stochastic fleet mix optimization: evaluating ... › files › 203637105 › allan_larsen... ·...

DTU Management5 September 2019

Stochastic Fleet Mix Optimization: Evaluating Electromobility in Urban Logistics

Satya Malladi, Jonas Christensen, David Ramirez,

Allan Larsen, Dario Pacino

Department of Technology, Management and Economics,

Technical University of Denmark

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Electro-mobility for urban logistics

EUFAL

Optimization

Planning

Demo

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Trends in electric vehicle adoption

https://www.ucsusa.org/clean-vehicles/electric-vehicles/electric-cars-battery-life-materials-cost#.W8hUemgzY2w

$125-$150 target that makes

EVs competitive with ICEVs

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https://www.ucsusa.org/clean-vehicles/electric-vehicles/electric-cars-battery-life-materials-cost#.W8hUemgzY2w


Trends in electric vehicle adoption

https://www.weforum.org/agenda/2018/05/china-surge-electric-vehicle-sales/

Pro

jecte

d s

ale

s o

f EV

s

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https://www.weforum.org/agenda/2018/05/china-surge-electric-vehicle-sales/


Electro-mobility + Urban logistics

Inner-city/ urban logistics - Opportunity

Incentive to reduce

pollution and noise

Short distances between

locations

Maneuverability of small

street vehicles

Electro-mobility – Potential and challenges

Reduced emissions and

noise

Electric range and

recharging timeCargo bikes

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Examples of urban service logistics

• Blood sample collection from private

physicians by Region Hovedstaten

– Tight time windows

• Technician services by MT Højgaard

– Matching electrician’s skill level with

customer request complexity

Customer request

Driver skill

Example Activity Unserved CompatibilityStochasticity

of requests

Urban

locations

Time

windowsElectric Fleet mix

Region

Hovedstaten

Blood sample

collection

(taxi)

E-minivans,

cargo bikes

MT HøjgaardTechnicians

routing EVs, ICEVs

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Operational hiccup: Mismatch between planned

and realized EV ranges

• Concern to firms: e.g. planned 175 km but realized 120 km.

• Underestimated energy consumption

• Energy for climate control ignored so far.

Vehicular power

Mechanical power

Climate control

Optional usage

Vehicular power

Mechanical power

Goeke and Schneider, 2015,

Bektas et. al 2014, Demir 2011 Current work Energy = Power x travel time

Strategic uncertainty: daily mean temperature;

deterministic on the operational day

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Power consumption model for climate control

Cooling mode: climate control

Cooling load

Convection load

Radiation load

Human metabolic

load

Heating mode: climate control

Heating load

Convection load

Heat balance method

Fayazbakhsh and Bahrami, 2013

Valentina et al., 2014

1 hour driving: 3.5 kWh, ~18% driving range hit

for a 22kWh EV

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Objectives of firms

• Strategic decision-making

– Minimize the total cost of ownership (TCO)

– (Fleet size and mix)

The number of vehicles will be fixed at the beginning of the horizon.

• Everyday decision-making

– Minimize operational costs: energy and maintenance costs + unserved customer penalty

– (Routing)

A general urban service logistics problem.

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Fleet size and mix world

1. Fleet Size and Mix VRP (FSMVRP): Golden, Assad, Levy, & Gheysens, 1984;

Gheysens, Golden, & Assad, 1984;

Desrochers & Verhoog, 1991;

Osman & Salhi, 1996;

Gendreau, Laporte, Musaraganyi, & Taillard, 1999; Taillard, 1999;

Renaud & Boctor, 2002;

Baldacci, Battarra, & Vigo, 2009

2. FSMVRPTW:Liu & Shen, 1999;

Dullaert, Janssens, Sörensen, & Vernimmen, 2002;

Dell’Amico, Monaci, Pagani, & Vigo, 2007

3. FSM-EVRPTW:Hiermann, Puchinger, Ropke, & Hartl, 2016

4. FSMVRP with varying deterministic demands

across multiple periodsPasha, Hoff, & Hvattum, 2016

Identical dete

rmin

istic d

ays

All c

usto

mers m

ust

be s

erved

.

Dete

rmin

istic d

ays

Fleet size and mix problem under

strategic uncertainty!

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Fleet size and mix optimization

• Uncertainty:

– Stochastic at the strategic stage

– Deterministic at the operational stage

• Uncertainty: customer set (request

uncertainty), temperature

• Requests are stochastic; demand

magnitudes are certain conditioned on

request occurrence.

Fleet mix

decisionObservation

Vehicle

routing

decisions

ObservationVehicle

routing

decisions

ObservationVehicle

routing

decisions

Current work: Two stage stochastic program

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Mixed Electric Fleet Sizing Problem (MEFSP)

flows

vehicle usage

unserved

customers

compatibility

arrival times

remaining

space

SOC updates

Total expected

operational cost

Fleet acquisition cost

Usage, energy, maintenance, unservedMFEVRPTWCC

MEFSP

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Solving the MEFSP by Sample Average

Approximation (SAA)

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Adaptive Large Neighborhood Search for

MFEVRPTWCC

ALNS

Greedy

Regret

Random

WorstShaw

Tour

SISR

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Mixed Fleet Electric VRP with Time Windows and Compatibility Constraints


Region H case

Renault Kangoo ZE Electric and TRIPL electric cargo bike

Fleet sizing for blood sample collection from private physicians by Region Hovedstaten

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Region H case

Kangoo TRIPL

Lane Car lane Bicycle lane

Kerb weight 1426 kg 322 kg

Max speed 130 kmph 45 kmph

Operation

speed

45 kmph 40 kmph

Battery 33 kWh 8.64 kWh

Capacity 720 vials 288 vials

Acquisition

price

28,223 USD 17,900 USD

Locations of doctors primarily in and around

Copenhagen city

Master list of 336 doctor locations

Bernoulli distribution for occurrence of doctor

request (estimated from historical data)

Fixed demand given summer/ non-summer and day

of the week

Temperature follows triangle distributions in each of

the four seasons

30 $/ unserved customer

Boundary conditions:

• nKangoos + nTRIPLS ≤ 16

• ⇒ 136 fleet mix combinations

TCO calculated over 10.6 years with two shifts

operating everyday16/28


Region H case: Half width analysis

• Half width of the 95%

confidence interval

• Penalty of 30$/unserved

customer

• Stable beyond 600 samples

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Variation of the half-width of operational cost with increase in the

number of samples


Region H case: Top ten solutions

• Cargo bikes are preferred

usually

• Tenth best solution costs 40k

USD (33%) more than the

best

• Average fill rate is under 75%

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Region H case: Difference w.r.t. previous energy models

• Operational cost with new

model up to 20% higher

than previous model in

summer

• 30% difference at -10

degree C

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Average operational cost per shift with 1 van and 4 cargo bikes


Region H case: Sensitivity to demand magnitudes

• Adding redundancy to

planning

• [1 van, 4 cargo bikes] remains

optimal between scaling

factor levels 0.95 to 1.15

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MTH case

• Currently 44 small diesel ICEVs + 91 large diesel ICEVs

• Small ICEVs up for replacement with EVs

Fleet sizing for technician routing at Lindpro, an electric installations subsidiary of MT Højgaard

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MTH case

TCO calculated over 10.6 years.

Current average diesel price: 1.34 $/liter (9.1 kr/ liter)

Current discounted electricity price: 0.1973 $/kWh (1.3

kr/kWh)

Master list of 900 customers in and around Copenhagen

Bernoulli distribution for occurrence of customer request

(estimated from historical data)

Temperature follows triangle distributions in each of the

four seasons

Small ICEV Small EV

Kerb weight 1623 kg 1430 kg

Battery - 30 kWh

Retail price 142,893 kr 215,155 kr

Private vehicle

tax rate23% 5.22%

Yellow plate

tax rate0% 0%

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MTH case: Half width analysis

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• Half width of the 95%

confidence interval

• No unserved customers

• Stable beyond 200 samples

Variation of the half-width of operational cost with increase in the

number of samples


MTH case: Operational cost variation

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Variation of the average operational when diesel costs 1.34 $/l

Variation of the average operational when diesel costs 1.82 $/l


MTH case: Yellow plate analysis

when diesel costs 1.34 $/ liter

Variation of TCO with EV composition in the fleet at different EV

price levels

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• Effective price less lower

than 180k kr required to

include EVs

• Price of small ICEV

143k kr

• Current retail prices not

conducive at current

average diesel price


MTH case: Yellow plate analysis

when diesel costs 1.82 $/ liter

Variation of TCO with EV composition in the fleet at different EV price

levels

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• Effective price less lower

than 200k kr required to

include Evs

• Price of small ICEV

143k kr

• Higher diesel prices

improve EV preference

• Current Danish retail

prices not conducive at

very high diesel price also


Takeaways and further work

Contributions:

• A novel stochastic fleet size and mix problem

• An upgraded energy consumption model

• A first solution method

• A well-performing metaheuristic for the operational problem

Takeaways:

• Impact of temperature on energy calculation

• Effect of uncertainty on fleet mix decisions

• Effect of diesel prices and EV prices on EV acquisition tendency

Future directions:

• Other solution methods for this type of two-stage stochastic programs

• Other recourse actions – availing temporary charter service, etc.

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Thank you!

stochastic fleet mix optimization: evaluating ... › files › 203637105 › allan_larsen... ·...

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