Resource Alloca,on in Flow‐Constrained Areas with Stochas,c
Termina,on Times Considering Both Op,mis,c and Pessimis,c Reroutes
Ca
se
Re
Stu
su
dy
Abstract
In this project we
formulate an optimi
zation problem
for the assignment
of dispositions to
flights whose
preferred flight pla
ns pass through a
flow-constrained
area. For each flig
ht, the disposition
can be either to
depart as scheduled
but via a secondary
route that
avoids the flow-co
nstrained area, or
to use the
originally intended
route but to depart
with a
controlled departure
time and accompan
ying ground
delay. We anticip
ate that the capaci
ty throug
flow-constrained are
a will increase at som h the
time once the weath
e future
er activity clears.
The model is a
two-stage stochastic
program that repres
ents the
time of this capaci
ty windfall as a ran
dom variable,
and determines exp
ected costs given
a secondstage decision, con
ditioning on that tim
e. The goal is
to minimize
ts ed
the
el Inpu
Mod
expect
cos
Area)
t
edire
ove
strain
r
the
-Con
ent
distribution of
oflethe FCA (Flow
tion
Loca
pos
sib
cap
the FCA
oftim
aci
city
ty
capa
inc
her)
rea
weat
se
d
es.
 Nominal (goo
of the
lts
Moein Ganji, David Lovell and Michael Ball
her) capacity
 Reduced FCA (bad weat
FCA
pace Flow Program )
 Start time of the AFP (Airs
AFP
 Planned end time of the
Objective Function
Model Outputs
nates whether a flight
 An initial plan that desig
route or secondary
is assigned to its primary
FCA
IP
Initial plan cost –possible
saving under each scenario U
M
od
el
Param
A
FP
route;
flight under each
 A recourse action for each
time.
e
ranc
clea
early
ible
poss
PDF
an
In
iti
al
Pl
an
ed
E[Cost]
Re
s
vi
Pl
Main Constraints
Under original plan each flight must either be assigned to a
secondary route or to its primary routes – possibly with a delay
FCA capacity constraints under original plan:
under revision, flight can only arrive earlier
than u + E(f) if it has already departed
Computation
al efficiency
Under revision, flight originally assigned to its secondary route
can go on primary route if it has not departed yet
Under revision flight on primary route can only arrive
earlier at FCA
secondary
ersions of a
Possible conv brid route
hy
into
Flight on hybrid route cannot arrive at FCA at time
t unless u plus the revision time is less than t
Flight cannot use a hybrid route unless it was originally
assigned to its secondary route
Under all scenarios each flight must either be assigned
to a time slot at FCA or complete its secondary route:
FCA capacity constraints under scenario u:
n model for
optimizatio
stochastic
cisions in
basics of a
reroute de
d
the
an
ed
fin
lay
de
we have de
g ground
estion.
usly makin
can
space cong
simultaneo
clearance
en route air
ting future
nt to note
response to pacted area anticipa hat is more importa timal
im
t an op
cost. W
en
d
res
cte
a weather
pe
rep
s
ex
en thi
lowest
wh
the
ne
e
mi
uc
ter
de
prod
model can
equal to
nal angle
is that our
a directio
erage of
option with
ses (the av
strategy.
add a third ic and pessimistic ca ow that this
we
9
se
In ca
optimist
results sh
r
the
Ou
of
e
).
max angle
the averag
gle of each
ngle and the ditional benefit.
ectional an
the zero-a
ad
optimal dir optimal is relative
very little
produces
ompute the
ere
(h
e-c
s
pr
int
we
tra
,
ns
tion and the
For case 10 dent of capacity co
ty distribu
en
are worse
e probabili
flight indep
arance tim te that the costs here g the
cle
er
ath
rin
to the we
t path). No
of conside
of the fligh g the importance
geometry
tin
ly
se 8 indica
respective
than in ca
8, 9 and 10 infinity (unnstraints.
r to cases
t to
capacity co
are simila
ge was se
nstraints,
12 and 13
co
second sta
y
the
cit
pa
of
Cases 11,
y
cit
ge ca
t the capa
second sta
timal
except tha
absence of that employs the op lowest cost
d). In the
capacitate pect, the approach
provides the
ex
(case 13)
n
ca
gle
e
an
on
l
as
tiona
ined direc
unconstra
at
search team
NEXTOR Re
Design:Moein Ganji
re work
tu
ns and fu
Conclusio
UMD