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This model includes one wholesaler and one retailer and our aim is to maximize the total profit. The demand rate in retailer is stock-dependent and in case of any shortages, the demand is partially backlogged. Retailer also introduces some promotional cost to boost the base demand of the item. It is established that if the wholesaler shares a part of promotional cost then channel profit as well as individual profit increase. The supply chain model is also considered for imprecise environment when different inventory parameters are fuzzy\/rough in nature. In this case individual profits as well as channel profit become fuzzy\/rough in nature. As optimization of fuzzy\/rough objective is not well defined, following credibility\/trust measure of fuzzy\/rough event, an approach is proposed for comparison of fuzzy\/rough objectives and a Particle Swarm Optimization (PSO) algorithm is used to find marketing decisions. Models are illustrated with numerical examples.<\/jats:p>","DOI":"10.3233\/jifs-16913","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T13:05:23Z","timestamp":1561727123000},"page":"565-581","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["A supply chain of deteriorating items with variable demand"],"prefix":"10.1177","volume":"37","author":[{"given":"Nilesh","family":"Pakhira","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, Paschim-Medinipur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manas Kumar","family":"Maiti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba-Medinipur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manoranjan","family":"Maiti","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, Paschim-Medinipur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,6,26]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(97)00091-9"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2011.07.019"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2006.05.008"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-010-0165-4"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2012.06.026"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2005.05.002"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2012.09.015"},{"issue":"2","key":"e_1_3_2_9_2","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s12351-009-0039-5","article-title":"A two ware house inventory model for deteriorating items with stock dependent demand rate and holding cost","volume":"9","author":"Gayen M.","year":"2009","unstructured":"GayenM. and PalA.K., A two ware house inventory model for deteriorating items with stock dependent demand rate and holding cost, Operational Research: An International Journal 9(2) (2009), 153\u2013165.","journal-title":"Operational Research: An International Journal"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.06.015"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2013.11.005"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2012.01.005"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2012.10.017"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2005.08.004"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.08.053"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(02)00101-3"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICNN.1995.488968"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.12.034"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00236-9"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00291-1"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(03)00079-3"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.06.021"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2009.06.085"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.2298\/YJOR120823018M"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2004.06.007"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2018.02.030"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1080\/23302674.2015.1004204"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-014-1759-3"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2012.09.049"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.04.004"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/0272-6963(95)00010-P"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.12.035"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2009.04.011"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2005.09.003"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2009.06.041"},{"key":"e_1_3_2_36_2","doi-asserted-by":"crossref","unstructured":"YuY. 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