{"id":"https://openalex.org/W4407131442","doi":"https://doi.org/10.1109/ieem62345.2024.10856982","title":"Two Formulations for Minimizing Weight-Distance Objective in Single Vehicle Routing Problem with Quadratic, Cubic Objective Function and its Linearization","display_name":"Two Formulations for Minimizing Weight-Distance Objective in Single Vehicle Routing Problem with Quadratic, Cubic Objective Function and its Linearization","publication_year":2024,"publication_date":"2024-12-15","ids":{"openalex":"https://openalex.org/W4407131442","doi":"https://doi.org/10.1109/ieem62345.2024.10856982"},"language":"en","primary_location":{"id":"doi:10.1109/ieem62345.2024.10856982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieem62345.2024.10856982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)","raw_type":"proceedings-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/A5012449520","display_name":"Vinay Singh","orcid":"https://orcid.org/0000-0002-6505-5948"},"institutions":[{"id":"https://openalex.org/I9747756","display_name":"Atal Bihari Vajpayee Indian Institute of Information Technology and Management","ror":"https://ror.org/008b3ap06","country_code":"IN","type":"education","lineage":["https://openalex.org/I9747756"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vinay Singh","raw_affiliation_strings":["ABV-Indian Institute of Information Technology and Management,Department of Management Studies,Gwalior,India,474015"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ABV-Indian Institute of Information Technology and Management,Department of Management Studies,Gwalior,India,474015","institution_ids":["https://openalex.org/I9747756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004343120","display_name":"Ruchi Sharma","orcid":"https://orcid.org/0000-0002-0702-7156"},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"R.R.K. Sharma","raw_affiliation_strings":["Indian Institute of Technology,Department of Industrial and Management Engineering,Kanpur,India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology,Department of Industrial and Management Engineering,Kanpur,India","institution_ids":["https://openalex.org/I94234084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101921474","display_name":"Kin Keung Lai","orcid":"https://orcid.org/0000-0003-0014-2095"},"institutions":[{"id":"https://openalex.org/I126145234","display_name":"Chaoyang University of Technology","ror":"https://ror.org/04xwksx09","country_code":"TW","type":"education","lineage":["https://openalex.org/I126145234"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"K.K. Lai","raw_affiliation_strings":["Chaoyang University of Technology,Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chaoyang University of Technology,Taiwan","institution_ids":["https://openalex.org/I126145234"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3768082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"102","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9937000274658203,"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":0.9937000274658203,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9927999973297119,"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/T12176","display_name":"Optimization and Packing Problems","score":0.989799976348877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.8038314580917358},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6924006938934326},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5612380504608154},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.554590106010437},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.5065113306045532},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.505779504776001},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.5011539459228516},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.4452096223831177},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44211331009864807},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3867175281047821},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35905158519744873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3238293528556824},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2284974455833435},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17073386907577515},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10199165344238281},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08371692895889282},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07079184055328369},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05679738521575928}],"concepts":[{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.8038314580917358},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6924006938934326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5612380504608154},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.554590106010437},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.5065113306045532},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.505779504776001},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.5011539459228516},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.4452096223831177},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44211331009864807},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3867175281047821},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35905158519744873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3238293528556824},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2284974455833435},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17073386907577515},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10199165344238281},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08371692895889282},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07079184055328369},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05679738521575928},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ieem62345.2024.10856982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieem62345.2024.10856982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1778127384","https://openalex.org/W1966716113","https://openalex.org/W2000702178","https://openalex.org/W2006756967","https://openalex.org/W2050130693","https://openalex.org/W2062245133","https://openalex.org/W2069286402","https://openalex.org/W2081508128","https://openalex.org/W2090118375","https://openalex.org/W2091932422","https://openalex.org/W2132719857","https://openalex.org/W2161546705","https://openalex.org/W3185149963"],"related_works":["https://openalex.org/W269925151","https://openalex.org/W222839857","https://openalex.org/W2000297171","https://openalex.org/W3096788047","https://openalex.org/W2101513891","https://openalex.org/W4315646767","https://openalex.org/W4386731488","https://openalex.org/W292276619","https://openalex.org/W4300487223","https://openalex.org/W2083427614"],"abstract_inverted_index":{"Here":[0],"we":[1,58],"consider":[2],"a":[3,92],"single":[4],"vehicle":[5,66],"routing":[6],"problem":[7,78],"(of":[8,112],"unlimited":[9],"capacity":[10,12],"and":[11,35,42,52,94,108,114,136],"constraint":[13],"can":[14],"be":[15,140],"easily":[16],"included)":[17],"that":[18,79],"visits":[19,24],"different":[20],"dealers.":[21],"As":[22],"it":[23,28],"the":[25,30,65,68,76,98,126],"first":[26,33],"dealer,":[27],"offloads":[29],"demand":[31],"of":[32,75,134],"dealer":[34,40],"moves":[36],"on":[37,48],"to":[38,60,139],"second":[39],"\u2018lighter\u2019,":[41],"so":[43],"on.":[44],"Fuel":[45],"consumption":[46],"depends":[47],"both":[49],"weight":[50],"carried":[51],"distance":[53],"travelled.":[54],"In":[55],"this":[56],"context":[57],"seek":[59],"minimize":[61],"weight-distance":[62],"travelled":[63],"by":[64],"for":[67,125],"entire":[69],"tour.":[70],"We":[71,120],"give":[72,121],"two":[73,122,127],"formulations":[74],"above":[77],"has":[80,131],"received":[81],"very":[82],"little":[83],"or":[84],"no":[85],"attention":[86],"in":[87,91,97,105,117],"literature.":[88],"It":[89],"results":[90],"\u2018cubic\u2019":[93,113],"\u2018quadratic\u2019":[95,115],"terms":[96],"objective":[99],"function":[100],"with":[101],"negative":[102],"cost":[103,110],"coefficients":[104,111],"one":[106],"formulation":[107],"positive":[109],"terms)":[116],"other":[118],"formulation.":[119],"linearization":[123,130],"schemes":[124],"formulations.":[128],"One":[129],"less":[132],"number":[133],"constraints":[135],"is":[137],"expected":[138],"more":[141],"efficient":[142],"CPU":[143],"time":[144],"wise.":[145]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}