{"id":"https://openalex.org/W2056080064","doi":"https://doi.org/10.1080/00207720500089465","title":"A mixed inventory model with variable lead time and random back-order rate","display_name":"A mixed inventory model with variable lead time and random back-order rate","publication_year":2005,"publication_date":"2005-05-15","ids":{"openalex":"https://openalex.org/W2056080064","doi":"https://doi.org/10.1080/00207720500089465","mag":"2056080064"},"language":"en","primary_location":{"id":"doi:10.1080/00207720500089465","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720500089465","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/A5019661001","display_name":"R\u00f3mulo I. Zequeira","orcid":null},"institutions":[{"id":"https://openalex.org/I140494188","display_name":"Universit\u00e9 de Technologie de Troyes","ror":"https://ror.org/01qhqcj41","country_code":"FR","type":"education","lineage":["https://openalex.org/I140494188"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R\u00f3mulo I. Zequeira *","raw_affiliation_strings":["Equipe Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes, Universit\u00e9 de Technologie de Troyes","ISTIT, Equipe Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes, Universit\u00e9 de Technologie de Troyes, Troyes, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equipe Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes, Universit\u00e9 de Technologie de Troyes","institution_ids":["https://openalex.org/I140494188"]},{"raw_affiliation_string":"ISTIT, Equipe Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes, Universit\u00e9 de Technologie de Troyes, Troyes, France#TAB#","institution_ids":["https://openalex.org/I140494188"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036204493","display_name":"Alfonso Dur\u00e1n Heras","orcid":"https://orcid.org/0000-0001-8018-6391"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alfonso Dur\u00e1n","raw_affiliation_strings":["\u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid","Departmento de Ingenier\u00eda Mec\u00e1nica, \u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid, Legan\u00e9s, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Departmento de Ingenier\u00eda Mec\u00e1nica, \u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid, Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082414614","display_name":"Gil Guti\u00e9rrez","orcid":null},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gil Guti\u00e9rrez","raw_affiliation_strings":["\u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid","Departmento de Ingenier\u00eda Mec\u00e1nica, \u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid, Legan\u00e9s, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Departmento de Ingenier\u00eda Mec\u00e1nica, \u00c1rea de Ingenier\u00eda de Organizaci\u00f3n, Universidad Carlos III de Madrid, Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.982,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79939124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"36","issue":"6","first_page":"329","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.996399998664856,"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":0.996399998664856,"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/T13706","display_name":"Management and Optimization Techniques","score":0.9718000292778015,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"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/T11918","display_name":"Forecasting Techniques and Applications","score":0.9351000189781189,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lead-time","display_name":"Lead time","score":0.7861603498458862},{"id":"https://openalex.org/keywords/reorder-point","display_name":"Reorder point","score":0.7628949880599976},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.708060622215271},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.6259102821350098},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5869973301887512},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5376495122909546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49814414978027344},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4967401623725891},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48709607124328613},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.44794607162475586},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.44309934973716736},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4356159269809723},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43328678607940674},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.43062686920166016},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3730091452598572},{"id":"https://openalex.org/keywords/economic-order-quantity","display_name":"Economic order quantity","score":0.35455113649368286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3036055564880371},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23764902353286743},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1261650025844574},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11330574750900269},{"id":"https://openalex.org/keywords/operations-management","display_name":"Operations management","score":0.10080435872077942}],"concepts":[{"id":"https://openalex.org/C2781468064","wikidata":"https://www.wikidata.org/wiki/Q1267117","display_name":"Lead time","level":2,"score":0.7861603498458862},{"id":"https://openalex.org/C90357287","wikidata":"https://www.wikidata.org/wiki/Q3933138","display_name":"Reorder point","level":4,"score":0.7628949880599976},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.708060622215271},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.6259102821350098},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5869973301887512},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5376495122909546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49814414978027344},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4967401623725891},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48709607124328613},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44794607162475586},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.44309934973716736},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4356159269809723},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43328678607940674},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.43062686920166016},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3730091452598572},{"id":"https://openalex.org/C1199943","wikidata":"https://www.wikidata.org/wiki/Q451299","display_name":"Economic order quantity","level":3,"score":0.35455113649368286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3036055564880371},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23764902353286743},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1261650025844574},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11330574750900269},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.10080435872077942},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C108713360","wikidata":"https://www.wikidata.org/wiki/Q1824206","display_name":"Supply chain","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207720500089465","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720500089465","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":27,"referenced_works":["https://openalex.org/W272785329","https://openalex.org/W1513004135","https://openalex.org/W1517701247","https://openalex.org/W1594994747","https://openalex.org/W1970741704","https://openalex.org/W1979379141","https://openalex.org/W1988750344","https://openalex.org/W1992623596","https://openalex.org/W2011984466","https://openalex.org/W2012938181","https://openalex.org/W2025023143","https://openalex.org/W2025822852","https://openalex.org/W2030700100","https://openalex.org/W2040312808","https://openalex.org/W2048806647","https://openalex.org/W2062981686","https://openalex.org/W2085367549","https://openalex.org/W2088218266","https://openalex.org/W2092162147","https://openalex.org/W2108517068","https://openalex.org/W2115438001","https://openalex.org/W2128731745","https://openalex.org/W2149210090","https://openalex.org/W2153558554","https://openalex.org/W2422403062","https://openalex.org/W4231397353","https://openalex.org/W4243556080"],"related_works":["https://openalex.org/W3036082204","https://openalex.org/W3000160762","https://openalex.org/W2065119603","https://openalex.org/W2360367491","https://openalex.org/W2913853144","https://openalex.org/W2785448325","https://openalex.org/W2948867527","https://openalex.org/W2497606098","https://openalex.org/W2337180795","https://openalex.org/W1966433557"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,8,19,32,35,39,44,52,55,67,79,82,100],"determination":[6,80],"of":[7,22,54,66,81],"optimal":[9,83],"lead":[10,68,89],"time,":[11],"reorder":[12,86],"point":[13,87],"and":[14,60,88],"order":[15,40,84],"quantity":[16],"considering":[17],"that":[18],"back-order":[20,56],"probability":[21],"a":[23,27],"demand":[24,70],"made":[25],"during":[26],"stock-out":[28],"period":[29],"depends":[30],"on":[31],"interval":[33],"from":[34],"moment":[36],"in":[37],"which":[38],"is":[41,71,91,96],"placed":[42],"until":[43],"next":[45],"replenishment.":[46],"Two":[47],"models":[48],"are":[49],"analysed":[50],"for":[51,78],"specification":[53],"probability:":[57],"exponential":[58],"functions":[59],"piecewise":[61],"constant":[62],"functions.":[63],"The":[64],"distribution":[65],"time":[69,90],"assumed":[72],"to":[73,98],"be":[74],"Poisson.":[75],"An":[76],"algorithm":[77],"quantity,":[85],"given.":[92],"A":[93],"numerical":[94],"example":[95],"presented":[97],"illustrate":[99],"results.":[101]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}