{"id":"https://openalex.org/W4406501296","doi":"https://doi.org/10.1007/s10479-024-06459-7","title":"Multi-stage stochastic districting: optimization models and solution algorithms","display_name":"Multi-stage stochastic districting: optimization models and solution algorithms","publication_year":2025,"publication_date":"2025-01-17","ids":{"openalex":"https://openalex.org/W4406501296","doi":"https://doi.org/10.1007/s10479-024-06459-7"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-024-06459-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-024-06459-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-024-06459-7.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10479-024-06459-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115915532","display_name":"Anika Pomes","orcid":"https://orcid.org/0009-0009-6087-5363"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anika Pomes","raw_affiliation_strings":["Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Kaiserstr.12, Karlsruhe, 76131, Germany"],"raw_orcid":"https://orcid.org/0009-0009-6087-5363","affiliations":[{"raw_affiliation_string":"Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Kaiserstr.12, Karlsruhe, 76131, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086537578","display_name":"Antonio Diglio","orcid":"https://orcid.org/0000-0002-9775-3927"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Diglio","raw_affiliation_strings":["Department of Industrial Engineering (DII), Universit\u00e0 degli Studi di Napoli Federico II, Piazzale Tecchio, 80, 80125, Naples, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9775-3927","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering (DII), Universit\u00e0 degli Studi di Napoli Federico II, Piazzale Tecchio, 80, 80125, Naples, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029808771","display_name":"Stefan Nickel","orcid":"https://orcid.org/0000-0002-8339-0117"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I143379178","display_name":"FZI Research Center for Information Technology","ror":"https://ror.org/04kdh6x72","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I143379178"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Nickel","raw_affiliation_strings":["Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Kaiserstr.12, Karlsruhe, 76131, Germany","Research Center for Information Technology (FZI), Haid-und-Neu-Str. 10-14, Karlsruhe, 76131, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8339-0117","affiliations":[{"raw_affiliation_string":"Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Kaiserstr.12, Karlsruhe, 76131, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Research Center for Information Technology (FZI), Haid-und-Neu-Str. 10-14, Karlsruhe, 76131, Germany","institution_ids":["https://openalex.org/I143379178"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014572640","display_name":"Francisco Saldanha\u2010da\u2010Gama","orcid":"https://orcid.org/0000-0002-2074-1856"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Francisco Saldanha-da-Gama","raw_affiliation_strings":["Sheffield University Management School, Sheffield, S10 1FL, UK"],"raw_orcid":"https://orcid.org/0000-0002-2074-1856","affiliations":[{"raw_affiliation_string":"Sheffield University Management School, Sheffield, S10 1FL, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5115915532"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.1995,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76562352,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"346","issue":"3","first_page":"2225","last_page":"2251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource 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"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7360907793045044},{"id":"https://openalex.org/keywords/stage","display_name":"Stage (stratigraphy)","score":0.6046930551528931},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5699664950370789},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5215137600898743},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4986894130706787},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29070961475372314}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7360907793045044},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.6046930551528931},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5699664950370789},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5215137600898743},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4986894130706787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29070961475372314},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10479-024-06459-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-024-06459-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-024-06459-7.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:222540","is_oa":false,"landing_page_url":"https://orcid.org/0009-0009-6087-5363>,","pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:econstor.eu:10419/323298","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/323298","pdf_url":"https://www.econstor.eu/bitstream/10419/323298/1/10479_2025_Article_6459.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:spr:annopr:v:346:y:2025:i:3:d:10.1007_s10479-024-06459-7","is_oa":true,"landing_page_url":"http://link.springer.com/10.1007/s10479-024-06459-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10479-024-06459-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-024-06459-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-024-06459-7.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406501296.pdf","grobid_xml":"https://content.openalex.org/works/W4406501296.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1690448612","https://openalex.org/W1966306904","https://openalex.org/W1971454274","https://openalex.org/W1974861471","https://openalex.org/W1996040720","https://openalex.org/W2003553510","https://openalex.org/W2013152254","https://openalex.org/W2014068360","https://openalex.org/W2014621992","https://openalex.org/W2040185995","https://openalex.org/W2068136185","https://openalex.org/W2073228814","https://openalex.org/W2091937574","https://openalex.org/W2113574878","https://openalex.org/W2137195743","https://openalex.org/W2167696076","https://openalex.org/W2181995536","https://openalex.org/W2554862317","https://openalex.org/W2580828413","https://openalex.org/W2791842797","https://openalex.org/W2805479295","https://openalex.org/W2912114734","https://openalex.org/W2953333356","https://openalex.org/W3021014158","https://openalex.org/W3026434540","https://openalex.org/W3030539481","https://openalex.org/W3132121554","https://openalex.org/W3168592082","https://openalex.org/W4246609154","https://openalex.org/W4281291322","https://openalex.org/W4295093536","https://openalex.org/W4386006887","https://openalex.org/W4399309645"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"investigates":[3],"a":[4,15,29,39,53,60,146,149,156],"Multi-Stage":[5],"Stochastic":[6],"Districting":[7],"Problem":[8],"(MSSDP).":[9],"The":[10,34,112,126,159],"goal":[11],"is":[12,36,45,91,114,141,152],"to":[13,69,84,102,143],"devise":[14],"districting":[16],"plan":[17],"(i.e.,":[18],"clusters":[19],"of":[20,56,72,82,131],"Territorial":[21],"Units\u2014TUs)":[22],"accounting":[23],"for":[24],"uncertain":[25],"parameters":[26,76],"changing":[27],"over":[28],"discrete":[30],"multi-period":[31,136],"planning":[32],"horizon.":[33],"problem":[35],"cast":[37],"as":[38],"multi-stage":[40],"stochastic":[41,75],"programming":[42,89],"problem.":[43],"It":[44],"assumed":[46],"that":[47,85,93,104,165],"uncertainty":[48,134],"can":[49,169],"be":[50],"captured":[51],"by":[52],"finite":[54],"set":[55],"scenarios,":[57],"which":[58],"induces":[59],"scenario":[61],"tree.":[62],"Each":[63],"node":[64],"in":[65,135],"the":[66,70,74,78,105,129,139,166],"tree":[67],"corresponds":[68],"realization":[71],"all":[73],"from":[77],"root":[79],"node\u2014the":[80],"state":[81],"nature\u2014up":[83],"node.":[86],"A":[87],"mathematical":[88],"model":[90,113,140],"proposed":[92,153],"embeds":[94],"redistricting":[95],"recourse":[96,100],"decisions":[97],"and":[98],"other":[99],"actions":[101],"ensure":[103],"districts":[106],"are":[107],"balanced":[108],"regarding":[109],"their":[110],"activity.":[111],"tested":[115],"on":[116,155],"instances":[117],"generated":[118],"using":[119,145],"literature":[120],"data":[121],"containing":[122],"real":[123],"geographical":[124],"data.":[125],"results":[127,161],"demonstrate":[128],"relevance":[130],"hedging":[132],"against":[133],"districting.":[137],"Since":[138],"challenging":[142],"tackle":[144],"general-purpose":[147],"solver,":[148],"heuristic":[150],"algorithm":[151,168],"based":[154],"restricted":[157],"model.":[158],"computational":[160],"obtained":[162],"give":[163],"evidence":[164],"approximate":[167],"produce":[170],"high-quality":[171],"feasible":[172],"solutions":[173],"within":[174],"acceptable":[175],"computation":[176],"times.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
