{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:07:22Z","timestamp":1777334842640,"version":"3.51.4"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T00:00:00Z","timestamp":1520812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T00:00:00Z","timestamp":1520812800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Maulana Azad National Fellowship, India","award":["F1-17.1\/2014-15\/MANF-2014-15-MUS-WES-35645"],"award-info":[{"award-number":["F1-17.1\/2014-15\/MANF-2014-15-MUS-WES-35645"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s12351-018-0391-4","type":"journal-article","created":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T09:15:05Z","timestamp":1520846105000},"page":"1559-1587","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Analyzing an inventory model with two-level trade credit period including the effect of customers\u2019 credit on the demand function using q-fuzzy number"],"prefix":"10.1007","volume":"20","author":[{"given":"Ateka","family":"Banu","sequence":"first","affiliation":[]},{"given":"Shyamal Kumar","family":"Mondal","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,12]]},"reference":[{"key":"391_CR1","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1057\/jors.1995.90","volume":"46","author":"SP Aggarwal","year":"1995","unstructured":"Aggarwal SP, Jaggi CK (1995) Ordering policies of deteriorating items under permissible delay in payments. J Oper Res Soc 46:658\u2013662","journal-title":"J Oper Res Soc"},{"key":"391_CR2","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1186\/s40064-016-2567-9","volume":"5","author":"A Banu","year":"2016","unstructured":"Banu A, Mondal S (2016) Analysis of credit linked demand in an inventory model with varying ordering cost. Springerplus 5:916. https:\/\/doi.org\/10.1186\/s40064-016-2567-9","journal-title":"Springerplus"},{"issue":"1","key":"391_CR3","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/S0305-0548(98)80007-5","volume":"25","author":"KJ Chung","year":"1998","unstructured":"Chung KJ (1998) A theorem on the determination of economic order quantity under conditions of permissible delay in payments. Comput Oper Res 25(1):49\u201352","journal-title":"Comput Oper Res"},{"key":"391_CR4","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1080\/05695557308974918","volume":"5","author":"RB Covert","year":"1973","unstructured":"Covert RB, Philip GS (1973) An EOQ model with Weibull distribution deterioration. AIIE Trans 5:323\u2013326","journal-title":"AIIE Trans"},{"key":"391_CR5","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1016\/j.cie.2012.12.020","volume":"64","author":"BC Das","year":"2013","unstructured":"Das BC, Das B, Mondal SK (2013) Integrated supply chain model for a deteriorating item with procurement cost dependent credit period. Comput Ind Eng 64:788\u2013796","journal-title":"Comput Ind Eng"},{"key":"391_CR7","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/j.asoc.2014.11.057","volume":"28","author":"BC Das","year":"2015","unstructured":"Das BC, Das B, Mondal SK (2015) An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Appl Soft Comput 28:435\u2013465","journal-title":"Appl Soft Comput"},{"key":"391_CR8","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.cie.2017.05.025","volume":"110","author":"BC Das","year":"2017","unstructured":"Das BC, Das B, Mondal SK (2017) An ingrated production\u2013inventory model with defective item dependent stochastic credit period. Comput Ind Eng 110:255\u2013263","journal-title":"Comput Ind Eng"},{"key":"391_CR9","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1016\/j.jmsy.2017.04.005","volume":"45","author":"A Diabat","year":"2017","unstructured":"Diabat A, Taleizadeh AA, Lashgari M (2017) A lot sizing model with partial downstream delayed payment, partialupstream advance payment, and partial backordering fordeteriorating items. J Manuf Syst 45:322\u2013342","journal-title":"J Manuf Syst"},{"key":"391_CR10","first-page":"238","volume":"14","author":"PM Ghare","year":"1963","unstructured":"Ghare PM, Schrader GP (1963) A model for an exponentially decaying inventory. J Ind Eng 14:238\u2013243","journal-title":"J Ind Eng"},{"key":"391_CR11","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1057\/jors.1985.56","volume":"36","author":"SK Goyal","year":"1985","unstructured":"Goyal SK (1985) Economic order quanity under conditions of permissible delay in payments. J Oper Res Soc 36:335\u2013338","journal-title":"J Oper Res Soc"},{"key":"391_CR12","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.cie.2010.10.009","volume":"60","author":"CH Ho","year":"2011","unstructured":"Ho CH (2011) The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit. Comput Ind Eng 60:117\u2013126","journal-title":"Comput Ind Eng"},{"key":"391_CR13","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1057\/palgrave.jors.2601588","volume":"54","author":"YF Huang","year":"2003","unstructured":"Huang YF (2003) Optimal retailer\u2019s ordering policies in the EOQ model under trade credit financing. J Oper Res Soc 54:1011\u20131015","journal-title":"J Oper Res Soc"},{"key":"391_CR14","first-page":"539","volume":"24","author":"H Hwang","year":"1997","unstructured":"Hwang H, Shinn SW (1997) Retailer\u2019s pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments. Comput Ind Eng 24:539\u2013547","journal-title":"Comput Ind Eng"},{"issue":"8","key":"391_CR15","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1016\/j.ijar.2010.07.001","volume":"51","author":"N Kazemi","year":"2010","unstructured":"Kazemi N, Shekarian E, Jaber MY (2010) An inventory model with backorders with fuzzy parameters and decision variables. Int J Approx Reason 51(8):964\u2013972","journal-title":"Int J Approx Reason"},{"key":"391_CR16","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.3233\/IFS-141519","volume":"28","author":"N Kazemi","year":"2015","unstructured":"Kazemi N, Olugu EU, Rashid SHA, Ghazilla RABR (2015a) Development of fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters. J Intell Fuzzy Syst 28:2377\u20132389","journal-title":"J Intell Fuzzy Syst"},{"key":"391_CR17","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1016\/j.cie.2015.05.014","volume":"87","author":"N Kazemi","year":"2015","unstructured":"Kazemi N, Shekarian E, Cardenas-Barron LE (2015b) Incorporating human learning into a fuzzy EOQ inventory model with backorders. Comput Ind Eng 87:540\u2013542","journal-title":"Comput Ind Eng"},{"key":"391_CR18","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.cie.2016.03.004","volume":"96","author":"N Kazemi","year":"2016","unstructured":"Kazemi N, Olugu EU, Rashid SHA, Ghazilla RABR (2016a) A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters: an empirical study. Comput Ind Eng 96:140\u2013148","journal-title":"Comput Ind Eng"},{"issue":"16","key":"391_CR19","doi-asserted-by":"publisher","first-page":"5010","DOI":"10.1080\/00207543.2016.1165874","volume":"54","author":"N Kazemi","year":"2016","unstructured":"Kazemi N, Rashid SHA, Shekarian E, Bottani E, Montanari R (2016b) A fuzzy lot-sizing problem with two-stage composite human learning. Int J Prod Res 54(16):5010\u20135025","journal-title":"Int J Prod Res"},{"issue":"3","key":"391_CR20","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.3934\/jimo.2016.12.1091","volume":"12","author":"M Lashgari","year":"2016","unstructured":"Lashgari M, Taleizadeh AA, Sana SS (2016a) An inventory control problem for deteriorating items with back-ordering and finantial consideration under two levels of trade credit linked to order quantity. J Ind Manag Optim 12(3):1091\u20131119","journal-title":"J Ind Manag Optim"},{"key":"391_CR21","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s10479-015-2100-5","volume":"238","author":"M Lashgari","year":"2016","unstructured":"Lashgari M, Taleizadeh AA, Ahmadi A (2016b) Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain. Ann Oper Res 238:329\u2013354","journal-title":"Ann Oper Res"},{"issue":"8","key":"391_CR22","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1080\/09537280701619117","volume":"18","author":"GC Mahata","year":"2007","unstructured":"Mahata GC, Goswami A (2007) An EOQ model for deteriorating items under trade credit financing in the fuzzy sense. Prod Plan Control 18(8):681\u2013692","journal-title":"Prod Plan Control"},{"issue":"1","key":"391_CR23","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.fss.2005.06.021","volume":"157","author":"MK Maiti","year":"2006","unstructured":"Maiti MK, Maiti M (2006) Fuzzy inventory model with two warehouses under possibility constraints. Fuzzy Set Syst 157(1):52\u201373","journal-title":"Fuzzy Set Syst"},{"issue":"4","key":"391_CR24","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1016\/j.camwa.2010.12.040","volume":"61","author":"SS Mishra","year":"2011","unstructured":"Mishra SS, Mishra PP (2011) An image model for fuzzified deterioration under cob-web phenomenon and permissible delay in payment. Comput Math Appl 61(4):921\u2013932","journal-title":"Comput Math Appl"},{"key":"391_CR25","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/S0360-8352(02)00187-0","volume":"44","author":"S Mondal","year":"2002","unstructured":"Mondal S, Maiti M (2002) Multi-item fuzzy EOQ models using genetic algorithm. Comput Ind Eng 44:105\u2013117","journal-title":"Comput Ind Eng"},{"key":"391_CR26","first-page":"115","volume":"35","author":"NH Shah","year":"1993","unstructured":"Shah NH (1993) A lot-size model for exponentially decaying inventory when delay in payments is permissible. Cahiers du CERO 35:115\u2013123","journal-title":"Cahiers du CERO"},{"key":"391_CR27","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.amc.2015.03.010","volume":"259","author":"NH Shah","year":"2015","unstructured":"Shah NH, Cardenas-Barron LE (2015) Retailer\u2019s decision for ordering and credit policies for deteriorating items when a supplier offers order-linked credit period or cash discount. Appl Math Comput 259:569\u2013573","journal-title":"Appl Math Comput"},{"issue":"3","key":"391_CR28","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1504\/EJIE.2014.060998","volume":"8","author":"E Shekarian","year":"2014","unstructured":"Shekarian E, Jaber MY, Kazemi N, Ehsani E (2014) A fuzzifed version of the economic production quantity (EPQ) model with backorders and rework for a single-stage system. Eur J Ind Eng 8(3):291\u2013324","journal-title":"Eur J Ind Eng"},{"key":"391_CR29","doi-asserted-by":"publisher","first-page":"2985","DOI":"10.3233\/IFS-151907","volume":"30","author":"E Shekarian","year":"2016","unstructured":"Shekarian E, Olugu EU, Rashid SHA, Kazemi N (2016) An economic order quantity model considering different holding costs for imperfect quality items subject to fuzziness and learning. J Intell Fuzzy Syst 30:2985\u20132997","journal-title":"J Intell Fuzzy Syst"},{"key":"391_CR30","doi-asserted-by":"publisher","first-page":"588","DOI":"10.1016\/j.asoc.2017.01.013","volume":"55","author":"E Shekarian","year":"2017","unstructured":"Shekarian E, Rashid SHA, Bottan E, De SK (2017) Fuzzy inventory models: a comprehensive review. Appl Soft Comput 55:588\u2013621","journal-title":"Appl Soft Comput"},{"key":"391_CR31","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1016\/0377-2217(94)00357-2","volume":"91","author":"SW Shinn","year":"1996","unstructured":"Shinn SW, Hwang HP, Sung S (1996) Joint price and lot size determination under conditions of permissible delay in payments and quantity discounts for freight cost. Eur J Oper Res 91:528\u2013542","journal-title":"Eur J Oper Res"},{"issue":"23","key":"391_CR32","doi-asserted-by":"publisher","first-page":"4263","DOI":"10.3923\/jas.2008.4263.4273","volume":"8","author":"AA Taleizadeh","year":"2008","unstructured":"Taleizadeh AA, Moghadasi H, Niaki STA, Eftekhari A (2008) An economic order quantity under joint replenishment policy to supply expensive imported raw materials with payment in advance. J Appl Sci 8(23):4263\u20134273","journal-title":"J Appl Sci"},{"issue":"10","key":"391_CR33","doi-asserted-by":"publisher","first-page":"1187","DOI":"10.1080\/00207720903171761","volume":"41","author":"AA Taleizadeh","year":"2010","unstructured":"Taleizadeh AA, Niaki STA, Aryanezha MB (2010) Optimising multi-product multi-chance-constraint inventory control system with stochastic period lengths and total discount under fuzzy purchasing price and holding costs. Int J Syst Sci 41(10):1187\u20131200","journal-title":"Int J Syst Sci"},{"key":"391_CR34","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1016\/j.mcm.2011.03.038","volume":"54","author":"AA Taleizadeh","year":"2011","unstructured":"Taleizadeh AA, Barzinpour F, Wee HM (2011) Meta-heuristic algorithms for solving a fuzzy single-period problem. Math Comput Model 54:1273\u20131285","journal-title":"Math Comput Model"},{"key":"391_CR35","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 (2013a) Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math Comput Model 57:1466\u20131479","journal-title":"Math Comput Model"},{"key":"391_CR36","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.knosys.2013.08.027","volume":"53","author":"AA Taleizadeh","year":"2013","unstructured":"Taleizadeh AA, Niaki STA, Meibodi RG (2013b) Replenish-up-to multi-chance-constraint inventory control system under fuzzy random lost-sale and backordered quantities. Knowl Based Syst 53:147\u2013156","journal-title":"Knowl Based Syst"},{"key":"391_CR37","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.ijpe.2014.01.023","volume":"155","author":"AA Taleizadeh","year":"2014","unstructured":"Taleizadeh AA (2014) An EOQ model with partial backordering and advance payments for an evaporating item. Int J Prod Econ 155:185\u2013193","journal-title":"Int J Prod Econ"},{"key":"391_CR38","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.apm.2013.05.065","volume":"38","author":"AA Taleizadeh","year":"2014","unstructured":"Taleizadeh AA, Nematollahi M (2014) An inventory control problem for deteriorating items with back-ordering and financial considerations. Appl Math Model 38:93\u2013109","journal-title":"Appl Math Model"},{"issue":"19\u201320","key":"391_CR39","doi-asserted-by":"publisher","first-page":"8777","DOI":"10.1016\/j.apm.2016.05.008","volume":"40","author":"AA Taleizadeh","year":"2016","unstructured":"Taleizadeh AA, Lashgari M, Akram R, Heydari J (2016) An imperfect EPQ model with up-stream trade credit periods linked to raw material order quantity and down-stream trade credit periods. Appl Math Model 40(19\u201320):8777\u20138793","journal-title":"Appl Math Model"},{"key":"391_CR40","first-page":"292","volume":"155","author":"J Wu","year":"2014","unstructured":"Wu J, Chan YL (2014) Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers. Int J Prod Res 155:292\u2013301","journal-title":"Int J Prod Res"},{"issue":"5","key":"391_CR41","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1016\/S0305-0548(02)00032-1","volume":"30","author":"PC Yang","year":"2003","unstructured":"Yang PC, Wee HM (2003) An integrated multi-lot-size production inventory model for deteriorating item. Comput Oper Res 30(5):671\u2013682","journal-title":"Comput Oper Res"},{"key":"391_CR42","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7949-0","volume-title":"Fuzzy set theory and its applications","author":"HJ Zimmermann","year":"1991","unstructured":"Zimmermann HJ (1991) Fuzzy set theory and its applications, 2nd revised edn. Kluwer, Dordrecht","edition":"2"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-018-0391-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12351-018-0391-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-018-0391-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T05:52:37Z","timestamp":1603950757000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12351-018-0391-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,12]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["391"],"URL":"https:\/\/doi.org\/10.1007\/s12351-018-0391-4","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,12]]},"assertion":[{"value":"16 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 March 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}