{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:56Z","timestamp":1777703936471,"version":"3.51.4"},"reference-count":53,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2017,7]]},"abstract":"<jats:p>In this paper, a multi-item economic production quantity (EPQ) model for deteriorating seasonal products is developed with stock and promotional effort dependent demand in an imperfect production process. The promotional efforts are advertising, delivery facilities, better services, etc. The production process produces some imperfect quality units which are instantly reworked at a cost to bring back its quality to the perfect ones. Here, the rate of production is time dependent. Unit production cost is a function of production rate including the defective ones and the deterioration rate is considered as constant. The model is formulated as a profit maximization problem with space and budget constraints in the form of an optimal control problem. The total profit function with the effect of inflation and time-value of money is expressed as a finite integral over a finite planning horizon. The problem is solved using variational calculus to determine the minimum defective rates of the production process for which the total profit is maximum. Another three models are developed considering the constraints as uncertain (fuzzy, random and rough) in nature. For fuzzy model, three types of fuzzy numbers are considered. To deal with the fuzzy constraints, fuzzy possibility measure is used. Also, stochastic and rough constraints are reduced to the approximate crisp ones following chance constrained approach and rough expectation respectively. Numerical experiments are performed to illustrate the models. Also, some sensitivity analyses are performed and presented.<\/jats:p>","DOI":"10.3233\/jifs-16875","type":"journal-article","created":{"date-parts":[[2017,6,23]],"date-time":"2017-06-23T11:55:10Z","timestamp":1498218910000},"page":"649-666","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["An imperfect EPQ model for deteriorating items with promotional effort dependent demand"],"prefix":"10.1177","volume":"33","author":[{"given":"Anindita","family":"Kundu","sequence":"first","affiliation":[{"name":"Department of Mathematics, NIT, Mahatma Gandhi Avenue, Durgapur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Partha","family":"Guchhait","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vidyasagar University, Midnapore, Paschim-Medinipur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Goutam","family":"Panigrahi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, NIT, Mahatma Gandhi Avenue, Durgapur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manoranjan","family":"Maiti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vidyasagar University, Midnapore, Paschim-Medinipur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,7]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151850"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1975.113"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.02.004"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2014.07.002"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2014.03.007"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.6.1.73"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2013.12.033"},{"key":"e_1_3_2_9_2","unstructured":"DuboisD. and PradeH. Fuzzy sets and system - Theory and application Academic New York 1980."},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.11.001"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0360-8352(95)00016-T"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207548308942352"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.07.028"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2014.07.003"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.02.003"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(02)00113-2"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1994.217"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/0305-0548(94)00032-4"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.05.024"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.4236\/ajor.2015.55036"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.12.034"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.04.008"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1781-2"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2011.12.010"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2005.04.006"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2011.02.014"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.07.024"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/RAMS.2000.816310"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.34.1.137"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1080\/07408178608975329"},{"issue":"5","key":"e_1_3_2_31_2","first-page":"341","article-title":"Rough sets","volume":"11","author":"Pawlak Z.","year":"1982","unstructured":"PawlakZ., Rough sets, Internal Journal Information Science11(5) (1982), 341\u2013356.","journal-title":"Internal Journal Information Science"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.06.003"},{"key":"e_1_3_2_33_2","unstructured":"RaoS.S. Engineering optimization theory and practice New age International (P) Limited India 2000 pp. 715\u2013761."},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-5273(97)00112-6"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.01.041"},{"key":"e_1_3_2_36_2","first-page":"13543","article-title":"An imperfect production process for time varying demand with ination and time value of money - An EMQ model","volume":"38","author":"Sarkar B.","year":"2011","unstructured":"SarkarB., SanaS.S. and ChaudhuriK.S., An imperfect production process for time varying demand with ination and time value of money - An EMQ model, Expert System with Applications38 (2011), 13543\u201313548.","journal-title":"Expert System with Applications"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.03.010"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2008.07.014"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2016.03.016"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2015.08.009"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2011.04.028"},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2008.07.014"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2008.08.017"},{"key":"e_1_3_2_44_2","doi-asserted-by":"publisher","DOI":"10.1504\/IJMOR.2011.037314"},{"key":"e_1_3_2_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2009.06.041"},{"key":"e_1_3_2_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2012.03.007"},{"key":"e_1_3_2_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2009.05.008"},{"key":"e_1_3_2_48_2","doi-asserted-by":"publisher","DOI":"10.12733\/jics20102025"},{"key":"e_1_3_2_49_2","doi-asserted-by":"publisher","DOI":"10.3846\/20294913.2015.1012657"},{"key":"e_1_3_2_50_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_51_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/136254"},{"key":"e_1_3_2_52_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2014.07.017"},{"key":"e_1_3_2_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.01.011"},{"key":"e_1_3_2_54_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2016.04.001"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-16875","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-16875","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-16875","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:58Z","timestamp":1777455598000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-16875"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7]]},"references-count":53,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["10.3233\/JIFS-16875"],"URL":"https:\/\/doi.org\/10.3233\/jifs-16875","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7]]}}}