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A Continuous Approximation Model for the Electric Vehicle Fleet Sizing Problem

hal.structure.identifierUniversity of Western Ontario [UWO]
dc.contributor.authorGONZÁLEZ-RODRÍGUEZ, Brais
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierFormulations étendues et méthodes de décomposition pour des problèmes génériques d'optimisation [EDGE]
dc.contributor.authorFROGER, Aurélien
hal.structure.identifierDipartimento di Electtronica, Informazione e Bioingegneria [Politecnico Milano] [POLIMI]
dc.contributor.authorJABALI, Ola
hal.structure.identifierUniversity of Western Ontario [UWO]
dc.contributor.authorNAOUM-SAWAYA, Joe
dc.date.accessioned2024-04-04T02:31:44Z
dc.date.available2024-04-04T02:31:44Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190329
dc.description.abstractEnEstablishing the size of an EV fleet is a vital decision for logistics operators. In urban settings, this issue is often dealt with by partitioning the geographical area around a depot into service zones, each served by a single vehicle. Such zones ultimately guide daily routing decisions. We study the problem of determining the optimal partitioning of an urban logistics area served by EVs. We cast this problem in a Continuous Approximation (CA) framework. Considering a ring radial region with a depot at its center, we introduce the electric vehicle fleet sizing problem (EVFSP). As the current range of EVs is fairly sufficient to perform service in urban areas, we assume that the EV fleet is exclusively charged at the depot, i.e., en-route charging is not allowed. In the EVFSP we account for EV features such as limited range, and non-linear charging and energy pricing functions stemming from Time-of-use (ToU) tariffs. Specifically, we combine non-linear charging functions with pricing functions into charging cost functions, establishing the cost of charging an EV for a target charge level. We propose a polynomial time algorithm for determining this function. The resulting function is non-linear with respect to the route length. Therefore, we propose a Mixed Integer Non-linear Program (MINLP) for the EVFSP, which optimizes both dimensions of each zone in the partition. We strengthen our formulation with symmetry breaking constraints. Furthermore, considering convex charging cost functions, we show that zones belonging to the same ring are equally shaped. We propose a tailored MINLP formulation for this case. Finally, we derive upper and lower bounds for the case of non-convex charging cost functions. We perform a series of computational experiments. Our results demonstrate the effectiveness of our algorithm in computing charging cost functions. We show that it is not uncommon that these functions are non-convex. Furthermore, we observe that our tailored formulation for convex charging cost functions improves the results compared to our general formulation. Finally, contrary to the results obtained in the CA literature for combustion engine vehicles, we empirically observe that the majority of EVFSP optimal solutions consist of a single inner ring.
dc.language.isoen
dc.subject.enContinuous Approximation
dc.subject.enElectric Vehicles
dc.subject.enFleet Sizing
dc.subject.enRegion Partitioning
dc.title.enA Continuous Approximation Model for the Electric Vehicle Fleet Sizing Problem
dc.typeDocument de travail - Pré-publication
dc.subject.halInformatique [cs]/Recherche opérationnelle [cs.RO]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04362876
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04362876v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GONZ%C3%81LEZ-RODR%C3%8DGUEZ,%20Brais&FROGER,%20Aur%C3%A9lien&JABALI,%20Ola&NAOUM-SAWAYA,%20Joe&rft.genre=preprint


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