{"id":"https://openalex.org/W2624928984","doi":"https://doi.org/10.1051/ro/2017047","title":"Use of \u201ce\u201d and \u201cg\u201d operators to a fuzzy production inventory control model for substitute items","display_name":"Use of \u201ce\u201d and \u201cg\u201d operators to a fuzzy production inventory control model for substitute items","publication_year":2017,"publication_date":"2017-06-13","ids":{"openalex":"https://openalex.org/W2624928984","doi":"https://doi.org/10.1051/ro/2017047","mag":"2624928984"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2017047","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2017047","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","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/A5069064107","display_name":"Debnarayan Khatua","orcid":"https://orcid.org/0000-0001-7453-9357"},"institutions":[{"id":"https://openalex.org/I175399479","display_name":"Haldia Institute of Technology","ror":"https://ror.org/0211bs523","country_code":"IN","type":"education","lineage":["https://openalex.org/I175399479"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debnarayan Khatua","raw_affiliation_strings":["Department of Basic Science and Humanities, Global Institute of Science and Technology, Haldia, Purba Medinipur-721657, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0001-7453-9357","affiliations":[{"raw_affiliation_string":"Department of Basic Science and Humanities, Global Institute of Science and Technology, Haldia, Purba Medinipur-721657, West Bengal, India","institution_ids":["https://openalex.org/I175399479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076044515","display_name":"Anupam De","orcid":"https://orcid.org/0000-0002-1602-0300"},"institutions":[{"id":"https://openalex.org/I175399479","display_name":"Haldia Institute of Technology","ror":"https://ror.org/0211bs523","country_code":"IN","type":"education","lineage":["https://openalex.org/I175399479"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anupam De","raw_affiliation_strings":["Department of Applied Sciences, Haldia Institute of Technology, Haldia, Purba Medinipur-721657, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Sciences, Haldia Institute of Technology, Haldia, Purba Medinipur-721657, West Bengal, India","institution_ids":["https://openalex.org/I175399479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063380569","display_name":"K. Maity","orcid":"https://orcid.org/0000-0001-6961-4148"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kalipada Maity","raw_affiliation_strings":["Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupatinagar, Purba Medinipur-721425, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupatinagar, Purba Medinipur-721425, West Bengal, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049214301","display_name":"Samarjit Kar","orcid":"https://orcid.org/0000-0002-2059-1755"},"institutions":[{"id":"https://openalex.org/I155837530","display_name":"National Institute of Technology Durgapur","ror":"https://ror.org/04ds0jm32","country_code":"IN","type":"education","lineage":["https://openalex.org/I155837530"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Samarjit Kar","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology, Durgapur-713209, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology, Durgapur-713209, West Bengal, India","institution_ids":["https://openalex.org/I155837530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1361,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8150212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"53","issue":"2","first_page":"473","last_page":"486"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9937999844551086,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6120241284370422},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.6099984645843506},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.546700119972229},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.492771178483963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4896991550922394},{"id":"https://openalex.org/keywords/profit","display_name":"Profit (economics)","score":0.48297420144081116},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.47333958745002747},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4732958674430847},{"id":"https://openalex.org/keywords/inventory-control","display_name":"Inventory control","score":0.46492719650268555},{"id":"https://openalex.org/keywords/production","display_name":"Production (economics)","score":0.4606189429759979},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.4433121085166931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4426393210887909},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43807774782180786},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4273883104324341},{"id":"https://openalex.org/keywords/fuzzy-transportation","display_name":"Fuzzy transportation","score":0.4250262379646301},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.41613057255744934},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.3629290759563446},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3533214330673218},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.25490128993988037},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.18586677312850952},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12777158617973328},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11543381214141846},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11159071326255798}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6120241284370422},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.6099984645843506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.546700119972229},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.492771178483963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4896991550922394},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.48297420144081116},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.47333958745002747},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4732958674430847},{"id":"https://openalex.org/C117938511","wikidata":"https://www.wikidata.org/wiki/Q3634830","display_name":"Inventory control","level":2,"score":0.46492719650268555},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.4606189429759979},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.4433121085166931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4426393210887909},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43807774782180786},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4273883104324341},{"id":"https://openalex.org/C21214244","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy transportation","level":5,"score":0.4250262379646301},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.41613057255744934},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.3629290759563446},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3533214330673218},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.25490128993988037},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.18586677312850952},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12777158617973328},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11543381214141846},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11159071326255798},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2017047","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2017047","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2019__53_2_473_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2017047/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W846594312","https://openalex.org/W1454233415","https://openalex.org/W1480859677","https://openalex.org/W1560538028","https://openalex.org/W1642042653","https://openalex.org/W1968847100","https://openalex.org/W1980389968","https://openalex.org/W1994433008","https://openalex.org/W1995728191","https://openalex.org/W2007653219","https://openalex.org/W2028579357","https://openalex.org/W2032995443","https://openalex.org/W2035474708","https://openalex.org/W2048747364","https://openalex.org/W2069722371","https://openalex.org/W2070992315","https://openalex.org/W2083742942","https://openalex.org/W2107382253","https://openalex.org/W2107983068","https://openalex.org/W2126246951","https://openalex.org/W2155097786","https://openalex.org/W2158182297","https://openalex.org/W2158380130","https://openalex.org/W2168402424","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W154865872","https://openalex.org/W2041241614","https://openalex.org/W2399109054","https://openalex.org/W3040599965","https://openalex.org/W2333950445","https://openalex.org/W3201823740","https://openalex.org/W2425342526","https://openalex.org/W2143072948","https://openalex.org/W4293055854","https://openalex.org/W1972170383"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,42],"fuzzy":[4,30,43,62],"optimal":[5],"control":[6,36,54,63],"model":[7,55],"for":[8],"substitute":[9],"items":[10],"with":[11],"stock":[12],"and":[13,76,101],"selling":[14],"price":[15],"dependent":[16],"demand":[17],"has":[18,65],"been":[19,66],"developed.":[20],"Here":[21],"the":[22,33,48,51],"state":[23],"variables":[24],"(stocks)":[25],"are":[26,96],"assumed":[27],"to":[28],"be":[29,39],"variables.":[31],"So":[32],"proposed":[34,61],"dynamic":[35],"system":[37,45,73,81],"can":[38],"represented":[40],"as":[41],"differential":[44,72],"which":[46],"optimize":[47],"profit":[49],"of":[50],"production":[52],"inventory":[53],"through":[56,90],"Pontryagin\u2019s":[57],"maximum":[58],"principle.":[59],"The":[60,79],"problem":[64],"transformed":[67],"into":[68],"an":[69],"equivalent":[70],"crisp":[71],"using":[74,86],"\u201ce\u201d":[75],"\u201cg\u201d":[77],"operators.":[78],"deterministic":[80],"is":[82],"then":[83],"solved":[84],"by":[85],"Newton\u2019s":[87],"forward-backward":[88],"method":[89],"MATLAB.":[91],"Finally":[92],"some":[93],"numerical":[94],"results":[95],"presented":[97],"both":[98],"in":[99],"tabular":[100],"graphical":[102],"form.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}
