","doi-asserted-by":"publisher","award":["N0.046\/RUSA\/MKU\/2022-2023"],"award-info":[{"award-number":["N0.046\/RUSA\/MKU\/2022-2023"]}],"id":[{"id":"10.13039\/501100020970","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s12351-025-01008-x","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T12:02:04Z","timestamp":1769083324000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A continuous-review retrial inventory system with repair options for defective items"],"prefix":"10.1007","volume":"26","author":[{"given":"Saranyadas","family":"Sivadasan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4567-9486","authenticated-orcid":false,"given":"Shophia Lawrence","family":"Arputham","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"key":"1008_CR1","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/978-981-15-5951-8_9","volume-title":"Applied probability and stochastic processes","author":"G Arivarignan","year":"2020","unstructured":"Arivarignan G, Keerthana M, Sivakumar B (2020) A production inventory system with renewal and retrial demands. In: Joshua VC, Varadhan SRS, Vishnevsky VM (eds) Applied probability and stochastic processes. Springer Singapore, Singapore, pp 129\u2013142"},{"key":"1008_CR2","unstructured":"Arivarignan G, Yadavalli V, Sivakumar B (2008) A perishable inventory system with multiserver service facility and retrial customers. Manag Sci Pract 3\u201327"},{"issue":"1","key":"1008_CR3","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s10479-006-5294-8","volume":"141","author":"J Artalejo","year":"2006","unstructured":"Artalejo J, Krishnamoorthy A, Lopez H (2006) Numerical analysis of (s, S) inventory systems with repeated attempts. Ann Oper Res 141(1):67\u201383","journal-title":"Ann Oper Res"},{"key":"1008_CR4","doi-asserted-by":"publisher","first-page":"2631","DOI":"10.1007\/s12351-021-00624-7","volume":"22","author":"J Asadkhani","year":"2022","unstructured":"Asadkhani J, Mokhtari H, Tahmasebpoor S (2022) Optimal lot sizing under learning effect in inspection errors with different types of imperfect quality items. Oper Res Int J 22:2631\u20132665","journal-title":"Oper Res Int J"},{"issue":"1","key":"1008_CR5","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1137\/040603371","volume":"17","author":"C Audet","year":"2006","unstructured":"Audet C, Dennis JE (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17(1):188\u2013217","journal-title":"SIAM J Optim"},{"key":"1008_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68913-5","volume-title":"Derivative-free and blackbox optimization springer series in operations research and financial engineering","author":"C Audet","year":"2017","unstructured":"Audet C, Hare W (2017) Derivative-free and blackbox optimization springer series in operations research and financial engineering. Springer International Publishing, Singapore"},{"key":"1008_CR7","doi-asserted-by":"publisher","first-page":"1105","DOI":"10.1016\/j.cie.2009.04.020","volume":"57","author":"LE Cardenas-Barron","year":"2009","unstructured":"Cardenas-Barron LE (2009) Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Comput Ind Eng 57:1105\u20131113","journal-title":"Comput Ind Eng"},{"key":"1008_CR8","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1080\/07408179108963838","volume":"23","author":"CE Cheng","year":"1991","unstructured":"Cheng CE (1991) An economic order quantity model with demand-dependent unit production cost and imperfect production processes. IIE Trans 23:23\u201328","journal-title":"IIE Trans"},{"key":"1008_CR9","unstructured":"Dorigo M (1992) Optimization, learning and natural algorithms. PhD thesis"},{"key":"1008_CR10","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-319-91086-4_10","volume-title":"Handbook of metaheuristics","author":"M Dorigo","year":"2019","unstructured":"Dorigo M, St\u00fctzle T (2019) Ant colony optimization: overview and recent advances. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics, 3rd edn. Springer International Publishing, Singapore, pp 311\u2013352","edition":"3"},{"key":"1008_CR11","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1016\/j.ijpe.2006.06.015","volume":"106","author":"A Eroglu","year":"2007","unstructured":"Eroglu A, Ozdemir G (2007) An economic order quantity model with defective items and shortages. Int J Prod Econ 106:544\u2013549","journal-title":"Int J Prod Econ"},{"key":"1008_CR12","first-page":"135","volume":"10","author":"FW Harris","year":"1913","unstructured":"Harris FW (1913) How many parts to make at once factory. Magazine Manag 10:135\u2013136","journal-title":"Magazine Manag"},{"issue":"2","key":"1008_CR13","first-page":"90","volume":"2","author":"T Karthick","year":"2015","unstructured":"Karthick T, Sivakumar B, Arivarignan G (2015) An inventory system with two types of customers and retrial demands. Int J Syst Sci Oper Logistics 2(2):90\u2013112","journal-title":"Int J Syst Sci Oper Logistics"},{"key":"1008_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijpe.2011.03.009","volume":"132","author":"M Khan","year":"2011","unstructured":"Khan M, Jaber MY, Guiffrida AL, Zolfaghari S (2011) A review of the extensions of a modified $${EOQ}$$ model for imperfect quality items. Int J Prod Econ 132:1\u201312","journal-title":"Int J Prod Econ"},{"key":"1008_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2007\/37848","volume":"2007","author":"A Krishnamoorthy","year":"2007","unstructured":"Krishnamoorthy A, Jose K (2007) Comparison of inventory systems with service, positive lead-time, loss and retrial of demands. J Appl Math Stoch Anal 2007:1\u201323","journal-title":"J Appl Math Stoch Anal"},{"issue":"3","key":"1008_CR16","doi-asserted-by":"publisher","first-page":"650","DOI":"10.2307\/3214773","volume":"30","author":"G Latouche","year":"1993","unstructured":"Latouche G, Ramaswami V (1993) A logarithmic reduction algorithm for quasi-birth-death processes. J Appl Probab 30(3):650\u2013674","journal-title":"J Appl Probab"},{"key":"1008_CR17","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.1287\/mnsc.33.9.1125","volume":"33","author":"HL Lee","year":"1987","unstructured":"Lee HL, Rosenblatt MJ (1987) Simultaneous determination of production cycles and inspection schedules in a production system. Manage Sci 33:1125\u20131137","journal-title":"Manage Sci"},{"key":"1008_CR18","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1002\/nav.3800300217","volume":"30","author":"TJ Lowe","year":"1983","unstructured":"Lowe TJ, Schwarz LB (1983) Parameter estimation for the $${EOQ}$$ lot-size model: minimax and expected-value choices. Naval Res Logist Quarterly 30:367\u2013376","journal-title":"Naval Res Logist Quarterly"},{"issue":"5","key":"1008_CR19","doi-asserted-by":"publisher","first-page":"241","DOI":"10.3390\/axioms11050241","volume":"11","author":"A Melikov","year":"2022","unstructured":"Melikov A, Aliyeva S, Nair S, Kumar B (2022) Retrial queuing-inventory systems with delayed feedback and instantaneous damaging of items. Axioms 11(5):241","journal-title":"Axioms"},{"key":"1008_CR20","unstructured":"Montoison A, Pascal P, Salomon L (2020) NOMAD.jl: a Julia interface for the constrained blackbox solver NOMAD. https:\/\/github.com\/bbopt\/NOMAD.jl"},{"issue":"6","key":"1008_CR21","first-page":"625","volume":"42","author":"S Namnabat","year":"2025","unstructured":"Namnabat S, Mokhtari H, Fallahi A (2025) Extended inventory planning models for repairable imperfect quality items under withdrawal policies and inspection errors. J Ind Prod Eng 42(6):625\u2013650","journal-title":"J Ind Prod Eng"},{"key":"1008_CR22","volume-title":"Matrix-geometric solutions in stochastic models: an algorithmic approach","author":"MF Neuts","year":"1994","unstructured":"Neuts MF (1994) Matrix-geometric solutions in stochastic models: an algorithmic approach. Dover, New York"},{"issue":"5","key":"1008_CR23","doi-asserted-by":"publisher","first-page":"102714","DOI":"10.1016\/j.asej.2024.102714","volume":"15","author":"AH Nobil","year":"2024","unstructured":"Nobil AH, Nobil E, Sedigh AH, C\u00e1rdenas-Barr\u00f3n LE, Garza-N\u00fa\u00f1ez D, Trevi\u00f1o-Garza G, C\u00e9spedes-Mota A, de Jes\u00fas Loera-Hern\u00e1ndez I, Smith NR (2024) Economic production quantity models for an imperfect manufacturing system with strict inspection. Ain Shams Eng J 15(5):102714","journal-title":"Ain Shams Eng J"},{"key":"1008_CR24","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1007\/s40305-021-00339-8","volume":"9","author":"H \u00d6zt\u00fcrk","year":"2021","unstructured":"\u00d6zt\u00fcrk H (2021) Modelling economic order quantities, considering buy and repair options for defective items, and allowing for shortages and inspection errors. J Oper Research Soci China 9:757\u2013795","journal-title":"J Oper Research Soci China"},{"key":"1008_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10479-025-06669-7","volume":"351","author":"H \u00d6zt\u00fcrk","year":"2025","unstructured":"\u00d6zt\u00fcrk H, Konstantaras I (2025) $${EOQ}$$ model with defective products, batch shipment andpartial backorders. Ann Oper Res 351:1\u201348","journal-title":"Ann Oper Res"},{"issue":"1","key":"1008_CR26","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s10479-013-1417-1","volume":"233","author":"I Padmavathi","year":"2015","unstructured":"Padmavathi I, Sivakumar B, Arivarignan G (2015) A retrial inventory system with single and modified multiple vacation for server. Ann Oper Res 233(1):335\u2013364","journal-title":"Ann Oper Res"},{"issue":"8","key":"1008_CR27","doi-asserted-by":"publisher","first-page":"998","DOI":"10.1287\/mnsc.31.8.998","volume":"31","author":"EL Porteus","year":"1985","unstructured":"Porteus EL (1985) Investing in reduced setups in the $${EOQ}$$ model. Manage Sci 31(8):998\u20131010","journal-title":"Manage Sci"},{"key":"1008_CR28","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 34:137\u2013144","journal-title":"Oper Res"},{"key":"1008_CR29","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1002\/nav.3800330104","volume":"33","author":"EL Porteus","year":"1986","unstructured":"Porteus EL (1986) Investing in new parameter values in the discounted $${EOQ}$$ model. Naval Res Log Quarterly 33:39\u201348","journal-title":"Naval Res Log Quarterly"},{"key":"1008_CR30","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/S0925-5273(99)00044-4","volume":"64","author":"MK Salameh","year":"2000","unstructured":"Salameh MK, Jaber MY (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64:59\u201364","journal-title":"Int J Prod Econ"},{"key":"1008_CR31","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s12597-019-00372-5","volume":"56","author":"N Saranya","year":"2019","unstructured":"Saranya N, Shophia Lawrence A (2019) A stochastic inventory system with replacement of perishable items. Opsearch 56:563\u2013582","journal-title":"Opsearch"},{"issue":"17","key":"1008_CR32","doi-asserted-by":"publisher","first-page":"5966","DOI":"10.1080\/03610926.2021.2023184","volume":"52","author":"N Saranya","year":"2022","unstructured":"Saranya N, Shophia Lawrence A, Sivakumar B (2022) An inventory system with replacement and refurbishment of failed items. Commun Stat-Theory Methods 52(17):5966\u20135988","journal-title":"Commun Stat-Theory Methods"},{"issue":"1","key":"1008_CR33","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.ejor.2015.06.021","volume":"248","author":"B Sarkar","year":"2016","unstructured":"Sarkar B, Saren S (2016) Product inspection policy for an imperfect production system with inspection errors and warranty cost. Eur J Oper Res 248(1):263\u2013271","journal-title":"Eur J Oper Res"},{"issue":"7","key":"1008_CR34","doi-asserted-by":"publisher","first-page":"1116","DOI":"10.1016\/j.asr.2012.11.006","volume":"51","author":"M Schl\u00fceter","year":"2013","unstructured":"Schl\u00fceter M, Erb SO, Gerdts M, Kemble S, R\u00fcckmann JJ (2013) MIDACO on MINLP space applications. Adv Space Res 51(7):1116\u20131131","journal-title":"Adv Space Res"},{"key":"1008_CR35","first-page":"22","volume":"29","author":"RL Schwaller","year":"1988","unstructured":"Schwaller RL (1988) $${EOQ}$$ under inspection costs. Prod Invent Manag 29:22\u201324","journal-title":"Prod Invent Manag"},{"issue":"3","key":"1008_CR36","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1080\/05695557208974855","volume":"4","author":"LB Schwarz","year":"1972","unstructured":"Schwarz LB (1972) Economic order quantities for products with finite demand horizons. AIIE Trans 4(3):234\u2013237","journal-title":"AIIE Trans"},{"key":"1008_CR37","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1080\/00207548008919699","volume":"18","author":"W Shih","year":"1980","unstructured":"Shih W (1980) Optimal inventory policies when stockouts result from defective products. Int J Prod Res 18:677\u2013686","journal-title":"Int J Prod Res"},{"issue":"1","key":"1008_CR38","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.ejor.2007.02.036","volume":"187","author":"B Sivakumar","year":"2008","unstructured":"Sivakumar B (2008) Two commodity inventory system with retrial demand. Eur J Oper Res 187(1):70\u201383","journal-title":"Eur J Oper Res"},{"issue":"1","key":"1008_CR39","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.cam.2008.03.041","volume":"224","author":"B Sivakumar","year":"2009","unstructured":"Sivakumar B (2009) A perishable inventory system with retrial demands and a finite population. J Comput Appl Math 224(1):29\u201338","journal-title":"J Comput Appl Math"},{"issue":"3","key":"1008_CR40","first-page":"165","volume":"2","author":"B Sivakumar","year":"2011","unstructured":"Sivakumar B, Anbazhagan N (2011) Stochastic inventory system with replaceable items. Comput Optim Econ Finance Res Compend 2(3):165\u2013179","journal-title":"Comput Optim Econ Finance Res Compend"},{"key":"1008_CR41","first-page":"1","volume":"1","author":"P Ushakumari","year":"2006","unstructured":"Ushakumari P (2006) On (s, S) inventory system with random lead time and repeated demands. J Appl Math Stoch Anal 1:1\u201322","journal-title":"J Appl Math Stoch Anal"},{"issue":"4","key":"1008_CR42","first-page":"597","volume":"57","author":"ID Wangsa","year":"2019","unstructured":"Wangsa ID, Wee HM (2019) A vendor-buyer inventory model for defective items with errors in inspection, stochastic lead time and freight cost. Inform Syst Oper Res 57(4):597\u2013622","journal-title":"Inform Syst Oper Res"},{"key":"1008_CR43","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.ijpe.2009.05.008","volume":"121","author":"S Yoo","year":"2009","unstructured":"Yoo S, Kim D, Park M (2009) Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return. Int J Prod Econ 121:255\u2013265","journal-title":"Int J Prod Econ"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-025-01008-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12351-025-01008-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-025-01008-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T04:54:28Z","timestamp":1773377668000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12351-025-01008-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1008"],"URL":"https:\/\/doi.org\/10.1007\/s12351-025-01008-x","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"21 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"23"}}