Dynamic Dispatch Waves for Same-day Delivery

Dynamic
Dispatch
Waves
for

Same-‐Day
Delivery

Mathias
Klapp,
Alejandro
Toriello,

Alan
Erera

School
of
Industrial
and
Systems
Engineering

Georgia
Tech

UC-‐Berkeley
ITS
Friday
Seminar

February
20,
2015

What
to
remember

1.  Last-‐mile
home
delivery
logis=cs
costly
due

to
poor
scale
economies,
and
same
day

delivery
adds
to
challenge

2. 
Dynamic
vehicle
dispatch
strategies
for
SDD

systems
may
provide
signiﬁcant
value
over

ﬁxed
wave
strategies

3.  Simple
rollout
policies
produce
high
quality

dynamic
solu=ons
in
idealized
seJng

This
talk
is
not
about…

Last-‐mile
home
delivery

•  Weak
scale
economies

– Ton-‐miles
/
operator-‐hour
compara=vely
low

– Small
vehicles,
opera=ng
cost
ineﬃcient

Distribution
center
Consumer delivery locations

Home
delivery
e-‐commerce

Same-‐day
home
delivery

Pick/pack/load
and
vehicle
dispatch

•  Both
beneﬁt
from
order
batching

– Pick
density
for
warehouse
opera=ons

– Stop
density
for
vehicle
rou=ng
opera=ons

Pick/pack/load
and
vehicle
dispatch

•  Both
beneﬁt
from
order
batching

– Pick
density
for
warehouse
opera=ons

– Stop
density
for
vehicle
rou=ng
opera=ons

Distribution
center
dense = shorter travel
time per delivery

Pick/pack/load
and
vehicle
dispatch

•  Both
beneﬁt
from
order
batching

– Pick
density
for
warehouse
opera=ons

– Stop
density
for
vehicle
rou=ng
opera=ons

Distribution
center
sparse = longer travel
time per delivery

Next-‐day
vs.
same-‐day

yesterday today time
orders arrive
Next-day Local Distribution System
order pick, pack, and load
vehicles for delivery dispatched

Next-‐day
vs.
same-‐day

orders arrive
Same-day Local Distribution System

Pick/pack/load
batching
economies?

orders arrive
many orders arrive after
first picks must be made

Dispatch
batching
economies?

orders arrive
some vehicles should
be dispatched before all
orders are ready

Vehicle
dispatch
challenges

•  Each
vehicle
dispatched
mul=ple
=mes
during

opera=ng
day
(10-‐12
opera=ng
hours)

– When
to
dispatch
vehicles?

•  Tradeoﬀs
between
wai=ng
to
dispatch,

dispatching
long
routes,
dispatching
short

routes

– When
to
wait
to
accumulate
stop
density?

– Which
orders
to
serve
with
each
vehicle

dispatch?

Dynamic
Dispatch
Waves
Problem

•  Determine
dispatch
epochs
dynamically

•  Explore
tradeoﬀs
ini=ally
with
single
vehicle

and
simpliﬁed
geography

time
wait
dispatch 1 dispatch 2 dispatch 3

Simpliﬁed
geography:
stops
on
line

di
•  Order
loca=on

– round-‐trip
travel
=me

from
DC

•  No
stop
=me

•  Dispatch

– serves
all
ready
orders

di
di
{j : dj  di}

Order
ready
Mme
process

di
time
Ready is picked, packed
for loading (no duration)
T 0⌧i
Orders served and
vehicle back to DC
by time 0

Order
ready
Mme
process

di
time
Ready orders for first
dispatch of day
T 0⌧i

Order
ready
Mme
process

di
time
Orders that come
available later in
operating day,
and unknown when
planning at time T
T 0⌧i

Dynamic
Dispatch
Waves
Problem

•  Each
=me
vehicle
at
distribu=on
center,
decide:

–  Whether
to
dispatch
vehicle,
or
wait

–  If
dispatched,
which
unserved
ready
orders
to
include

in
the
route

•  Given
set
of
poten.al
orders

–  Round-‐trip
dispatch
=me

–  Stochas=c
=me
(or
wave)
when
order
ready

–  Penalty
if
order
remains
unserved

•  Operate
to
minimize
total
cost
of
all
dispatches

plus
total
unserved
order
penal=es

N = {1, ..., n}
di
⌧i
i

Dynamic
programming
formulaMon

for
DDWP
on
the
line

•  State:

–  Number
of
remaining
waves,

–  Ready
and
unserved
orders,

–  Poten=al
orders
not
yet
ready,

•  Ac=ons:

wait
one
wave,
or
serve

–  Cost:

–  Possible
dispatch
ac=ons:

–  Must
return
by
0:

•  At
end
horizon,
pay
penal=es
for
unserved
orders

(t, R, P)
t
R
P
S ✓ R
|R|
x = maxi2S di
x  t

Dynamic
programming
formulaMon

for
DDWP
on
the
line

Bellman
recursion
for
DDWP

DeterminisMc
DDWP
on
line

•  Request
ready
=mes
known
in
advance,
but

requests
cannot
be
served
before
ready
=me

•  Proper=es
of
op=mal
solu=on

–  Dispatch
lengths

x

strictly
decreasing

–  No
wai=ng
a]er
ﬁrst
dispatch

DeterminisMc
DDWP
on
line

•  New
DP
state:
remaining
waves
t,
length
d
of
prior
dispatch

•  Recursion
O(n2
T)

Using
determinisMc
DDWP

•  Es=ma=ng
an
a
posteriori
cost
lower
bound

– Average
cost
for
sample
of
order
realiza.on
days

– Any
dynamic
policy
for
stochas=c
DDWP
can
have

no
lower
expected
cost

•  Building
a
priori
policy
solu=ons
to
the

stochas=c
DDWP

A
priori
soluMon

•  Before
ﬁrst
dispatch
(i.e.,
at
wave
T),
ﬁnd

complete
set
of
vehicle
dispatches:

•  Theorem

{(xk
, tk
)}
Optimal a priori solution is solution to
deterministic DDWP where each order i
replicated for each wave t 2 {T, ..., 1} with
known ready time t and penalty i Pr(⌧i = t)

Dynamic
policies

1.  Implement
a
priori
solu=on,
but
adjust
during

opera=ons

–  Shorten,
delay,
and
cancel
some
dispatches

2.  Rollout
using
a
priori
solu=ons

– Execute
ﬁrst
decision
in
adjusted
a
priori
solu=on

– Build
new
a
priori
plan
any
=me
vehicle
at

distribu=on
center,
using
new
informa=on

Experiment
1

•  Request
ready
=me
process

– Condi=onal
arrival
likelihoods

each
wave

•  Request
loca=ons
and
penal=es

– Loca=on
discrete
uniform
up
to
a
maximum

– Penal=es
discrete
uniform
on
quarters
of

• 
20
random
instances
for
class

– r
measures
=me
ﬂexibility

✓i
T
`
`
✓
n, `, r =
T
`
◆

Experiment
1:
Results
AvgGaptoaposteriorilowerbound

Experiment
1:
Results,
r
=
2

Dynamic
policies
via
ALP

•  Dual
LP
reformula=on
of
Bellman’s
equa=on

– massive
LP:
exponen=al
variables,
constraints

max ERT
[CT (RT , N RT )]
C0(R, P) 
X
i2R
i
Ct(R, P)  EF t
1
[Ct 1(R [ Ft
1, P Ft
1)]
Ct(R, P)  d + EF t
d
[Ct d(Rd [ Ft
d, P Ft
d)]

Dynamic
policies
via
ALP

•  ALP
restric=on
provides
lower
bound,
and

poten=ally
useful
approxima=on
of
C

•  Restrict
C
:

•  “cost
of
unserved
known
requests”,
“cost
of

unserved
poten=al
requests”,
“value
of

remaining
waves”

Ct(R, P) ⇡
X
i2R
at
i +
X
j2P
bt
j
tX
k=1
vk

Dynamic
policies
via
ALP

•  Proposi=ons

– Using
this
restric=on
in
dual
LP,
the
ALP
lower

bound
LP
requires

variables
and

constraints

– (*)
For
determinis=c
problems,
the
ALP
lower

bound
is
=ght,
equal
to
op=mal
cost

•  Hybrid
ALP-‐A
priori
rollout
policy

– Use
a
priori
rollout
ﬁrst,
then
switch
to
ALP
rollout

later
in
opera=ng
period

O(nT) O(n2
T)

Experiment
2

•  New
ready
=me
process

– p:
Likelihood
ready
by
T

– q:
Likelihood
of
no
request

– Remaining
likelihood
discrete
uniform:

•  Request
loca=ons
and
penal=es
as
before

•  20
random
instances

(n = 20, ` = 10, r = 3)
µi
µi + vµi v

Experiment
2:
Results
vs.
q
-‐
p

Experiment
2:
Results
vs.
v

ObservaMons:
1

•  Dynamic
soluMons
valuable

– Dispatching
scheme
from
A
priori-‐rollout

approach
usually
provides
significant
savings
over

instance-‐specific
A
priori
solu=ons

– Schemes
with
fixed
dispatch
waves
could
be
no

befer
in
this
seJng

time
wave I wave II wave III

ObservaMons:
1

•  Fixed-‐but-‐flexible
dispatch
waves
(?)

– Fixed
planning
waves
useful
to
DC
pick/pack/load,

and
for
customer
order
management

– Design
and
performance
of
a
fixed-‐but-‐flexible

dispatch
wave
system?

time
wave I wave II wave III

ObservaMons:
2

•  LocaMons
on
line
creates
maximum
batching

benefit

– Compounded
by
assump=on
of
no
fixed
stop
=me

required
per
delivery

– Incen=ve
to
wait
and
batch
may
be
too
strong

– Inves=ga=ng
problems
with
fixed
stop
=mes
and

two-‐dimensional
delivery
loca=ons

ObservaMons:
2

T 0⌧i
latest wave and
dispatch duration

Other
extensions

•  MulMple
vehicles
per
delivery
zone

– How
to
coordinate
dispatch
waves
for
two

vehicles
serving
a
single
zone?

Other

conﬁgura=ons?

•  Customer
order
management

– Reject/not
oﬀer
same
day
delivery
op=on

dynamically
as
orders
are
received

Dynamic Dispatch Waves for Same-day Delivery

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