{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T12:56:17Z","timestamp":1769691377315,"version":"3.49.0"},"reference-count":42,"publisher":"EDP Sciences","issue":"1","license":[{"start":{"date-parts":[[2019,1,21]],"date-time":"2019-01-21T00:00:00Z","timestamp":1548028800000},"content-version":"vor","delay-in-days":20,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"funder":[{"name":"Basic Science Research Program through the National Research Foundation of Korea","award":["Project Number: 2017R1D1A1B03033846"],"award-info":[{"award-number":["Project Number: 2017R1D1A1B03033846"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2018,1,31]]},"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>This paper develops a sustainable integrated inventory model for maximizing profit with a controllable lead time, discrete setup cost reduction, and consideration of environmental issues. Contrary to the available literature, this paper considers a discrete setup cost for the vendor, thus making the integrated model sustainable. The customer\u2019s demand is assumed to be selling-price dependent to increase the number of sales, and the lead time demand follows a Poisson distribution. The integrated model is used to optimized the total shipment number, volume of shipments, safety factor, investments, selling-price, and probability of moving between the<jats:italic>\u201cin-control\u201d<\/jats:italic>to<jats:italic>\u201cout-of-control\u201d<\/jats:italic>states. An algorithm is developed to obtain the numerical results. Numerical examples and sensitivity analyses are given to illustrate the model.<\/jats:p>","DOI":"10.1051\/ro\/2018009","type":"journal-article","created":{"date-parts":[[2018,2,5]],"date-time":"2018-02-05T08:55:05Z","timestamp":1517820905000},"page":"39-57","source":"Crossref","is-referenced-by-count":96,"title":["An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment"],"prefix":"10.1051","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-6858","authenticated-orcid":false,"given":"Bikash Koli","family":"Dey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6583-8416","authenticated-orcid":false,"given":"Biswajit","family":"Sarkar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitali","family":"Sarkar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sarla","family":"Pareek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2019,1,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0925-5273(02)00142-1","volume":"83","author":"Abad","year":"2003","journal-title":"Int. J. Prod. Econ."},{"key":"R2","doi-asserted-by":"crossref","first-page":"3465","DOI":"10.1016\/j.apm.2010.02.035","volume":"34","author":"Annadurai","year":"2010","journal-title":"Appl. Math. Mod."},{"key":"R3","first-page":"403","volume":"15","author":"Azadeh","year":"2017","journal-title":"Ind. Eng. Manag. Syst."},{"key":"R4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.ejor.2012.01.041","volume":"220","author":"Bijvank","year":"2012","journal-title":"Eur. J. Oper. Res."},{"key":"R5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.ijpe.2010.10.024","volume":"143","author":"Ben-Daya","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"R6","doi-asserted-by":"crossref","first-page":"2394","DOI":"10.1016\/j.apm.2010.11.053","volume":"35","author":"C\u00e1rdenas-Barr\u00f3n","year":"2011","journal-title":"Appl. Math. Mod."},{"key":"R7","doi-asserted-by":"crossref","first-page":"2196","DOI":"10.1016\/j.apm.2008.05.028","volume":"33","author":"Chang","year":"2009","journal-title":"Appl. Math. Mod."},{"key":"R8","first-page":"44","volume":"16","author":"Deyi","year":"2017","journal-title":"Ind. Eng. Manag. Syst."},{"key":"R9","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1111\/j.1540-5915.1988.tb00264.x","volume":"19","author":"Goyal","year":"1988","journal-title":"Decis. Sci."},{"key":"R10","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1080\/095372897235415","volume":"8","author":"Ha","year":"1997","journal-title":"Prod. Plann. Cont."},{"key":"R11","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1080\/00207541003610270","volume":"49","author":"Huang","year":"2011","journal-title":"Int. J. Prod. Res."},{"key":"R12","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0925-5273(93)90090-8","volume":"30","author":"Johansen","year":"1993","journal-title":"Int. J. Prod. Econ."},{"key":"R13","first-page":"21","volume":"3","author":"Kara\u00f6z","year":"2011","journal-title":"J. Alanya Fac. Bus.\/Alanya Isletme Fak\u00fcltesi Dergisi"},{"key":"R14","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/j.jclepro.2016.11.052","volume":"144","author":"Kim","year":"2017","journal-title":"J. Clean. Prod."},{"key":"R15","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1016\/S0305-0548(01)00051-X","volume":"29","author":"Ouyang","year":"2002","journal-title":"Comput. Oper. Res."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"Pal B. and Adhikari S., Price-sensitive imperfect production inventory model with exponential partial backlogging. To appear in: Int. J. Syst. Sci. Oper. Logist. (2017). DOI: 10.1080\/23302674.2017.1323133","DOI":"10.1080\/23302674.2017.1323133"},{"key":"R17","doi-asserted-by":"crossref","first-page":"2283","DOI":"10.1016\/j.econmod.2012.06.039","volume":"29","author":"Pal","year":"2012","journal-title":"Econ. Model."},{"key":"R18","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.ijpe.2013.11.027","volume":"155","author":"Pal","year":"2014","journal-title":"Int. J. Prod. Econ."},{"key":"R19","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1111\/itor.12131","volume":"22","author":"Pal","year":"2015","journal-title":"Int. Trans. Oper. Res."},{"key":"R20","first-page":"113","volume":"2","author":"Pal","year":"2015","journal-title":"Int. J. Syst. Sci. Oper. Logist."},{"key":"R21","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1080\/00207721.2014.911383","volume":"47","author":"Pal","year":"2016","journal-title":"Int. J. Syst. Sci."},{"key":"R22","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1017\/S0269964814000126","volume":"28","author":"Pang","year":"2014","journal-title":"Prob. Eng. Inf. Sci."},{"key":"R23","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1287\/opre.34.1.137","volume":"34","author":"Porteus","year":"1986","journal-title":"Oper. Res."},{"key":"R24","first-page":"6248","volume":"217","author":"Sana","year":"2011","journal-title":"Appl. Math. Mod."},{"key":"R25","doi-asserted-by":"crossref","first-page":"3138","DOI":"10.1016\/j.apm.2012.07.026","volume":"37","author":"Sarkar","year":"2013","journal-title":"Appl. Math. Mod."},{"key":"R26","unstructured":"Sarkar B., Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Math. Prob. Eng. 2016 (2016) 6318737."},{"key":"R27","unstructured":"Sarkar B. and Mahapatra A.S., Periodic review fuzzy inventory model with variable lead time and fuzzy demand. Int. Trans. Oper. Res. 24 (2017) 1197\u20131227."},{"key":"R28","first-page":"362","volume":"224","author":"Sarkar","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"R29","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.ijpe.2013.11.014","volume":"155","author":"Sarkar","year":"2014","journal-title":"Int. J. Prod. Econ."},{"key":"R30","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/j.econmod.2012.11.045","volume":"31","author":"Sarkar","year":"2013","journal-title":"Econ. Mod."},{"key":"R31","unstructured":"Sarkar B., Sana S.S. and Chaudhuri K.S., An inventory model with finite replenishment rate, trade credit policy and price-discount offer. J. Ind. Eng. 2013 (2013) 672504."},{"key":"R32","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.jmsy.2014.02.001","volume":"33","author":"Sarkar","year":"2014","journal-title":"J. Manuf. Syst."},{"key":"R33","first-page":"414","volume":"231","author":"Sarkar","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"R34","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.jmsy.2014.11.003","volume":"34","author":"Sarkar","year":"2015","journal-title":"J. Manuf. Syst."},{"key":"R35","unstructured":"Sarkar B., Saren S., Sinha D. and Hur S., Effect of unequal lot sizes, variable setup cost, and carbon emission cost in a supply chain model. Math. Prob. Eng. 2015 (2015) 469486."},{"key":"R36","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.tre.2016.03.018","volume":"91","author":"Sarkar","year":"2016","journal-title":"Trans. Res. E: Logist. Transp. Rev."},{"key":"R37","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.3934\/jimo.2016063","volume":"13","author":"Sarkar","year":"2017","journal-title":"J. Ind. Manag. Opt."},{"key":"R38","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1016\/j.mcm.2008.08.017","volume":"49","author":"Shah","year":"2009","journal-title":"Math. Comp. Mod."},{"key":"R39","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.ejor.2012.03.032","volume":"221","author":"Taleizadeh","year":"2012","journal-title":"Eur. J. Oper. Res."},{"key":"R40","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1016\/j.cie.2012.11.005","volume":"64","author":"Wee","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"R41","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/S0377-2217(01)00345-9","volume":"143","author":"Yang","year":"2002","journal-title":"Eur. J. Oper. Res."},{"key":"R42","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/j.ejor.2010.10.001","volume":"210","author":"Zhang","year":"2011","journal-title":"Eur. J. Oper. Res."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2018009\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,13]],"date-time":"2022-08-13T22:28:49Z","timestamp":1660429729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2018009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":42,"journal-issue":{"issue":"1"},"alternative-id":["ro170324"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2018009","relation":{},"ISSN":["0399-0559","1290-3868"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"1290-3868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}