{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T10:22:41Z","timestamp":1783938161823,"version":"3.55.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T00:00:00Z","timestamp":1624320000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T00:00:00Z","timestamp":1624320000000},"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":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s40815-021-01111-z","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T16:04:10Z","timestamp":1624896250000},"page":"44-56","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Optimization in Fuzzy Economic Order Quantity Model Involving Pentagonal Fuzzy Parameter"],"prefix":"10.1007","volume":"24","author":[{"given":"S.","family":"Rajeswari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Sugapriya","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Nagarajan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Kavikumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,6,22]]},"reference":[{"issue":"1","key":"1111_CR1","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/S0925-5273(99)00044-4","volume":"64","author":"MK Salameh","year":"2000","unstructured":"Salameh, M.K., Jaber, M.Y.: Economic production quantity model for items with imperfect quality. Int. J. Prod. Econ. 64(1), 59\u201364 (2000)","journal-title":"Int. J. Prod. Econ."},{"issue":"1","key":"1111_CR2","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/j.ijpe.2004.11.004","volume":"100","author":"S Papachristos","year":"2000","unstructured":"Papachristos, S., Konstantaras, I.: Economic ordering quantity models for items with imperfect quality. Int. J. Prod. Econ. 100(1), 148\u2013154 (2000)","journal-title":"Int. J. Prod. Econ."},{"key":"1111_CR3","doi-asserted-by":"publisher","first-page":"5334","DOI":"10.1016\/j.apm.2011.12.005","volume":"36","author":"I Konstantaras","year":"2012","unstructured":"Konstantaras, I., Skouri, K., Jaber, M.Y.: Inventory models for imperfect quantity items with shortages and learning in inspection. Appl. Math. Model. 36, 5334\u20135343 (2012)","journal-title":"Appl. Math. Model."},{"key":"1111_CR4","first-page":"16","volume":"1","author":"C Sugapriya","year":"2008","unstructured":"Sugapriya, C., Jeyaraman, K.: An EPQ model for non-instantaneous deteriorating item in which holding cost varies with time. Electronic Journal of Applied Statistical Analysis 1, 16\u201323 (2008)","journal-title":"Electronic Journal of Applied Statistical Analysis"},{"key":"1111_CR5","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.ijpe.2010.01.023","volume":"133","author":"M Khan","year":"2011","unstructured":"Khan, M., Jaber, M.Y., Bonney, M.: An economic order quantity (EOQ) for items with imperfect quality and inspection errors. Int. J. Prod. Econ. 133, 113\u2013118 (2011)","journal-title":"Int. J. Prod. Econ."},{"issue":"1","key":"1111_CR6","first-page":"73","volume":"2","author":"M Al-Salamah","year":"2012","unstructured":"Al-Salamah, M., Alsawafy, O.: Economic order quantity for items with two types of imperfect quality. An international journal of optimization and control. Theories Appl 2(1), 73\u201382 (2012)","journal-title":"Theories Appl"},{"key":"1111_CR7","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.ijpe.2012.12.025","volume":"143","author":"JT Hsu","year":"2013","unstructured":"Hsu, J.T., Hsu, L.F.: An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns. Int. J. Prod. Econ. 143, 162\u2013170 (2013)","journal-title":"Int. J. Prod. Econ."},{"key":"1111_CR8","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.ijpe.2013.10.014","volume":"155","author":"MY Jaber","year":"2014","unstructured":"Jaber, M.Y., Zanoni, S., Zanavella, L.E.: Economic order quantity models for imperfect items with buy and repair options. Int. J. Prod. Econ. 155, 126\u2013131 (2014)","journal-title":"Int. J. Prod. Econ."},{"issue":"2","key":"1111_CR9","doi-asserted-by":"publisher","first-page":"1012","DOI":"10.1016\/j.apm.2015.06.020","volume":"40","author":"Y Zhou","year":"2015","unstructured":"Zhou, Y., Chen, C., Li, C., Zhong, Y.: A synergic economic order quantity model with trade credit, shortages, imperfect quality and inspection errors. Appl Math Model 40(2), 1012\u20131028 (2015)","journal-title":"Appl Math Model"},{"issue":"1","key":"1111_CR10","first-page":"92","volume":"23","author":"P Pimsap","year":"2018","unstructured":"Pimsap, P., Srisodaphol, W.: Economic order quantity model for imperfect items under repair option and inspection errors. Brupa J Sci 23(1), 92\u2013104 (2018)","journal-title":"Brupa J Sci"},{"key":"1111_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.orp.2018.11.004","author":"M Sebatjane","year":"2019","unstructured":"Sebatjane, M., Adetunji, O.: Economic order quantity model for growing items with imperfect quality. Operat Res Perspect (2019). https:\/\/doi.org\/10.1016\/j.orp.2018.11.004","journal-title":"Operat Res Perspect"},{"key":"1111_CR12","doi-asserted-by":"publisher","first-page":"1863","DOI":"10.1007\/s13369-020-05131-z","volume":"46","author":"HK Alfares","year":"2021","unstructured":"Alfares, H.K., Afzal, A.R.: An economic order quantity model for growing items with imperfect quality and shortages. Arab. J. Sci. Eng. 46, 1863\u20131875 (2021). https:\/\/doi.org\/10.1007\/s13369-020-05131-z","journal-title":"Arab. J. Sci. Eng."},{"key":"1111_CR13","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"L Zadeh","year":"1965","unstructured":"Zadeh, L.: Fuzzy sets. Inform Control 8, 338\u2013353 (1965)","journal-title":"Inform Control"},{"issue":"4","key":"1111_CR14","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1109\/TFUZZ.2002.800692","volume":"10","author":"B Liu","year":"2002","unstructured":"Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Transact Fuzzy Syst 10(4), 445\u2013450 (2002)","journal-title":"IEEE Transact Fuzzy Syst"},{"issue":"4","key":"1111_CR15","first-page":"486","volume":"9","author":"Z Wang","year":"2010","unstructured":"Wang, Z., Tian, F.: A note of the expected value and variance of fuzzy variables. Int J Nonlinear Sci 9(4), 486\u2013492 (2010)","journal-title":"Int J Nonlinear Sci"},{"issue":"3","key":"1111_CR16","first-page":"131","volume":"1","author":"A Panda","year":"2015","unstructured":"Panda, A., Pal, M.: A study on pentagonal fuzzy number and its corresponding matrices. Pacific Sci Rev B Humanities Soc Sci 1(3), 131\u2013139 (2015)","journal-title":"Pacific Sci Rev B Humanities Soc Sci"},{"key":"1111_CR17","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10700-007-9002-1","volume":"6","author":"X Wang","year":"2007","unstructured":"Wang, X., Tang, W., Zhao, R.: Random fuzzy EOQ model with imperfect quality items. Fuzzy Optim. Decis. Making 6, 139\u2013153 (2007)","journal-title":"Fuzzy Optim. Decis. Making"},{"key":"1111_CR18","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1016\/j.sepro.2011.11.077","volume":"4","author":"J Liu","year":"2012","unstructured":"Liu, J., Zheng, H.: Fuzzy economic order quantity model with imperfect items, shortage and inspection errors. Syst Eng Procedia 4, 282\u2013289 (2012)","journal-title":"Syst Eng Procedia"},{"key":"1111_CR19","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.cie.2012.09.003","volume":"64","author":"GC Mahata","year":"2013","unstructured":"Mahata, G.C., Goswami, A.: Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables. Comput. Ind. Eng. 64, 190\u2013199 (2013)","journal-title":"Comput. Ind. Eng."},{"issue":"1","key":"1111_CR20","first-page":"33","volume":"16","author":"S Bhaya","year":"2014","unstructured":"Bhaya, S., Pal, M., Nayak, P.K.: Intuitionistic fuzzy optimization technique in EOQ model with two types of imperfect quality items. Adv Model Optim 16(1), 33\u201350 (2014)","journal-title":"Adv Model Optim"},{"issue":"3","key":"1111_CR21","first-page":"260","volume":"1","author":"S Priyan","year":"2014","unstructured":"Priyan, S., Palanivel, M., Uthayakumar, R.: Mathematical modeling for EOQ inventory system with advance payment and fuzzy Parameters. Int J Suppl Operat Manag 1(3), 260\u2013278 (2014)","journal-title":"Int J Suppl Operat Manag"},{"issue":"6","key":"1111_CR22","first-page":"61","volume":"7","author":"MF Eshkiki","year":"2018","unstructured":"Eshkiki, M.F., Saberifard, N., Ajalli, M.: A fuzzy economic order quantity (EOQ) model with consideration of quality items, inspection errors and sales return. Int J Supp Chain Manag 7(6), 61\u201371 (2018)","journal-title":"Int J Supp Chain Manag"},{"key":"1111_CR23","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, M.M., Acharya, M.: An EOQ model for fuzzy defective rate with allowable proportionate discount. OPSEARCH 56, 191\u2013215 (2019)","journal-title":"OPSEARCH"},{"key":"1111_CR24","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1007\/s40092-019-0310-1","volume":"15","author":"SK De","year":"2019","unstructured":"De, S.K., Mahata, G.C.: A cloudy fuzzy economic order quantity model for imperfect-quality items with allowable proportionate discounts. J Indust Eng Int 15, 571\u2013583 (2019). https:\/\/doi.org\/10.1007\/s40092-019-0310-1","journal-title":"J Indust Eng Int"},{"issue":"1","key":"1111_CR25","doi-asserted-by":"publisher","first-page":"627","DOI":"10.36872\/LEPI\/V51I1\/301058","volume":"51","author":"S Rajeswari","year":"2020","unstructured":"Rajeswari, S., Sugapriya, C.: Fuzzy economic order quantity model with imperfect quality items under repair option. J Res Lepidoptera 51(1), 627\u2013643 (2020). https:\/\/doi.org\/10.36872\/LEPI\/V51I1\/301058","journal-title":"J Res Lepidoptera"},{"key":"1111_CR26","doi-asserted-by":"publisher","DOI":"10.1080\/23302674.2020.1826594","author":"P Supakar","year":"2020","unstructured":"Supakar, P., Mahato, S.K.: An EPQ model with time proportion deterioration and ramp type demand under different payment schemes with fuzzy uncertainties. Int J Syst Sci Operat Logistics (2020). https:\/\/doi.org\/10.1080\/23302674.2020.1826594","journal-title":"Int J Syst Sci Operat Logistics"},{"key":"1111_CR27","doi-asserted-by":"publisher","DOI":"10.24018\/ejers.2020.5.10.2184","author":"H Tahami","year":"2020","unstructured":"Tahami, H., Fakhravar, H.: A fuzzy inventory model considering imperfect quality items with receiving reparative batch and order. Eur J Eng Res Sci (2020). https:\/\/doi.org\/10.24018\/ejers.2020.5.10.2184","journal-title":"Eur J Eng Res Sci"},{"key":"1111_CR28","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.ijpe.2014.01.023","volume":"155","author":"AA Taleizadeh","year":"2014","unstructured":"Taleizadeh, A.A.: An EOQ model with partial backordering and advance payments for an evaporating item. Int. J. Prod. Econ. 155, 185\u2013193 (2014)","journal-title":"Int. J. Prod. Econ."},{"key":"1111_CR29","doi-asserted-by":"publisher","first-page":"5357","DOI":"10.1016\/j.apm.2014.02.014","volume":"38","author":"AA Taleizadeh","year":"2014","unstructured":"Taleizadeh, A.A.: An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Appl. Math. Model. 38, 5357\u20135366 (2014)","journal-title":"Appl. Math. Model."},{"issue":"19\u201320","key":"1111_CR30","doi-asserted-by":"publisher","first-page":"8605","DOI":"10.1016\/j.apm.2016.05.022","volume":"40","author":"JT Teng","year":"2016","unstructured":"Teng, J.T., C\u00e1rdenas-Barr\u00f3n, L.E., Chang, H.J., Wu, J., Hu, Y.: Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Appl. Math. Model. 40(19\u201320), 8605\u20138616 (2016)","journal-title":"Appl. Math. Model."},{"key":"1111_CR31","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1051\/ro\/2018093","volume":"53","author":"M Al-Amin Khan","year":"2019","unstructured":"Al-Amin Khan, M., Shaikh, A.A., Panda, G.C., Konstantaras, I.: Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme. RAIRO-Oper. Res. 53, 1691\u20131708 (2019). https:\/\/doi.org\/10.1051\/ro\/2018093","journal-title":"RAIRO-Oper. Res."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-021-01111-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-021-01111-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-021-01111-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T18:17:29Z","timestamp":1644257849000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-021-01111-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,22]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["1111"],"URL":"https:\/\/doi.org\/10.1007\/s40815-021-01111-z","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,22]]},"assertion":[{"value":"20 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}