{"id":"https://openalex.org/W7120074006","doi":"https://doi.org/10.3390/fi18010045","title":"Linearization Strategies for Energy-Aware Optimization of Single-Truck, Multiple-Drone Last-Mile Delivery Systems","display_name":"Linearization Strategies for Energy-Aware Optimization of Single-Truck, Multiple-Drone Last-Mile Delivery Systems","publication_year":2026,"publication_date":"2026-01-09","ids":{"openalex":"https://openalex.org/W7120074006","doi":"https://doi.org/10.3390/fi18010045"},"language":"en","primary_location":{"id":"doi:10.3390/fi18010045","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fi18010045","pdf_url":"https://www.mdpi.com/1999-5903/18/1/45/pdf?version=1767967836","source":{"id":"https://openalex.org/S34838331","display_name":"Future Internet","issn_l":"1999-5903","issn":["1999-5903"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Future Internet","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-5903/18/1/45/pdf?version=1767967836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107450928","display_name":"Ornela Gordani","orcid":null},"institutions":[{"id":"https://openalex.org/I68784830","display_name":"University of Tirana","ror":"https://ror.org/03g9v2404","country_code":"AL","type":"education","lineage":["https://openalex.org/I68784830"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Ornela Gordani","raw_affiliation_strings":["Faculty of Natural Sciences, University of Tirana, 1016 Tirana, Albania"],"affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences, University of Tirana, 1016 Tirana, Albania","institution_ids":["https://openalex.org/I68784830"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Eglantina Kalluci","orcid":"https://orcid.org/0009-0001-9039-1310"},"institutions":[{"id":"https://openalex.org/I68784830","display_name":"University of Tirana","ror":"https://ror.org/03g9v2404","country_code":"AL","type":"education","lineage":["https://openalex.org/I68784830"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Eglantina Kalluci","raw_affiliation_strings":["Faculty of Natural Sciences, University of Tirana, 1016 Tirana, Albania"],"affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences, University of Tirana, 1016 Tirana, Albania","institution_ids":["https://openalex.org/I68784830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107204839","display_name":"Fatos Xhafa Xhafa","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Fatos Xhafa","raw_affiliation_strings":["Department of Computer Science, Universitat Polit\u00e8cnica de Catalunya, 08028 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universitat Polit\u00e8cnica de Catalunya, 08028 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5107204839"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06859673,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"45","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11133","display_name":"UAV Applications and Optimization","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11133","display_name":"UAV Applications and Optimization","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.01269999984651804,"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/T11942","display_name":"Transportation and Mobility Innovations","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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":0.7408999800682068},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.671500027179718},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6269000172615051},{"id":"https://openalex.org/keywords/energy-consumption","display_name":"Energy consumption","score":0.5633999705314636},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5160999894142151},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5067999958992004},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4399000108242035}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8126000165939331},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7408999800682068},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.671500027179718},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6413000226020813},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6269000172615051},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5160999894142151},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5067999958992004},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4212000072002411},{"id":"https://openalex.org/C59519942","wikidata":"https://www.wikidata.org/wiki/Q650665","display_name":"Drone","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C134066672","wikidata":"https://www.wikidata.org/wiki/Q1424639","display_name":"Payload (computing)","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/fi18010045","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fi18010045","pdf_url":"https://www.mdpi.com/1999-5903/18/1/45/pdf?version=1767967836","source":{"id":"https://openalex.org/S34838331","display_name":"Future Internet","issn_l":"1999-5903","issn":["1999-5903"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Future Internet","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/452153","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/452153","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:4473599f74e24fe196ad6be39a35baec","is_oa":true,"landing_page_url":"https://doaj.org/article/4473599f74e24fe196ad6be39a35baec","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Future Internet, Vol 18, Iss 1, p 45 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/fi18010045","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fi18010045","pdf_url":"https://www.mdpi.com/1999-5903/18/1/45/pdf?version=1767967836","source":{"id":"https://openalex.org/S34838331","display_name":"Future Internet","issn_l":"1999-5903","issn":["1999-5903"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Future Internet","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4557722210884094,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7120074006.pdf","grobid_xml":"https://content.openalex.org/works/W7120074006.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,139],"increasing":[1],"demand":[2],"for":[3],"rapid":[4],"and":[5,45,72,102,126,166,260],"sustainable":[6],"parcel":[7],"delivery":[8,30,43,86,252],"has":[9,32],"motivated":[10],"the":[11,26,57,80,93,115,118,122,150,159,180,193,197,205,227,239,248,251],"exploration":[12],"of":[13,56,62,83,104,161,177,213,219,247],"innovative":[14],"logistics":[15],"systems":[16,51],"that":[17,131,204],"integrate":[18],"drones":[19],"with":[20,88],"traditional":[21],"ground":[22],"vehicles.":[23],"Among":[24],"these,":[25],"single-truck,":[27],"multiple-drone":[28],"last-mile":[29],"configuration":[31],"attracted":[33],"significant":[34],"attention":[35],"due":[36],"to":[37,40,157,216,229,241,254,257],"its":[38],"potential":[39],"reduce":[41,210],"both":[42],"time":[44,165,212],"environmental":[46],"impact.":[47],"However,":[48],"optimizing":[49],"such":[50,68],"remains":[52],"computationally":[53],"challenging":[54],"because":[55],"nonlinear":[58,98,214],"energy":[59,106,223],"consumption":[60,107],"behavior":[61],"drones,":[63],"which":[64],"depends":[65],"on":[66,92,163],"factors":[67],"as":[69,96],"payload":[70],"weight":[71],"travel":[73],"time,":[74],"among":[75],"others.":[76],"This":[77,235],"study":[78],"investigates":[79],"energy-aware":[81],"optimization":[82,211],"truck\u2013drone":[84],"collaborative":[85],"systems,":[87],"a":[89,153,175,188,200,242],"particular":[90],"focus":[91],"mathematical":[94],"formulation":[95],"mixed-integer":[97,142],"problem":[99,144,171,232],"(MINLP)":[100],"formulations":[101,146],"linearization":[103,129,162,207],"drone":[105],"constraints.":[108],"Building":[109],"upon":[110],"prior":[111],"models":[112],"proposed":[113],"in":[114,117,179,199],"literature":[116,194],"field,":[119],"we":[120],"analyze":[121],"MINLP":[123],"computational":[124,184],"complexity":[125],"introduce":[127],"alternative":[128],"strategies":[130],"preserve":[132],"model":[133,228],"accuracy":[134],"while":[135],"improving":[136],"performance":[137,236],"solvability.":[138],"resulting":[140],"linearized":[141],"linear":[143],"(MILP)":[145],"are":[147],"solved":[148],"using":[149],"PuLP":[151],"software,":[152],"Python":[154],"library":[155],"solver,":[156],"evaluate":[158],"efficacy":[160],"computation":[164],"solution":[167,246],"quality":[168],"across":[169],"diverse":[170],"instance":[172],"sizes":[173],"from":[174,187,192],"benchmark":[176,191],"instances":[178,233],"literature.":[181],"Thus,":[182],"extensive":[183],"results":[185],"drawn":[186],"standard":[189],"dataset":[190],"by":[195],"running":[196],"solver":[198],"cluster":[201],"infrastructure":[202],"demonstrated":[203],"designed":[206],"methods":[208],"can":[209],"solvers":[215],"several":[217],"orders":[218],"magnitude":[220],"without":[221],"compromising":[222],"estimation":[224],"accuracy,":[225],"enabling":[226],"handle":[230],"larger":[231],"effectively.":[234],"improvement":[237],"opens":[238],"door":[240],"real-time":[243],"or":[244],"near-real-time":[245],"problem,":[249],"allowing":[250],"system":[253],"dynamically":[255],"react":[256],"operational":[258],"changes":[259],"uncertainties":[261],"during":[262],"delivery.":[263]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2026-01-10T00:00:00"}