S Pradère

Dilhaire

Infrared thermotransmittance-based temperature field measurements in semitransparent media


P Ruyer

Recently revisited TH issues and associated R&D A french perspective

This paper presents an overview of some recent evolutions in the field of thermal-hydraulics (TH) within nuclear safety studies in France, therefore restricted to Pressurized Water Reactors (PWR) design, from the perspective of the French Technical Support Organization IRSN (Institut de Radioprotection et de Sûreté Nucléaire). These evolutions can concern either the hypothetical accident scenario (recently raised questions, modified rulemaking, new methodology) or the development of recent sources of knowledge (experimental programs, advanced numerical simulation tools).

Introduction

This paper presents an overview of some recent evolutions in the field of thermal-hydraulics (TH) within nuclear safety studies in France, therefore restricted to Pressurized Water Reactors (PWR) design, from the perspective of the French Technical Support Organization IRSN (Institut de Radioprotection et de Sûreté Nucléaire). These evolutions can concern either the hypothetical accident scenario (recently raised questions, modified rulemaking, new methodology) or the development of recent sources of knowledge (experimental programs, advanced numerical simulation tools). As far as TH is concerned, the recent evolution of methods reveals an attempt to more precisely determine the flow structure by taking into account 3D effects. During last decades, lot of development have been made that consider either the extension toward 3D capabilities of system scale or component scales simulation tools or the application of Computational Fluid Dynamics to nuclear safety related issues. We refer here to recent CSNI reports as well as companion papers of this special issue about "Capabilities of 3D thermal-hydraulic codes (3DSYSTH)", [START_REF] Ch | CSNI Status Report "3D capabilities of Thermalhydraulic system codes": lesson learned, Nucl. Eng. Des. Virtual Special Section on "NEA/CSNI/WGAMA "Specialists meeting on Nuclear Thermal-Hydraulics in water cooled reactors[END_REF][START_REF] Nea | Status on Simulation Capability of 3D System-Scale Thermal-Hydraulic (T/H) Analysis Codes[END_REF], and about the CFD activities, [START_REF] Nea | Technical Opinion Paper on the Use of CFD for Nuclear Safety[END_REF][START_REF] Ruyer | Status and perspectives of CFD, A short overview based on WGAMA activities, Nuclear Eng. Design. Virtual Special Section on "NEA/CSNI/WGAMA "Specialists meeting on Nuclear Thermal-Hydraulics in water cooled reactors[END_REF]. As an illustrative example, in France, CFD is now considered in more and more safety studies, [START_REF] Ruyer | Using CFD in the frame of safety studies -Some IRSN experiences[END_REF].

Recent evolutions of understanding of the fuel behaviors at high burnup also lead to better consideration of the burnup impact during accidental conditions [START_REF] Zhang | Safety and Performance of High Burnup Fuels: A Utility's Perspective[END_REF], and more especially on Hydrogen assisted PCMI brittle failure during Reactivity Initiated Accidents (RIA) This leads to needs for updates of safety models and codes. Moreover, those elements led to recent updates of Burnup dependent safety criteria proposed by the USNRC and the regulators of other countries. Their review allows for identifying current trends in TH and potential needs for future research and development programs.

In the first part, the evolution of the French Loss Of Coolant Accident (LOCA) Fuel Safety Criteria demonstration is presented with corresponding methodology assessment and on-going R&D programs. In the second part, the Spent Fuel Pools Loss of Cooling scenario is reviewed according to the lessons learned from Fukushima. In the third part, the question of the post-DNB fuel behavior is raised through different accident scenarios (RIA, LOCA, SGTR). The last fourth part addresses the generic evolutions related to the 3D capabilities of numerical tools (for system scale, component scale and CFD approaches).

Loss Of Coolant Accident

Based on the technical assessment of IRSN, the French Advisory Committee for nuclear reactors (GPR) recommended in 2010 in the frame of the French LOCA rulemaking to examine the validity of the safety requirements related to the two modes of fuel degradation during LOCA (ductile mode and brittle mode) in the light of state-of-the-art of the last thirty years. French utility EDF proposed a new methodology to address those points and IRSN made its assessment [START_REF] Graff | New LOCA and RIA Fuel Safety Criteria in France[END_REF].

A first evolution concerns the reference transients in the safety demonstration, [START_REF] Boutin | A new method taking into account physical phenomena related to fuel behavior during LOCA[END_REF][START_REF] Boutin | A new LOCA safety demonstration in France[END_REF]: EDF takes now into account the same break sizes limited by pipe whip restraints for both thermal-hydraulics and mechanical analysis. Regarding the thermal-hydraulics analysis, it is important to emphasize that such an evolution of LOCA reference transients leads to focus on a better modeling of the physical phenomena for Intermediate Breaks (IB) LOCA conditions rather than focus only on the 2A break that is now excluded from the safety demonstration (according to justifications concerning pipe break risks). For such IB-LOCA conditions, the level of the core pressure during the transient is higher than for the largest 2A break. At those pressure levels, steam has larger cooling efficiency than at low pressure, but studies revealed that there are still issues regarding the core uncovery phase of the transient, [START_REF]NEA, Nuclear Fuel Behaviour in Loss-of-coolant Accident (LOCA) Conditions[END_REF]. Most of the past R&D programs regarding reflooding have been devoted to 2A break scenario and constitute the validation database of TH system scale tools for LOCA. Therefore, this reference transients' evolution certainly revealed interest in experimental programs related to IB-LOCA TH's conditions. Moreover, the evolution of the French methodology includes a 3D model for the RPV-TH (including downcomer). Both evolutions require revisiting the database and identifying the pertinent tests conditions for evaluating numerical simulation performances with respect to those aspects, [START_REF] Bestion | 3D core thermalhydraulic phenomena in PWR SBLOCAs and IBLOCAs[END_REF]. IB-LOCA conditions and/or 3D flows in undegraded core geometries have been addressed in several past programs (e.g. PERICLES at high pressure, [START_REF] Veteau | PERICLES programme: boil-up, boil-off and reflooding high pressure experiments in a PWR assembly[END_REF], LSTF/ROSA [START_REF] Jaea | Final Data Report of ROSA-2/LSTF IB-CL-05 (Cold Leg Intermediate Break LOCA[END_REF], PKL [START_REF] Sanchez | Simulation of the LSTF-PKL Counterpart G7.1 Test at PKL Facility Using TRACE 5[END_REF], BETHSY [START_REF] Bazin | Investigation of PWR accident situations at BETHSY facility[END_REF], ATLAS [START_REF] Nea | Summary and Conclusions of the Joint PKL-ATLAS Workshop on Analytical Activities Related to the NEA PKL-4 and ATLAS-2 Projects[END_REF], and for 3D aspects, SCTF and CCTF [START_REF] Damerell | 2D/3D Program Work Summary Report[END_REF], and PERICLES 2D [START_REF] Morel | Validation of the Cathare code against Pericles 2D boil up tests[END_REF], for the core or DYNAS for the downcomer [START_REF] Euh | Identification of twodimensional void profile in a large slab geometry using an impedance measurement method[END_REF]). Moreover, plant applications revealed higher sensitivity of the transient in IB-LOCA conditions (with respect to LB-LOCA) to some parameters e.g. the flow rate of the safety injection system. For smaller breaks, the pressure decrease is slower and this leads to a delayed injection of water, and a lower driving force for the flow rate. Location of the break can therefore play a different role according to the LB-LOCA scenario. This led the Utility better justifying how conservatisms could cover the induced uncertainty. Moreover, in the frame of the NEPTUNE joint project (French platform on TH gathering CEA, EDF, IRSN and FRAMATOME) a specific METERO-V program has been defined for validation of 3D crossflows, [START_REF] Bestion | Improved PWR LOCA Simulations Through Refined Core 3D Simulations -An Advanced 3D Modelling and the Associated METERO Validation Program[END_REF].

A review of past experimental programs notably revealed a TH issue related to the criterion of "coolability" for French PWRs. This criterion must be satisfied for the safety demonstration for PPC-4 postulated accidents (like LOCA). It corresponds to the following objective for the first barrier of the fuel containment: the geometrical structure of the core must not be damaged to ensure adequate core coolability. During the core uncovering, the clad temperature increases up to values about 750-800°C. From a thermo-mechanical viewpoint, due to the pressure drop in the primary system, fuel rods are subjected to internal pressure higher than the external one. Thus, under the effect of tensile stresses and high temperatures reached during the transient, clads are able to balloon. The clad ballooning phenomenon leads to blocked geometry, which can under a number of conditions reduce the heat exchange surfaces between the fuel rods and the coolant and redistribute coolant flows, jeopardizing core coolability [START_REF] Grandjean | A state-of-the-art review of past programs devoted to fuel behaviour under LOCA conditions -part1 Clad Swelling and Rupture Assembly Flow Blockage[END_REF][START_REF] Grandjean | A state-of-the-art review of past programs devoted to fuel behaviour under LOCA conditions -part2 Impact of clad swelling upon assembly cooling[END_REF].

Considering those phenomena in the safety demonstration requires additional models (taking into account fuel deformation impacts on TH) and the corresponding experimental database for validation. The state of the art study revealed that past experimental programs devoted to the reflooding with ballooned fuel rods had a systematic bias: they did not simulate properly the ballooned region thermal inertia associated with the potential fuel relocation within balloons, [START_REF] Grandjean | Coolability of blocked regions in a rod bundle after ballooning under LOCA conditions Main findings from a review of past experimental programmes[END_REF].

The IRSN PERFROI program, [START_REF] Repetto | The R&D PERFROI project on Thermal mechanical and thermal hydraulics behaviors of a fuel rod assembly during a Loss Of Coolant Accident[END_REF], addresses both thermal-mechanics and thermal-hydraulics aspects of the LOCA with respect to the renewed French rulemaking. For thermal-mechanics, it focused on the role of H2 pickup that plays a major role on clad mechanical properties besides the more classical focus on clad oxidation. Clad deformation dynamics due to pressure differential between internal and coolant pressure, impact of neighboring contact on balloon diameter and length are studied in the corresponding ranges of temperature and pressures thanks to dedicated experimental devices. It will allow improving the accuracy of LOCA predictions and validation of the R&D software for coupled thermal-hydraulics and thermal-mechanics DRACCAR, [START_REF] Glantz | DRACCAR: A multi-physics code for computational analysis of multi-rod ballooning, coolability and fuel relocation during LOCA transients. Part Two: Overview of modeling capabilities for LOCA[END_REF][START_REF] Glantz | DRACCAR: A multi-physics code for computational analysis of multi-rod ballooning, coolability and fuel relocation during LOCA transients Part one: General modeling description[END_REF]. More especially, the COAL experiments are dedicated to the coolability of ballooned regions simulating the effect of fuel relocation through a wide range of TH conditions covering IB-LOCA cases, that clearly impact the reflooding [START_REF] Repetto | Core Coolability in Loss of Coolant Accident: the Coal Experiments[END_REF].

LOCA is one of the most typical transients for TH in the field of nuclear safety. Despite decades of R&D on the topic from the very first developments of power plants, the subject will still lead part of the future TH developments.

Spent Fuel Pools Loss of Cooling accident

Fukushima Daïchi 2011 events certainly draw attention to the safety issues related to SFP accident scenario and extend the interest about transients of loss of cooling. It led to several plant actions in order to improve the reliability of cooling systems. In the frame of the NEA/CSNI activities, the state of the art report produced in 2015, [START_REF] Adorni | Status Report on Spent FuelPools under Loss-of-Cooling and Loss-of-Coolant Accident Conditions[END_REF], also revealed some lacks of knowledge that were more precisely addressed in the PIRT exercise, [START_REF] Adorni | Phenomena Identification and Ranking Table: R&D Priorities for Loss-of-Cooling and Loss-of-Coolant Accidents in Spent Nuclear Fuel Pools[END_REF]. Please refer to the companion paper of this issue for more information, [START_REF] Trégourès | NEA/CSNI/WGAMA "Specialists meeting on Nuclear Thermal-Hydraulics in water cooled reactors[END_REF].

In France, EDF addressed updated safety demonstration of the scenario of loss of cooling and studied for example the ability to restart the cooling system within a boiling pool. This situation requires evaluating precisely the temperature and potential void fields within the pool under buoyancy driven flow conditions with evaporation at the pool's free surface. Numerical solving of this fully 3D problem is nothing but trivial. For this purpose, EDF developed CFD based studies [START_REF] Simoneau | Numerical Investigations of a Spent Fuel Storage Pool in Abnormal Conditions[END_REF][START_REF] Mérigoux | Modelling of the natural circulation flow in pool boiling with NEPTUNE_CFD[END_REF], that were assessed by IRSN in the frame of the safety demonstration of French EPR FA3, [START_REF] Asn | Réacteurs électronucléaires -EDF -Réacteur EPR de Flamanville 3 Sûreté de l'entreposage et de la manutention du combustible dans le bâtiment combustible[END_REF]. EDF had to provide complementary elements to ensure the restart of the cooling system since CFD codes were still insufficiently validated for such flow conditions. In particular, the evaporation at the free surface in such highly turbulent natural convection requires specific validation data that are not available. Moreover, the potential nucleation of gas (dissolved and vapor) bubbles within liquid water at temperature close to the saturation one have to be considered. Meanwhile, IRSN developed the R&D program DENOPI, [START_REF] Martin | The IRSN DENOPI Project: A Research Program on Spent-Fuel-Pool Loss-Of-Cooling and Loss-Of-Coolant Accidents[END_REF]. It covers TH issues for both loss of coolant and loss of cooling issues. Within this project, MEDEA already provided results concerning potential CCFL (Counter Current Flow Limitation) issue in fuel assemblies within a pool under a spray cooling system, [START_REF] Brillant | Experimental Study of an Adiabatic Two-Phase Flow in a Simulated PWR Spent Fuel Bundle[END_REF]. ASPIC did provide data for the thermal aspects of the problem and evaluate spray cooling efficiency for partially uncovered assemblies, [START_REF] Migot | DENOPI project devoted to spent fuel pool accidents: overview on the thermal hydraulics experimental facilities[END_REF]. MIDI facility, [START_REF] Migot | DENOPI project devoted to spent fuel pool accidents: overview on the thermal hydraulics experimental facilities[END_REF], is a large basin built for the study of buoyancy driven flow of large pools near boiling conditions. A first test matrix achieved during DENOPI project revealed the facility can determine the partition between the three main vapor regimes (namely 1/Evaporation at the free surface, 2/ Flashing of superheated water in the upper part of the pool, 3/ Nucleate boiling into the assemblies) in competition during loss of cooling conditions. Tests analysis revealed that both flashing and dissolved gases are playing a significant role in the process. Further tests with potential improved instrumentation are required to deeper understand those phenomena. IRSN is currently in discussion with interested partners for the proposal of an OECD joint project based on those facilities to extend the actual database and propose experiments vs numerical simulation benchmarks on these topics.

It is worth pointing out that during the last decade, SFP became a renewed subject of interest and led to focus on complex buoyancy driven flows. But the topic of buoyancy driven flow of large pools as being heat exchangers is not restricted to Loss of Cooling accidental scenarios in SFP. Many under development passive systems (either for Small Modular Reactors projects but also for next generation of Light Water Reactors) have large basins that under accidental conditions may encounter similar flow conditions. For such high Rayleigh number conditions and close to nucleation or nucleate boiling conditions, the capability of numerical simulation tools must be assessed [START_REF] Ch | IRSN activities related to passive safety systems assessment[END_REF][START_REF] Nea | Status Report on Reliability of Thermal-Hydraulic Passive Systems[END_REF][START_REF] Mascari | Small modular reactors and insights on passive mitigation strategy modeling[END_REF].

Post-DNB fuel behavior

Reactivity Initiated Accidents (RIA), and more especially Rod Ejection Accident scenario for PWR (REA), a PPC-41 scenario for which the fuel's cladding is particularly stressed. It has some similarities with the rod drop accident (RDA) for Boiling Water Reactors (BWR). In this scenario, a large power pulse initiated by reactivity transient leads to a very rapid heating of the fuel. The first phase of the transient is a purely thermomechanical phenomenology leading to a Pellet-Clad Mechanical Interaction. It is followed by a potential large temperature increase of the cladding. This could lead to film boiling over the cladding: the so-called post-DNB (Departure from Nucleate Boiling) phase. Clad failure risk evaluation must cover both phases of the transient. For the post-DNB phase, the coupling between thermal-mechanics and thermal-hydraulics is strong: at high temperatures, the cladding yield stress strongly decreases, but meanwhile, large deformation cladding induced by internal pressurization thermally insulates cladding from hot fuel. Recent CSNI/WGFS fuel code benchmark showed a huge scattering of clad behavior as soon as DNB events occur, [START_REF] Marchand | Reactivity initiated accident (RIA) fuel codes benchmark Phase-II: Uncertainty and sensitivity analyses[END_REF]. It led to recommendations in the recently updated version of the OECD RIA state of the art report [START_REF]NEA, State-of-the-art Report on Nuclear Fuel Behaviour Under Reactivity-initiated Accident Conditions (RIA SOAR)[END_REF]. The experimental database for RIA is still very limited as soon as realistic TH conditions for a PWR REA are concerned. This concerns both the prediction of the occurrence of the boiling crisis (transient CHF) and the post-DNB clad-to-coolant heat transfer. The on-going OECD CABRI International Program led by IRSN allows for simulating RIA in those conditions, [START_REF] Biard | Reactivity Initiated Accident transient testing on irradiated fuel rods in PWR conditions: The CABRI International Program[END_REF]. It will provide new insights of these transient boiling conditions at convective high pressure and high temperature conditions.

In the field of research reactors with plate fuels for material testing, the BORAX scenario is currently considered. This reactivity-initiated accident could lead to massive melting of the core and subsequent vapor explosion. Determination of the thermal energy for this explosion was in the past estimated using conservative assumptions, [START_REF] Couturier | Elements of nuclear safety: research reactors[END_REF]. CEA recently updated the safety demonstration method by considering a best-estimate simulation of the transient for the JHR project, [START_REF] Maugard | BORAX publication[END_REF]. In such a BORAX transient, determination of the void related reactivity feedback could play a role in mitigating the violence of the explosion. In those transient boiling conditions, DNB could occur. Validation of the coolant vaporization is clearly a challenge since (i) the deposited energy depends on the void creation and (ii) melting of the fuel elements depends on the clad-to-coolant heat transfer, both void creation and heat transfer varying in order of magnitude according to the boiling regime. A coupled (neutronics and thermal hydraulics) solving method is used to estimate the melting of the fuel elements. Validation of the methodology is based on the past SPERT-IV inpile program, [START_REF] Day | The use of experimental data in an MTR-type nuclear reactor safety analysis[END_REF][START_REF] Crocker | Reactor Power Excursion Tests in the SPERT IV Facility[END_REF], and on a dedicated R&D program on transient boiling, e.g. [START_REF] Kossolapov | Transient flow boiling CHF under exponentially escalating heat inputs[END_REF].

EDF recently modified its safety demonstration regarding LOCA and Steam Generator Tube Rupture (SGTR) scenarios, [START_REF] Th | Projet EPR de Flamanville-Analyse des éléments transmis par EDF à la suite de la réunion du GPR « Examen du rapport de sûreté EPR de Flamanville » des 4 et 5 juillet 2018[END_REF]. This modification concerns the determination of the risk of failure of the fuel rods that experience DNB during the very first times of the transient. The demonstration now studies more precisely the potential consequences of the DNB in those specific conditions. During the assessment process, IRSN and EDF considered the review of past experimental programs. The Power Cooling Mismatch experiments program, [START_REF] Levine | Power Burst Facility (PBF) single Rod Power-Cooling Mismatch (PCM) Test Results[END_REF], is of particular interest regarding the fuel behavior under high pressure high temperature post-DNB events and revealed very specific phenomenology like post-DNB induced bowing of the rods. This bowing could lead to potential consequences in the next phases of the considered transients. Such bowing is initiated by localized and transient azimuthal temperature gradients along the rod, [START_REF] Gunnerson | Behavior of a nine-rod fuel assembly during Power-Cooling-Mismatch conditions -Results of test PCM-5[END_REF]: prediction of its occurrence in an accidental scenario is a challenge that intimately couples local thermal-hydraulics and thermal-mechanics predictions. Complementary experiments could be required to validate the conditions of bowing occurrence for well characterized thermal conditions representative of post-DNB.

Therefore, it appears that post-DNB and fast transient boiling phenomenology are still challenges for some nuclear safety related issues. Many past experimental programs are very valuable for the analysis, but corresponding data can be insufficient for validation of best-estimate methodologies. Therefore, this topic can be identified for future TH R&D activities.

Conclusions

The not exhaustive but illustrative set of examples of the previous sections clearly illustrates that thermalhydraulics for nuclear safety studies in water cooled reactors is still a very active field. Evolutions of either safety demonstration methods or scientific new knowledge provide renewed challenges. It also reveals that ongoing R&D considers a more extended validation range for coupling TH with neutronics and thermalmechanics or for 3D TH computations. This requires revised PIRT and potentially a new experimental database.

Plan Condition Category (PCC): PCC-4 corresponds to Category 4 Operating Conditions in the french set of events considered for the safety demonstration ; Category 4 accidents are hypothetical accidents nevertheless taken into account for safety purposes.


Antoine Robichet
email: antoine.robichet@univ-eiffel.fr

Patrick Nierat
email: patrick.nierat@univ-eiffel.fr

Francois Combes
email: francois.combes@univ-eiffel.fr

Delivering Paris by Cargo Bikes: Ecological Commitment or Economically Feasible? The Case of a Parcel Service Company

Keywords: Urban Good Movement, Cargo Bikes, Urban logistics, Micro hub, Last mile, parcel service

come

INTRODUCTION

Urban logistics is a key step in the delivery chain. The use of trucks in crowded areas such as city centers generates numerous negative externalities (congestion, noise, pollution, etc.) [START_REF] Hammami | The Impact of Optimizing Delivery Areas on Urban Traffic Congestion[END_REF][START_REF] Olsson | Framework of Last Mile Logistics Research: A Systematic Review of the Literature[END_REF]. Moreover, consumer habits are currently undergoing changes that tend to significantly increase e-commerce (especially small parcels), increasing the number of delivery channels within cities [START_REF] Savelsbergh | City Logistics: Challenges and Opportunities[END_REF].

The proposed solutions to reduce negative externalities mainly rely on breakthrough technologies that change the current codes of delivery (a round starting from and ending at a cross-docking platform located in the urban periphery) [START_REF] Szymczyk | Challenges in General Cargo Distribution Strategy in Urban Logistics -Comparative Analysis of the Biggest Logistics Operators in EU[END_REF]. Nowadays, most of new ideas (cargo bikes, delivery robots) are based on the presence of additional transfers. These transfers imply additional smaller platforms, often referred to as micro-hubs, which can be buildings (e.g., a small warehouse in a building), or mobile assets (e.g., parked container in street during the day). From this point, operations are conducted on a star-shape around it [START_REF] Gruber | A New Vehicle for Urban Freight? An Ex-Ante Evaluation of Electric Cargo Bikes in Courier Services[END_REF][START_REF] Affonso | Using Urban Consolidation Centre with Cycloscargos Support to Increase the Performance and Sustainability of Urban Logistics: A Literature Review and a Case Study in the City of São Paulo[END_REF][START_REF] Lenz | Bikes for Urban Freight?[END_REF][START_REF] Marujo | Assessing the Sustainability of Mobile Depots: The Case of Urban Freight Distribution in Rio de Janeiro[END_REF]. These micro hubs are not intended to be connected to all the platforms on a national scale, but to operate and communicate only with the peripheral platforms and thus to operate as satellites of the latter [START_REF] Robichet | Consequences of Logistics Sprawl: Order or Chaos? -The Case of a Parcel Service Company in Paris Metropolitan Area[END_REF][START_REF] Klauenberg | Dynamics of the Spatial Distribution of Hubs in Groupage Networks -The Case of Berlin[END_REF][START_REF] Heitz | The Parcel Industry in the Spatial Organization of Logistics Activities in the Paris Region: Inherited Spatial Patterns and Innovations in Urban Logistics Systems[END_REF].

However, micro-hubs are costly (rent, additional needed managers, etc.). With a high density of pickup and delivery operations, it is possible that the cost of the micro-hub is more than compensated by savings on transportation costs [START_REF] Choubassi | Economic Analysis of Cargo Cycles for Urban Mail Delivery[END_REF][START_REF] Arnold | Simulation of B2C E-Commerce Distribution in Antwerp Using Cargo Bikes and Delivery Points[END_REF][START_REF] Mcleod | Quantifying Environmental and Financial Benefits of Using Porters and Cycle Couriers for Last-Mile Parcel Delivery[END_REF]. On the other hand, the high cost of land is a key limitation in the implementation of these new solutions (15). For instance, in Paris, land pressure is extremely high and platforms are driven to the periphery [START_REF] Dablanc | The Impacts of Logistics Sprawl: How Does the Location of Parcel Transport Terminals Affect the Energy Efficiency of Goods' Movements in Paris and What Can We Do about It[END_REF]. Among these solutions, the bicycle has the advantage of being already technically mature as well as being already present in the urban environment (by the previous presence of cyclists). Furthermore, using bikes is possible under current regulation (which isn't true for drones, for example). However, the use of cargo bikes adds a link to the chain and multiplies the number of vehicles used to carry out the entire operation. Furthermore, the last mile is mostly done by subcontractors, which can make it more difficult for companies to fully control how parcels are operated [START_REF] Rème-Harnay | Evolution Des Stratégies de Gestion de La Main d'oeuvre Du Dernier Kilomètre à l'ère Des Plateformes Numériques : Impact Sur Le Marché Du Travail et La Précarité[END_REF]. Nevertheless, the possibility to use electric cargo bikes allows to transport important loads (up to 200 kg) with no major difficulty. A review of the literature was done by [START_REF] Llorca | Assesment of the Potential of Cargo Bikes and Electrification for Last-Mile Parcel Delivery by Means of Simulation of Urban Freight Flows[END_REF] [START_REF] Llorca | Assesment of the Potential of Cargo Bikes and Electrification for Last-Mile Parcel Delivery by Means of Simulation of Urban Freight Flows[END_REF]. Amongst the important points, cargo bikes offer other advantages such as:

-Lower vehicle costs (purchase, maintenance and insurance); -Fast and reliable movement in dense areas (less dependent on traffic jam); -The possibility to park close to the delivery/shipping points [START_REF] Mcleod | Quantifying Environmental and Financial Benefits of Using Porters and Cycle Couriers for Last-Mile Parcel Delivery[END_REF]; -Less road and parking consumption due to the smaller size of the vehicle; -Cleaner and less negative externalities than most other modes of transportation (especially trucks) [START_REF] Arnold | Simulation of B2C E-Commerce Distribution in Antwerp Using Cargo Bikes and Delivery Points[END_REF][START_REF] Mcleod | Quantifying Environmental and Financial Benefits of Using Porters and Cycle Couriers for Last-Mile Parcel Delivery[END_REF][START_REF] Koning | The Good Impacts of Biking for Goods: Lessons from Paris City[END_REF][START_REF] Melo | Evaluating the Impacts of Using Cargo Cycles on Urban Logistics: Integrating Traffic[END_REF][START_REF] De Mello Bandeira | Electric Vehicles in the Last Mile of Urban Freight Transportation: A Sustainability Assessment of Postal Deliveries in Rio de Janeiro-Brazil[END_REF][START_REF] Fraselle | Cost and Environmental Impacts of a Mixed Fleet of Vehicles[END_REF].

These new technologies are implemented to anticipate new regulations which aimed at reducing negative externalities in cities. Nowadays, these regulations mainly focus on the type of motorization (emission limitation via low emission zone), traffic and parking regulations in order to diminish negative externalities [START_REF] Dablanc | Best Practices in Urban Freight Management : Lessons from an International Survey[END_REF]. In the case of cargo bikes, cities can play a crucial role via the creation of cycle lanes, zero-emission zones, reduction of drive-through traffic, etc. [START_REF] Choubassi | Economic Analysis of Cargo Cycles for Urban Mail Delivery[END_REF][START_REF] Schliwa | Sustainable City Logistics -Making Cargo Cycles Viable for Urban Freight Transport[END_REF][START_REF] Rudolph | Cargo Cycles in Commercial Transport: Potentials, Constraints, and Recommendations[END_REF]. The policy objective is to constrain vehicle types to reduce negative externalities without preventing carriers from operating. Different studies have already been made in Portland and Seattle to compare cargo bikes and electric light commercial vehicles but with a smaller sample size and over a smaller geographic area compared to this study [START_REF] Tipagornwong | Analysis of Competitiveness of Freight Tricycle Delivery Services in Urban Areas[END_REF][START_REF] Sheth | Measuring Delivery Route Cost Trade-Offs between Electric-Assist Cargo Bicycles and Delivery Trucks in Dense Urban Areas[END_REF] In this study, we address the possibility to deliver by cargo bikes shipments which are traditionally delivered by trucks. To compare two low-emission solutions, delivery by cargo bikes will be evaluated against a fleet of electric LCVs (Light Commercial Vehicles). Thermal trucks are not considered because their costs are not comparable (much cheaper) to the two solutions mentioned above. The originality of this study is that it is based on an operational database of DB Schenker's activities during two months in the Ile-de-France region (600,000 data) in a sector where the lack of data is problematic [START_REF] Llorca | Assesment of the Potential of Cargo Bikes and Electrification for Last-Mile Parcel Delivery by Means of Simulation of Urban Freight Flows[END_REF][START_REF]A Concept for a National Freight Data Program[END_REF][START_REF] Chow | State-of-the Art of Freight Forecast Modeling: Lessons Learned and the Road Ahead[END_REF][START_REF] Outwater | Tour Based and Supply Chain Modeling for Freight: Integrated Model Demonstration in Chicago[END_REF]. DB Schenker is the second largest parcel company in France after the Geodis group and is principally oriented B2B (Business to Business consists of transactions between two companies, it is opposed to B2C, Business to Consumers) [START_REF] Faibis | Messagerie et Le Fret Express. Xerfi[END_REF]. From there, it was possible to conduct an economic analysis to compare the current costs to those of a cargo bikes' delivery system by estimating the fleet needed in both scenarios. In the scenario using cargo bikes, micro hubs are needed. We have studied two methods to implement micro hubs by district or by minimizing the distance between the delivery/pickup points and micro hubs (facility location problem).

This study is based on the same data base that Robichet and Nierat (2021) [START_REF] Robichet | Consequences of Logistics Sprawl: Order or Chaos? -The Case of a Parcel Service Company in Paris Metropolitan Area[END_REF]. This last study discusses the geographical implementation of DB Schenker's terminals in regards to the logistics sprawl at the Paris metropolitan area scale. In comparison, this study focuses on Paris intramuros and the possibilities for a green last mile. From a geographical point of view, as shown in Figure 1, Paris is cut in two (North/South) by the river Seine and is composed of 20 districts (built in a snail shape). Districts 12 and 16 are mainly composed of two large parks, the Bois de Vincennes and Bois de Boulogne.

MODEL PRESENTATION Territory studied

Running of parcel service carrier

Parcel service is a specific segment of freight transport. Goods are transported from the sender to the recipient under the supervision of a single company (which may deal with subcontractors). Transported goods generally weight between 1 and 500 kg. The average weight for Paris city is 88 kg in our database (Table 1). In terms of volume, shipments are generally limited to 3 pallets (beyond that, it is generally more attractive to use LTLless than truckloadservice).

Parcels are collected via rounds and transported to cross-docking terminals. From there, parcels are carried to the final terminal by heavy goods vehicles making long-distance connections (tractions).

There may be additional transshipments between the first and the last terminals. There, the parcels are affected to rounds to be transported to the recipients. Deliveries and pick-ups are integrated in same rounds. In this study, we aim at comparing two scenarios in terms of GHG emissions for the last mile. The first case consists in keeping the traditional organization and substituting the thermal LCV by electric LCV.

Rounds being relatively short in dense areas such as Paris, they are rarely more than 80 km long, a distance that can be achieved with the autonomy of an electric LCV. This is scenario S1. The second one is based on the use of cargo bikes. As the operating area of a cargo bike is smaller than that of a LCV, supplementary hubs, called micro hubs, are set up in dense areas. Micro-hubs support the national hubs at the local level (they are not directly connected to the national network). Cargo bikes operate in a radial pattern around micro hub. The number of operations per round is limited by their payload (200 kg). In addition to cargo bikes, electric LCV provide, firstly, the connection between terminals and micro hubs, and, secondly, operations for parcels over 200 kg and parcels more than 2 km away from the micro hubs. This is scenario S2. Those operations are summarized in Figure 3.

Data

The database has been acquired by extracting all DB Schenker's parcel activities in Paris metropolitan area over the period January to February 2018 (only 34 days over the two-month period were retained to avoid side effects). It is composed of two tables: deliveries and pick-ups. One record represents one shipment, it can be composed of one or several parcels. For both tables, each record has 19 variables including an ID (identification's key), date and time of the pick-up, names and addresses of senders and recipients, weight, first and last terminals, date and time of delivery and the round ID of delivery (the round ID of pick-up is not available).

The average weight of parcels (deliveries and pick-ups) in the Paris area is 88 kg (Table 1), which is lower than the average weight for the whole Ile-de-France region (105 kg). Furthermore, 91% of these parcels weigh less than 200 kg, which is the limit to be operated by cargo bikes. This high percentage encourages to study the feasibility of cargo bikes from an economic point of view. Furthermore, in comparison to the literature, the share of parcels that can be operated by cargo bikes (91%) is much higher than the 55% announced by Llorca et al. (2021) however the weight limit in [START_REF] Llorca | Assesment of the Potential of Cargo Bikes and Electrification for Last-Mile Parcel Delivery by Means of Simulation of Urban Freight Flows[END_REF] is 10 kg compared to the 200 kg limit in this study [START_REF] Llorca | Assesment of the Potential of Cargo Bikes and Electrification for Last-Mile Parcel Delivery by Means of Simulation of Urban Freight Flows[END_REF] (some cargo bike trailers can also moveas a cart of dollypackages weighing more than 50 kg).

Table 1 shows that there is a strong imbalance between deliveries (31,536) and pick-ups (5,098) within Paris. Conversely, there are more pick-ups than deliveries in the whole Paris metropolitan area.

Paris city

Paris

Geographical distribution

First, when studying the proportion of deliveries (31,536) vs. pick-ups (5,098) (Table 1), it is clear that Paris receives many more shipments than it sends. This is due to the limited number of production sites inside Paris.

Figure 4 shows the density of DB Schenker's operations (deliveries and pick-ups) within Paris for the two months. The scale is linear from 0 to 800 operation per km 2 , excepted one cell with a much higher density (1,216 operations/km 2 ), colored black.

The concentration of operations is high (in average 10.3 operations/km 2 /day) inside Paris; however, it is not uniformly distributed. Density peaks are mostly in the northern half. Finally, the figure shows that the delivery density is heterogenous inside administrative districts: it is relevant noting that this administrative partition is not necessarily the most relevant one to design a delivery operation process (section Model).

Model

In this section, the cost models of the different scenarios are described, and so are the two algorithms (facility location and vehicle routing problem) used for this study. The P-median algorithm is used to solve the facility location problem and for the spatial partitioning of Paris. Secondly, the vehicle routing problem was used to determine the size of the fleet needed to perform all the operations. Both algorithms are accessible in the Matlog package's [START_REF] Kay | Logistics Engineering Using Matlab[END_REF]. Those models were chosen over other more complex models as we do not have all necessary information to implement those (among the missing information, the delivery and pick-up time slots) [START_REF] Caggiani | A Green Logistics Solution for Last-Mile Deliveries Considering e-Vans and e-Cargo Bikes[END_REF] .

Cost models and assumptions

The following equipment was taken as a basis to derive the cost model:

an electric LCV with a payload of 1,420 kg (Renault Master): it was chosen because it is the electric vehicle with the highest payload without need for a heavy vehicle license;

an electric LCV with a payload of 4,500 kg (Fuso eCanter): it was chosen because it is an electric vehicle that is already part of DB Schenker's fleet;

an electric cargo bike with a payload of 200 kg.

The daily costs (total cost of vehicles, energy, maintenance, driver) are available in Under scenario S2, additional costs come from the micro-hubs, and the vehicles to supply those from the peripheral terminals. Each micro hub has a fixed rental cost (𝐶 𝑀𝐻 ), calculated from the average commercial actual estate prices for a 150 m 2 space (around 310 €/day). Therefore, the total retail cost is proportional to the number of micro-hubs.

To supply one micro-hub, we assume that LCVs (𝑁 𝐿𝐶𝑉𝑠𝑢𝑝𝑝𝑙𝑦,𝑖 ) are required for 2 hours per day (the LCV type depends on the actual load, the least expensive solution is kept).

The question is then to derive the number and location of these micro-hubs. Denote by n the number of micro-hubs. From micro hub 𝑖 ∈ {1, … , 𝑛}, the cargo bikes can operate p parcels up to 2 km around (this spatial limitation is an exogenous assumption ; it is consistent with the organization of DB Schenker in Paris and other French cities, and with the literature ( 27)).Therefore, the total cost per day (𝑇𝐶 𝐶𝐵,𝑖 ) to deliver p parcels for the micro hub i with N cargo bikes (𝑁 𝐶𝐵,𝑖 ) is:

𝑇𝐶 𝐶𝐵,𝑖 ሺ𝑝ሻ = 𝐶 𝑀𝐻 + 𝐶 𝐶𝐵 * 𝑁 𝐶𝐵,𝑖 ሺ𝑝ሻ + 2 7 * 𝐶 𝐿𝐶𝑉 * 𝑁 𝐿𝐶𝑉𝑠𝑢𝑝𝑝𝑙𝑦,𝑖 ሺ𝑝ሻ

𝐶 𝐶𝐵 and 𝐶 𝐿𝐶𝑉 denote, respectively, the daily cost of a cargo bike and a LCV (values in Table 2.) For the cost of the LCV, it depends on the actual type of vehicle required to supply the micro-hub (either a Renault Master or a Fuso eCanter).

𝑇𝐶 𝐹𝑙𝑒𝑒𝑡𝐿𝐶𝑉,𝑛 is the per day cost of the fleet of LCVs needed to operate parcels that cannot be operated by cargo bike, i.e. all the parcels that either weigh more than 200 kg and/or that are to be delivered 2 km from each of the micro hubs (see Vehicle Routing Problem). Hence, 𝑇𝐶 𝐹𝑙𝑒𝑒𝑡𝐿𝐶𝑉,𝑛 depends on the number of micro hubs.

Therefore, the total cost of S2 for n micro hubs is:

𝑇𝐶 𝑆2,𝑛 = 𝑇𝐶 𝐶𝐵,𝑖 𝑛 𝑖=1 + 𝑇𝐶 𝐹𝑙𝑒𝑒𝑡𝐿𝐶𝑉,𝑛 (2)
For both scenarios, the cost was calculated for each day over the study period. From this, a sizing at 80% of the activity has been chosen, in order not to consider the non-representative peak periods of activity or inactivity. During the study period a snowy episode has impacted the activity (decrease of activity) and the following days (increase in activity to balance).

Facility location -P-median Problem

Based on the carrier's activity, the question is whether or not it would be possible to optimize the location of the micro hubs. The algorithm is based on the P-median Model [START_REF] Hakimi | Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph[END_REF]. This continuous optimization model finds optimal locations for the terminals by minimizing the sum of the distances between these terminals (variable) and the delivery and pick-up points (input parameters). The following assumptions are made:

-Euclidean distance (assumption that the topography of the Paris road network has no impact); -Land price ignored;

-Existing infrastructures and buildings not considered;

-No construction of the rounds in the minimization (congestion ignored).

In order to respect DB Schenker's current organization (i.e. operations at the north of the Seine river are carried out from a platform which is located in the North of Paris, and vice versa for the South), Paris has been divided into two areas (referred to as North and South), and the cargo-bikes and electric LCV can hardly go from one of these areas of the other. In other words, a micro-hub cannot have a catchment area that overlaps the two sides of the river. Thus, the results are in line with the current organization of DB Schenker. Numbers of micro hubs from 1 to 20 were tested.

The locations of the micro hubs were calculated considering all delivery and pickup points over the whole period. To ensure that the set of locations found was a global solution and not a local optimum, the algorithm was run 100 times for each set of parameters with randomized initial states to avoid local optimum.

Vehicle Routing Problem (VRP)

The VRP problem is solved with the Matlog package [START_REF] Kay | Logistics Engineering Using Matlab[END_REF]. The objective is not to study the distances traveled but to obtain the minimal number of vehicles needed to operate a given number of parcels, considering:

-The payload of the vehicles;

-The weight of the parcels;

-The number of operations per round (Table 2). It appears from interviews and field visits that there are few parcels with time constraint for this operator, therefore, it is not considered.

The fleet optimization is performed separately for cargo bikes and electric LCVs. For cargo bikes, the fleet is calculated at the micro hub level and includes all parcels under 200 kg and within 2 km of the micro hub.

RESULTS

This study provides results on two levels: first, the optimization of the location of the micro hubs is essential to cost-efficiency and, second, the renting price of the micro hubs is the most limiting element for the implementation of a delivery by cargo bikes.

Location of micro hubs

There is a practical importance for a parcel operator to organize their operations with respect to existing administrative partitions, as it leverages easily available information, eases the burden on information provision and processing, both at the level of information systems and at the level of the operators actually making the deliveries. However, this principle may be costly, as it comes with an exogenous constraint on the design of the delivery process. This is tested below.

To address the impact of location of the micro hubs, two scenarios were compared:

-In the first one, administrative districts are used as a basis for micro-hub location;

-In the second one, the number and location of the micro hubs are optimized without considering the administrative division.

More precisely, in the first case, for each district, the potential location of one micro hub is fixed and set at the centroid of all operations in that district. As for the order of opening of the micro hubs, they are opened from the most economically profitable to the least profitable.

In the second case, for each iteration (i.e. number of micro hubs, ranging from 0 to 20), we start from a blank slate. For each iteration, the share of parcels operated by cargo bikes, the total cost (cargo bikes, micro hubs rent, needed LCVs) are calculated.

Figure 5 shows the evolution of the daily cost of operation and of the share of parcels operated by cargo bikes of both scenarios, as functions of the number of micro hubs. For scenario S2, two solutions are represented: the one with unconstrained optimization of the localization of micro hubsthe bright red curveand the one where the locations of micro-hubs are constrained to the district centroidsthe purple curve. Scenario S1 is also presented (dotted red line). In this case, no parcel is operated by cargo bike.

First of all, for this particular stakeholder, it is not profitable to deliver the entire Paris area by cargo bikes. The cost would be much greater than that of using a 100% electric fleet.

The second result is that it is possible to set up a network of 3 micro hubs (optimal location) performing 67% of the daily operations for a similareven slightly lowercost than the one with a 100% electric LCVs fleet. However, with more than 3 micro hubs, the network of micro hubs and cargo bikes quickly gets more expensive than a traditional organization with a fleet of electric LCVs.

Assume that the objective is to maximize the share of operations done by cargo bikes (with optimal micro-hub location), it is possible to do by increasing the number of micro hubs. However, there are decreasing returns: beyond 10 micro-hubs, the share of parcels operated by cargo bike increases by less than 2% per additional micro-hub. A network of 10 micro hubs optimally located is sufficient to address more than 90% of the eligible shipments. However, the daily operation cost would be 30% higher than a fully electric fleet of LCVs. Coming back to the question of the administrative division: it appears, expectedly, that respecting the administrative division is costly. More precisely, the lowest cost is obtained with two micro-hubs, and only 53% of shipments are operated by cargo-bikes. Moreover, in that scenario, the number of microhubs necessary to cover a sizable share of eligible shipments would be much higher than in the unconstrained scenario. This mirrors the very important spatial heterogeneity of the density of operations.

Impact of the micro hubs rent price

The rent of the micro hubs is a critical limitation to the implementation of cargo bikes. In order to further investigate the sensitivity of cargo-bike financial profitability to real estate prices, the following was done. Consider the scenario with electric LCVs as a base case: for each share between 0 and 100%, it is possible to determine the maximum micro-hub renting cost per m² such that it is possible to transport that share of shipments by cargo-bikes for a lower daily cost than the base case: 100% of electric LCV.

Figure 6 is built with the following input parameters from the data:

-𝑆 𝑀𝐻 : Surface of the micro hub: 150m

Function 𝑀𝑎𝑥_𝑟𝑒𝑛𝑡_𝑝𝑒𝑟_𝑚² is represented on Figure 5. Due of the number of operations that differ between vehicles, the curve is by plateau, according to the number of operations to realize. For example, three cargo bikes and one electric LCV for supply or three electric LCVs (similar cost) are needed to perform 41 to 52 operations per day. However, four cargo bikes and one electric LCV for supply or only three electric LCVs are required to perform 52 to 60 operations.

With our assumptions, cargo bikes are interesting when there is a significant number of daily operations (81 in Paris). Even if local authorities provide free premises or space for mobile premises, a minimum of 41 daily operations is required for it to be economically viable for the transporters. This underlines the importance of having a high density of operations to set up a network of micro hubs for cargo bikes deliveries.

In addition, it is found that while high density is necessary to implement cargo bikes, due to the different number of operations per transportation mode, increasing the density does not necessarily imply a direct decrease in the operating cost per cargo bike. [START_REF] Conway | Urban Micro-Consolidation and Last Mile Goods Delivery by Freight-Tricycle in Manhattan: Opportunities and Challenges[END_REF]. The study was conducted with the data of one company, however, the method, and some results, are generalizable. On one hand, it appears that a high density of operations is necessary for cargo bike operations to be competitive. On the other hand, a higher density of operations is found in places where land prices are higher, thus compromising the competitivity of cargo bikes operations, given the fact that those require a micro-hub at close hand.

This raises the issue of pooling shipments between several operators. Consolidation has been shown to be highly advantageous through modeling, especially in the Frankfurt case [START_REF] Elbert | Urban Consolidation and Cargo Bikes: A Simulation Study[END_REF] as it is the easiest way to increase density, but it does come with specific issues (cost of delivery, responsibility for the parcel, additional sorting points, etc.). The use of subcontractors specialized in cargo bikes deliveries can represent an opportunity to pool flows.

Moreover, in this study, the condition to operate a parcel by cargo bikes is the weight (200 kg max). We have no information about the volume of the parcels. It would be interesting to take this aspect into account as a cargo bike can carry a limited volume (approximately 1.5 m 3 ).

Finally, it seemed interesting to raise the question of the rent cost of the micro hub as a limiting element.

The analysis of the maximum rent as a function of the number of operations per day in the micro hub catchment area highlights the non-linear nature of the two parameters (rent and number of operations).

This implies that, depending on the input parameters, there is no single threshold passed which one solution is universally better than the other. In addition, it is true that the input parameters (cost of rent, number of operations per tour, etc.) vary among case studies (territory studied, operator); however, the equation remains valid. Therefore, so is the shape of the curve, and the previous result is generalizable.

This brings another point of view to the widely discussed comparison in the literature between cargo bikes and LCV by discussing the relationship between one limiting parameter of the cargo bike solution and a LCV fleet. One direction for further research is to conduct a more detailed analysis accounting for the variation of rents between districts (in this paper, the average rent is considered) and the density of operations.

Figure 1 -

 1 Figure 1 -Map of Paris with districts Paris has a population of 2,175,601 inhabitants for an area of 105.4 km 2 , which corresponds to a density of 21,000 inhabitants/km 2 (32). Paris is part of an urban area of 12,475,808 inhabitants and is located in the center of the Paris metropolitan area, a region that generates 30% of the French Gross Domestic Product.

Figure 2 -

 2 Figure 2 -Diagram of the operation of a parcel service carrier company, (9) DB Schenker operates in Paris from two hubs on the outskirts (one to the north and one to the south) which respectively manage the north and the south areas of Paris. These two hubs are connected to other hubs nationwide via the national transport plan.

Figure 3 -

 3 Figure 3 -Current situation with electric LCV and the scenario studied with the use of cargo bikes

Figure 4 -

 4 Figure 4 -Density of deliveries and pick-ups in Paris city for two months, 1.5 km 2 grid, MATLAB

Figure 5 -

 5 Figure 5 -Comparison of the daily cost of operating a solution with and without cargo bikes according to the number of micro hubs

Figure 6 -

 6 Figure 6 -Maximum price per m 2 of a micro-hub rent according to the number of parcels per day DISCUSSION Results show that it is technically possible to pick up or deliver a large majority of the parcels by cargo bikes (91%). However, it is not economically interesting to operate all parcels by cargo bikes. This confirms the hypothesis made by Conway et al. (2012) about the economic feasibility of delivering Paris by cargo bikes without subsidy[START_REF] Conway | Urban Micro-Consolidation and Last Mile Goods Delivery by Freight-Tricycle in Manhattan: Opportunities and Challenges[END_REF]. The study was conducted with the data of one company, however,

Table 1 -General information of DB Schenker's activity in Paris metropolitan area, two months flow

 1

				metropolitan area
		Deliveries	Pick-ups	Deliveries	Pick-ups
	Average weight [kg]	91	71	112	98
	Median weight [kg]	53	35	54	52
	Share with a weight <200 kg	90%	93%	87%	88%
	Stock	31,536	5,098	271,293	311,971
	North terminal	21,912	3,702	-	-
	South terminal	9,624	1,396	-	-

  Table 2 assuming vehicles are used 7 h/day. It is assumed that a driver needing a heavy goods vehicle license (total weight over 3.5t) is paid on the basis of a heavy goods vehicle driver, while the others are paid the minimum wage.

				Number of
	Vehicle	Daily cost [€] Payload [kg]	operations per day
	Cargo bike	80	200	17
	Renault Master	143	1,420	22
	Fuso eCanter	211	4,500	22

Table 2 -Characteristics per vehicle

 2 Under scenario S1, the fleet is calculated as the minimization of the total transport cost. The fleet mixes small LCVs and large LCVs (see Vehicle Routing Problem).

2 ;

 2 -𝑁 𝐶𝐵 : Number of operations per day per cargo bike (value: 17); -𝑁 𝐿𝐶𝑉 : Number of operations per day per electric LCV (value: 22).Thus, it is possible to define the equivalent electric LCVs fleet needed to operate p parcels (𝑇𝐶 𝐿𝐶𝑉𝑒𝑞𝐶𝐵 ).

	From Equation (1), by equalizing the costs of the two formulas (i.e.𝑇𝐶 𝐿𝐶𝑉𝑒𝑞𝐶𝐵 = 𝑇𝐶 𝐶𝐵 ), we deduce
	the maximum rent per m 2 as:
	𝑀𝑎𝑥_𝑟𝑒𝑛𝑡_𝑝𝑒𝑟_𝑚 2 ሺ𝑝ሻ =	ቂ𝑇𝐶 𝐿𝐶𝑉𝑒𝑞𝐶𝐵 ሺ𝑝ሻ -ቀ𝐶 𝐶𝐵 * 𝑁 𝐶𝐵 ሺ𝑝ሻ + 𝑆 𝑀𝐻	2 7	* 𝐶 𝐿𝐶𝑉 * 𝑁 𝐿𝐶𝑉𝑠𝑢𝑝𝑝𝑙𝑦 ሺ𝑝ሻቁቃ

CONCLUSION

The objective of this study is to compare two sustainable scenarios for the last mile via cargo bikes and/or electric LCVs fleet within Paris based on DB Schenker's operating data. The first important result is that it is economically feasible to operate a part of the parcels via cargo bikes but not all of them.

Secondly, the renting of micro hubs is a major cost barrier. As the average price of a commercial space in Paris is high, this requires a minimum density of parcels to make cargo bike operations profitable.

Even if there were no rent to pay (i.e. subvention, free provision of facilities, etc.), it is necessary to have a minimum density to compensate for the cost of transporting the parcels between the micro-hubs and the cross-docking terminal by vehicle.

Moreover, as far as the location of micro hubs is concerned, it is interesting to be free of administrative borders. Indeed, it allows to operate cheaper a large number of operations (67% of daily operations) with only 3 micro hubs and with a relatively small catchment area (2 km radius around the micro hubs).

A priority direction for future research is the integration of negative externalities. Indeed, both electric LCVs and cargo bikes would strongly reduce greenhouse gas emissions, compared to today's situation.

However, LCVs' impacts with regard to congestion and noise pollution would be distinct. As a final note, it is important to keep in mind that even if cargo bikes became prominent, trucks would not be simply put out of the picture, as they would be needed to, first, supply the micro hubs and, second, pick up and deliver oversize or overweight packages.

AUTHOR CONTRIBUTION STATEMENT

The authors confirm contribution to the paper as follows: study conception and design: F. Combes, P. Nierat, A. Robichet; data collection: F. Combes, P. Nierat, A. Robichet; analysis and interpretation of


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text:
Gonzalo Romero-García

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published or not. The documents may come     Un outil d'analyse/synthèse utilisant la morphologie mathématique basé en le modèle audio sinusoïdes+bruit+transitoires

Introduction Analysis/Synthesis diagram

Contact: romero@ircam.fr Analysis/Synthesis is a process that takes a sound as input and retrieves parameters in order to generate a synthetic approximation of it. This process requires a Synthesis Model and Parameter Estimation Method. The diagram below illustrates the steps of the process and the choices involved.

Analysis/Synthesis

Parameters