{"id":"https://openalex.org/W2126246951","doi":"https://doi.org/10.1080/00207720802303218","title":"Optimal inventory policies for deteriorating complementary and substitute items","display_name":"Optimal inventory policies for deteriorating complementary and substitute items","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2126246951","doi":"https://doi.org/10.1080/00207720802303218","mag":"2126246951"},"language":"en","primary_location":{"id":"doi:10.1080/00207720802303218","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720802303218","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063380569","display_name":"K. Maity","orcid":"https://orcid.org/0000-0001-6961-4148"},"institutions":[{"id":"https://openalex.org/I28630478","display_name":"Kanya Maha Vidyalaya","ror":"https://ror.org/04svcpx91","country_code":"IN","type":"education","lineage":["https://openalex.org/I28630478"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"K. Maity","raw_affiliation_strings":["Mugberia Gangadhar Ma-havidyalaya","Department of Mathematics, Mugberia Gangadhar Ma-havidyalaya, Bhupatinagar, W.B., India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mugberia Gangadhar Ma-havidyalaya","institution_ids":["https://openalex.org/I28630478"]},{"raw_affiliation_string":"Department of Mathematics, Mugberia Gangadhar Ma-havidyalaya, Bhupatinagar, W.B., India#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043058161","display_name":"Manoranjan Maiti","orcid":"https://orcid.org/0000-0002-4323-1330"},"institutions":[{"id":"https://openalex.org/I41549804","display_name":"Vidyasagar University","ror":"https://ror.org/027jsza11","country_code":"IN","type":"education","lineage":["https://openalex.org/I41549804"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"M. Maiti","raw_affiliation_strings":["Vidyasagar University","Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vidyasagar University","institution_ids":["https://openalex.org/I41549804"]},{"raw_affiliation_string":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-, India","institution_ids":["https://openalex.org/I41549804"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043058161"],"corresponding_institution_ids":["https://openalex.org/I41549804"],"apc_list":null,"apc_paid":null,"fwci":2.9155,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.90919905,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"267","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9498000144958496,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9275000095367432,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pontryagins-minimum-principle","display_name":"Pontryagin's minimum principle","score":0.6194303631782532},{"id":"https://openalex.org/keywords/inventory-control","display_name":"Inventory control","score":0.5727292895317078},{"id":"https://openalex.org/keywords/economic-shortage","display_name":"Economic shortage","score":0.5492076277732849},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.500838041305542},{"id":"https://openalex.org/keywords/stock","display_name":"Stock (firearms)","score":0.49616703391075134},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48420146107673645},{"id":"https://openalex.org/keywords/profit","display_name":"Profit (economics)","score":0.47578704357147217},{"id":"https://openalex.org/keywords/holding-cost","display_name":"Holding cost","score":0.4728177785873413},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.45250993967056274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4335190951824188},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.42309463024139404},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.4214271903038025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4187451899051666},{"id":"https://openalex.org/keywords/production","display_name":"Production (economics)","score":0.41010046005249023},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.33606693148612976},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.14855891466140747},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10241904854774475}],"concepts":[{"id":"https://openalex.org/C141803461","wikidata":"https://www.wikidata.org/wiki/Q3491629","display_name":"Pontryagin's minimum principle","level":3,"score":0.6194303631782532},{"id":"https://openalex.org/C117938511","wikidata":"https://www.wikidata.org/wiki/Q3634830","display_name":"Inventory control","level":2,"score":0.5727292895317078},{"id":"https://openalex.org/C194051981","wikidata":"https://www.wikidata.org/wiki/Q1337691","display_name":"Economic shortage","level":3,"score":0.5492076277732849},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.500838041305542},{"id":"https://openalex.org/C204036174","wikidata":"https://www.wikidata.org/wiki/Q909380","display_name":"Stock (firearms)","level":2,"score":0.49616703391075134},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48420146107673645},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.47578704357147217},{"id":"https://openalex.org/C192365026","wikidata":"https://www.wikidata.org/wiki/Q5046829","display_name":"Holding cost","level":2,"score":0.4728177785873413},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.45250993967056274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4335190951824188},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.42309463024139404},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.4214271903038025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4187451899051666},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.41010046005249023},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.33606693148612976},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.14855891466140747},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10241904854774475},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2778137410","wikidata":"https://www.wikidata.org/wiki/Q2732820","display_name":"Government (linguistics)","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207720802303218","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720802303218","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1965767627","https://openalex.org/W1970069622","https://openalex.org/W1973193728","https://openalex.org/W1984505435","https://openalex.org/W1989267697","https://openalex.org/W1993674123","https://openalex.org/W1995342995","https://openalex.org/W2000879791","https://openalex.org/W2008107608","https://openalex.org/W2024427262","https://openalex.org/W2028579357","https://openalex.org/W2029603912","https://openalex.org/W2036264711","https://openalex.org/W2045168835","https://openalex.org/W2054048601","https://openalex.org/W2061494558","https://openalex.org/W2069987759","https://openalex.org/W2081167021","https://openalex.org/W2085507138","https://openalex.org/W2103736545","https://openalex.org/W2108429259","https://openalex.org/W2127576890","https://openalex.org/W2153558554","https://openalex.org/W2164010570","https://openalex.org/W2396748756","https://openalex.org/W2772574932","https://openalex.org/W3206777520","https://openalex.org/W4243082658"],"related_works":["https://openalex.org/W2962746246","https://openalex.org/W1967384683","https://openalex.org/W4285534277","https://openalex.org/W3031081244","https://openalex.org/W162218241","https://openalex.org/W4302321938","https://openalex.org/W4292923857","https://openalex.org/W3209004265","https://openalex.org/W1643670820","https://openalex.org/W15954510"],"abstract_inverted_index":{"The":[0,49,63,111,132],"optimal":[1,103],"production":[2,26,72],"for":[3,87,118,128],"an":[4],"inventory":[5,74],"control":[6,34,104],"system":[7],"of":[8,40,68],"deteriorating":[9],"multi-items":[10],"where":[11],"items":[12,42,60,127],"are":[13,43,55,61,135],"either":[14,44],"complementary":[15],"and/or":[16],"substitute":[17],"is":[18,28,51,79,113,123],"formulated":[19,80,114],"with":[20,125],"a":[21,33,82],"resource":[22],"constraint.":[23],"Here,":[24],"the":[25,37,41,69,107],"function":[27],"unknown":[29],"and":[30,58,90,93,102,120,141],"considered":[31],"as":[32,81],"variable.":[35],"Also,":[36],"deterioration":[38],"rates":[39],"stock":[45,52],"dependent":[46],"or":[47],"constant.":[48],"demand":[50],"dependent,":[53],"shortages":[54],"not":[56],"allowed":[57],"deteriorated":[59],"salvaged.":[62],"total":[64],"profit,":[65],"which":[66],"consists":[67],"sales":[70],"proceeds,":[71],"cost,":[73,76],"holding":[75],"salvage":[77],"value,":[78],"Pontryagin's":[83],"Optimal":[84],"Control":[85],"problem":[86],"both":[88,137],"steady":[89],"transient":[91],"states":[92],"evaluated":[94],"using":[95],"Taylor's":[96],"theorem,":[97],"generalised":[98],"reduced":[99],"gradient":[100],"technique":[101],"theory":[105],"satisfying":[106],"Generalised":[108],"Legendre":[109],"conditions.":[110],"model":[112],"in":[115,121,138],"general":[116],"form":[117,140],"n-items,":[119],"particular,":[122],"illustrated":[124],"three":[126],"some":[129],"numerical":[130],"data.":[131],"optimum":[133],"results":[134],"presented":[136],"tabular":[139],"graphically.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}