{"id":"https://openalex.org/W7224077356","doi":"https://doi.org/10.3390/math14213930","title":"Robust Heterogeneous Vehicle Routing Optimization for Hazmat Transportation Under Time-Varying Risk","display_name":"Robust Heterogeneous Vehicle Routing Optimization for Hazmat Transportation Under Time-Varying Risk","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224077356","doi":"https://doi.org/10.3390/math14213930"},"language":"en","primary_location":{"id":"doi:10.3390/math14213930","doi":"https://doi.org/10.3390/math14213930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14213930","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14213930","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102555300","display_name":"Lijuan DING","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I75390827","display_name":"Beijing University of Chemical Technology","ror":"https://ror.org/00df5yc52","country_code":"CN","type":"education","lineage":["https://openalex.org/I75390827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijuan Ding","raw_affiliation_strings":["School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China","institution_ids":["https://openalex.org/I75390827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071895025","display_name":"Jun Wu","orcid":"https://orcid.org/0000-0002-3986-6923","observed_orcids":["https://orcid.org/0000-0002-3986-6923"]},"institutions":[{"id":"https://openalex.org/I75390827","display_name":"Beijing University of Chemical Technology","ror":"https://ror.org/00df5yc52","country_code":"CN","type":"education","lineage":["https://openalex.org/I75390827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Wu","raw_affiliation_strings":["School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China","institution_ids":["https://openalex.org/I75390827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071895025"],"corresponding_institution_ids":["https://openalex.org/I75390827"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85998846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"21","first_page":"3930","last_page":"3930"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9692000150680542,"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":0.9692000150680542,"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/T11357","display_name":"Risk and Safety Analysis","score":0.014100000262260437,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision 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":0.009499999694526196,"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/hazardous-materials-transportation","display_name":"dangerous goods transport","score":0.8090000152587891},{"id":"https://openalex.org/keywords/time-varying-risk","display_name":"time-varying risk","score":0.9509999752044678},{"id":"https://openalex.org/keywords/demand-uncertainty","display_name":"demand uncertainty","score":0.8939999938011169},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"robust optimization","score":0.8220000267028809},{"id":"https://openalex.org/keywords/bi-objective-optimization","display_name":"bi-objective optimization","score":0.8410000205039978},{"id":"https://openalex.org/keywords/population-exposure","display_name":"population exposure","score":0.5789999961853027},{"id":"https://openalex.org/keywords/environmental-degradation","display_name":"environmental degradation","score":0.9200000166893005},{"id":"https://openalex.org/keywords/multi-objective-evolutionary-algorithms","display_name":"multi-objective evolutionary algorithms","score":0.8629999756813049},{"id":"https://openalex.org/keywords/price-of-robustness","display_name":"price of robustness","score":0.6110000014305115}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.692300021648407},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.544700026512146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5067999958992004},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5055999755859375},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.43479999899864197},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.39320001006126404},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C2778304055","wikidata":"https://www.wikidata.org/wiki/Q657474","display_name":"Beijing","level":3,"score":0.37130001187324524},{"id":"https://openalex.org/C22507642","wikidata":"https://www.wikidata.org/wiki/Q1069369","display_name":"Hazardous waste","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C22212356","wikidata":"https://www.wikidata.org/wiki/Q775325","display_name":"Transport engineering","level":1,"score":0.3028999865055084},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C182299520","wikidata":"https://www.wikidata.org/wiki/Q1289588","display_name":"Total cost","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C2778711553","wikidata":"https://www.wikidata.org/wiki/Q924286","display_name":"Transport network","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C2779888511","wikidata":"https://www.wikidata.org/wiki/Q244156","display_name":"Traffic congestion","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C2985733770","wikidata":"https://www.wikidata.org/wiki/Q1233007","display_name":"Travel time","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C8505890","wikidata":"https://www.wikidata.org/wiki/Q605095","display_name":"Budget constraint","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C12174686","wikidata":"https://www.wikidata.org/wiki/Q1058438","display_name":"Risk assessment","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.26409998536109924},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.26190000772476196},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/math14213930","doi":"https://doi.org/10.3390/math14213930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14213930","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/math14213930","doi":"https://doi.org/10.3390/math14213930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14213930","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7646999955177307,"id":"https://metadata.un.org/sdg/11"},{"display_name":"Industry, innovation and infrastructure","score":0.5378999710083008,"id":"https://metadata.un.org/sdg/9"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325902","display_name":"Beijing Municipal Science and Technology Commission","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W2118578357","https://openalex.org/W2168210873","https://openalex.org/W2185712591","https://openalex.org/W2551495154","https://openalex.org/W2585442625","https://openalex.org/W2588539916","https://openalex.org/W2899318436","https://openalex.org/W2953220880","https://openalex.org/W3001444716","https://openalex.org/W3011841712","https://openalex.org/W3030108690","https://openalex.org/W3039249296","https://openalex.org/W3119520108","https://openalex.org/W3157853365","https://openalex.org/W3160410360","https://openalex.org/W3196186171","https://openalex.org/W3203945758","https://openalex.org/W3217094696","https://openalex.org/W4252801674","https://openalex.org/W4281612177","https://openalex.org/W4383215577","https://openalex.org/W4386520298","https://openalex.org/W4393237968","https://openalex.org/W4400412725","https://openalex.org/W4411711340","https://openalex.org/W4411868919","https://openalex.org/W4412076628","https://openalex.org/W4413001286","https://openalex.org/W7092602543"],"related_works":["https://openalex.org/W3000284535","https://openalex.org/W7202258685","https://openalex.org/W3197059557","https://openalex.org/W2896713431","https://openalex.org/W2807729037","https://openalex.org/W2349479872","https://openalex.org/W2896675513","https://openalex.org/W4381468577","https://openalex.org/W3044688879","https://openalex.org/W3121980869"],"abstract_inverted_index":{"This":[0],"study":[1,116],"addresses":[2],"the":[3,23,43,82,87,130,141,150,165,179,188,196],"heterogeneous":[4],"vehicle":[5],"routing":[6],"problem":[7],"for":[8],"hazardous":[9],"material":[10],"transportation":[11],"under":[12,93],"time-varying":[13],"risk":[14,39,55,191],"and":[15,34,46,52,67,79,91,102,107,112,134,152],"demand":[16,94],"uncertainty.":[17,95],"To":[18],"reflect":[19],"realistic":[20],"urban":[21],"conditions,":[22],"road":[24],"network":[25],"is":[26,98,168],"constructed":[27],"as":[28],"an":[29],"incomplete":[30],"graph":[31],"from":[32,118],"geographic":[33],"administrative":[35],"connectivity":[36],"rules.":[37],"The":[38,96],"assessment":[40],"model":[41,74,97],"captures":[42],"spatial":[44],"heterogeneity":[45],"temporal":[47],"variation":[48],"in":[49,170],"population":[50,65],"density":[51],"incorporates":[53],"vehicle-type-specific":[54],"coefficients,":[56],"with":[57,81,187],"each":[58],"trip":[59],"discretized":[60],"into":[61],"segments":[62],"to":[63],"evaluate":[64],"exposure":[66],"environmental":[68],"damage.":[69],"A":[70],"bi-objective":[71],"robust":[72,166],"optimization":[73],"minimizes":[75],"total":[76],"transport":[77],"cost":[78,185],"risk,":[80],"Bertsimas\u2013Sim":[83],"uncertainty":[84],"budget":[85,148],"controlling":[86],"trade-off":[88],"between":[89],"robustness":[90],"optimality":[92],"solved":[99],"by":[100],"NSGA-II":[101,128],"benchmarked":[103],"against":[104],"NSGA-III,":[105],"SPEA2,":[106],"MOEA/D":[108],"at":[109,182],"both":[110],"solution":[111],"front":[113,132],"levels.":[114],"Case":[115],"results":[117],"one":[119],"Beijing":[120],"chlorine":[121],"plant":[122],"serving":[123],"30":[124],"customers":[125],"show":[126],"that":[127,164],"achieves":[129],"best":[131],"quality":[133],"favorable":[135],"cost\u2013risk":[136],"balance.":[137],"Sensitivity":[138],"analysis":[139],"reveals":[140],"nonlinear":[142],"price":[143],"of":[144,195],"robustness:":[145],"a":[146,183],"minimal":[147],"restructures":[149],"fleet":[151],"routes,":[153],"whereas":[154],"further":[155],"increases":[156],"yield":[157],"only":[158],"marginal":[159],"adjustments.":[160],"Out-of-sample":[161],"experiments":[162],"confirm":[163],"plan":[167,181],"feasible":[169],"all":[171],"budget-covered":[172],"realizations,":[173],"delivering":[174],"36~65-percentage-point":[175],"feasibility":[176],"gains":[177],"over":[178],"deterministic":[180],"4.71%":[184],"premium,":[186],"mean":[189],"realized":[190],"staying":[192],"within":[193],"0.55%":[194],"nominal":[197],"value.":[198]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-29T00:00:00"}