Integrated decision support system for optimizing the training and transition of airline pilots
View Patent ↗An automated optimization system for generating multiple alternative training and transition plans for airline pilots which include a recall of furloughed pilots, and limits to deviation of pilot start bid periods for training assignments from a specific bid period, wherein such plans are cost optimized to track payroll costs of pilots recalled from furlough, and the combined time for solving an MIP Model representation and generating such plans therefrom is less than one hour.
1. A system for rapidly generating multiple alternative pilot training and transition plans which include a recall of furloughed pilots for an entire airline, which comprises:
a user interface receiving input data and user requests including a request to recall said furloughed pilots;
a database having stored therein said input data and a current pilot training and transition plan; and
an optimizer system in electrical communication with said user interface and said database for receiving said user requests, said input data, and said current pilot training and transition plan for generating MIP (mixed integer programming) Model which includes said recall of said furloughed pilot, wherein MIP is mixed integer problem, and rapidly solving said MIP Model to provide said multiple alternative pilot training and transition plans;
wherein said MIP Model includes following objective function:
Minimize
PNH
∑
t
∑
h
NH
Cost
ht
y
NHht
+
PNA
∑
t
∑
i
∈
NA
NA
Cost
it
y
it
+
PF
∑
t
∑
i
∈
F
F
Cost
it
y
it
+
Ppay
(
∑
i
∈
λ
1
a
i
R
i
+
∑
i
∈
58
Y
a
i
R
58
i
+
∑
i
∈
λ
2
a
i
M
i
)
+
PS
*
PBH
∑
h
∑
t
S
ht
/
Blockhrs
ht
+
PE
*
PBH
*
(
1
/
3
)
∑
h
∑
t
E
ht
/
Blockhrs
ht
+
PF
∑
t
∑
i
∈
λ
FR
FR
Cost
it
y
FRit
wherein PNH is Level of importance of New Hire Cost in the solution;
NHCost ht is Cost per new hire advanced to position h in period t (computed as the number of month between t and the end of the planning horizon, times the pay rate, times the average pay hours);
PNA is Level of importance of no-awards cost in the solution;
NACost it is Cost if pilot iεNA is released in bid period t (computed as the number of months between t and the beginning of the planning horizon, times the pay rate, times the average pay hours);
FCost it is Cost if pilot iεF is furloughed in bid period t (computed as the number of months between t and the beginning of the planning horizon, times the pay rate, times the average pay hours);
Ppay is Level of importance of pay protection cost in the solution;
PS is Level of importance of shortages in block hours in the solution;
PE is Level of importance of excess in block hours in the solution;
PF is Level of importance of furloughs cost in the solution;
PBH is Cost associated to each block hour missed due lack of crews; and
Block ht is Business plan block hours for position h in bid period t.
2. The system of claim 1 , wherein said multiple alternative pilot training and transition plans are generated in less than one hour, and are cost optimized.
3. The system of claim 1 , wherein said recall of said furloughed pilots occurs in order of seniority and before any new pilots are hired.
4. The system of claim 1 , wherein said user requests include a user option to limit percentage of pilots whose start bid periods for training assignments occur outside of a bid period of said current pilot training and transition plan.
5. The system of claim 1 , wherein said user requests include a user option to limit total percentage of pilots whose start bid periods for training assignments occur within a bid period of said current pilot training and transition plan, and of said pilots whose start bid periods for training assignments occur outside of said bid period.
6. The system of claim 1 , wherein said MIP Model includes following constraint to ensure that said furloughed pilots are recalled in seniority order:
∑
t
=
k
N
y
FRit
-
∑
t
=
k
N
y
FRi
-
1
t
≤
0
∀
i
∈
λ
FR
,
k
∈
{
1
…
N
}
.
7. The system of claim 1 , wherein said MIP Model includes following constraint to ensure that new pilots are hired after all of said furloughed pilots are recalled:
y
NHht
-
MNH
ht
∑
t
=
1
k
y
FRi
′
t
≤
0
∀
h
,
k
∈
{
1
…
N
}
.
8. The system of claim 1 , wherein said MIP Model includes following constraints to limit percentage of pilots whose start bid periods for training assignments may deviate from a bid period of said current pilot training and transition plan:
∑
t
ty
it
-
L
(
i
)
-
W
i
-
d
i
+
q
i
=
0
∀
i
∈
λ
;
(
i
)
d i +q i ≦Big M*h i ∀i ελ; and (ii)
(
∑
i
∈
Adv
t
h
i
/
U
t
)
≤
P_U
t
∀
t
∈
{
1
…
N
}
.
(
iii
)
9. The system of claim 1 , wherein said MIP Model includes following constraints to limit total percentage of pilots whose start bid period for training assignments may be changed to occur within a bid period of said current pilot training and transition plan, and of said pilots whose start bid period for training assignments may be changed to occur outside of said bid period:
diff it =1 −y it ∀iελ,tε{ 1 . . . N}|CM it =1; (i)
diff it =y it ∀iελ,tε{ 1 . . . N}|CM it =0; and (ii)
∑
i
∈
λ
diff
it
/
U
t
≤
P_U
t
∀
t
∈
{
1
…
N
}
.
(
iii
)
10. A system for rapidly generating multiple alternative pilot training and transition plans which include a limit to changing start bid periods for training assignments for an entire airline, which comprises:
a user interface receiving input data and user requests including a request to limit changes to said start bid periods;
a database having stored therein said input data and a current pilot training and transition plan; and
an optimizer system in electrical communication with said user interface and said database for receiving said user requests, said input data, and said current pilot training and transition plan, for generating an MIP (mixed integer programming) Model which includes said limit, wherein MIP is mixed integer problem and rapidly solving said MIP Model to provide said multiple alternative pilot training and transition plans;
wherein said MIP Model includes a following objective component for tracking payroll cost of pilots recalled from furlough:
PF
∑
t
∑
i
∈
λ
FR
FR
Cost
it
y
FRit
wherein PF is Level of importance of furloughs cost in the solution;
wherein FRCost it is Cost if pilot i εFR is advanced in bid period t (computed as the number of bid periods between t and the end of the planning horizon, times the pay rate, times the average pay hours); and
wherein y FRit is a binary variable indicating whether pilot i ε FR is recalled in bid period t, taking a value 1 if the pilot is recalled and 0 otherwise.
11. The system of claim 10 , wherein said limit applies to a percentage of pilots whose start bid periods for training assignments may deviate from a bid period of said current pilot training and transition plan.
12. The system of claim 10 , wherein said limit applies to total percentage of pilots whose start bid period for training assignments may be changed to occur within a bid period of said current pilot training and transition plan, and of said pilots whose start bid period for training assignments may be changed to occur outside of said bid period.
13. The system of claim 10 , wherein said multiple alternative pilot training and transition plans are cost optimized, and a following objective component for tracking payroll costs of pilots recalled from furlough is included in the MIP model:
PF
∑
t
∑
i
∈
λ
FR
FR
Cost
it
y
FRit
.
14. A system for generating multiple alternative pilot training and transition plans which include a recall of furloughed pilots for an entire airline, which comprises:
a user interface receiving input data and user requests including a request to recall said furloughed pilots;
a database having stored therein said input data; and
an optimizer system in electrical communication with said user interface and said database for receiving said user requests and said input data, and generating therefrom an MIP (mixed integer programming) Model including said recall of said furloughed pilots, wherein MIP is mixed integer problem, and for solving said MIP Model to rapidly generate said multiple alternative pilot training and transition plans;
wherein said multiple alternative pilot training and transition plans are cost optimized and generated in less than one hour, and said MIP Model includes a following objective component for tracking payroll costs of pilots recalled from furlough:
PF
∑
t
∑
i
∈
λ
FR
FR
Cost
it
y
FRit
wherein PF is Level of importance of furloughs cost in the solution;
wherein FRCost it is Cost if pilot iεFR is advanced in bid period t (computed as the number of bid periods between t and the end of the planning horizon, times the pay rate, times the average pay hours); and
wherein y FRit is a binary variable indicating whether pilot iεFR is recalled in bid period t, taking a value 1 if the pilot is recalled and 0 otherwise.
15. The system of claim 14 , wherein said MIP Model includes following constraints to limit percentage of pilots whose start bid periods for training assignments may differ from a specific bid period:
∑
t
ty
it
-
L
(
i
)
-
W
i
-
d
i
+
q
i
=
0
∀
i
∈
λ
;
(
i
)
d i +q i ≦Big M*h i ∀i ελ; and (ii)
(
∑
i
∈
Adv
t
h
i
/
U
t
)
≤
P_U
t
∀
t
∈
{
1
…
N
}
.
(
iii
)
16. The system of claim 14 , wherein said MIP Model includes following constraints to limit total percentage of pilots whose start bid period for training assignments may be changed to occur within a specific bid period, and of said pilots whose start bid period for training assignments may be changed to occur outside of said bid period:
diff it =1 −y it ∀iελ,tε{ 1 . . . N}|CM it =1; (i)
diff it =y it ∀iελ,tε{ 1 . . . N}|CM it =0; and (ii)
∑
i
∈
λ
diff
it
/
U
t
≤
P_U
t
∀
t
∈
{
1
…
N
}
.
(
iii
)
17. An optimizer system including a database for rapid generation of multiple alternative pilot training and transition plans that accommodate a recall of furloughed pilots, which comprises:
data means for receiving user requests and input data from a user;
operating means in electrical communication with said data means for generating variables and constraints from said user requests and said input data, for generating an MIP (mixed integer programming) Model from said variables and said constraints which provides for said recall of said furloughed pilots in seniority order and before hiring of new pilots, wherein MIP is mixed integer problem; and
means for solving said MIP Model with said variables and said constraints to generate therefrom said multiple alternative pilot training and transition plans with cost factor optimization;
wherein said MIP Model includes a following objective function:
Minimize
PNH
∑
t
∑
h
NH
Cost
ht
y
NHht
+
PNA
∑
t
∑
i
∈
NA
NA
Cost
it
y
it
+
PF
∑
t
∑
i
∈
F
F
Cost
it
y
it
+
Ppay
(
∑
i
∈
λ
1
a
i
R
i
+
∑
i
∈
58
Y
a
i
R
58
i
+
∑
i
∈
λ
2
a
i
M
i
)
+
PS
*
PBH
∑
h
∑
t
S
ht
/
Blockhrs
ht
+
PE
*
PBH
*
(
1
/
3
)
∑
h
∑
t
E
ht
/
Blockhrs
ht
+
PF
∑
t
∑
i
∈
λ
FR
FR
Cost
it
y
FRit
wherein PNH is Level of importance of New Hire Cost in the solution;
NHCost ht is Cost per new hire advanced to position h in period t (computed as the number of month between t and the end of the planning horizon, times the pay rate, times the average pay hours);
PNA is Level of importance of no-awards cost in the solution;
NACost it is Cost if pilot iεNA is released in bid period t (computed as the number of months between t and the beginning of the planning horizon, times the pay rate, times the average pay hours);
FCost it is Cost if pilot iεF is furloughed in bid period t (computed as the number of months between t and the beginning of the planning horizon, times the pay rate, times the average pay hours);
Ppay is Level of importance of pay protection cost in the solution;
PS is Level of importance of shortages in block hours in the solution;
PE is Level of importance of excess in block hours in the solution;
PF is Level of importance of furloughs cost in the solution;
PBH is Cost associated to each block hour missed due lack of crews; and
Block ht is Business plan block hours for position h in bid period t.
18. An optimizer system including a database for rapid generation of multiple alternative pilot training and transition plans that include a recall of furloughed pilots, which comprises:
data means for receiving user requests including a request to recall said furloughed pilots, and for receiving input data, and a current pilot training and transition plan;
operating means in electrical communication with said data means for receiving said user requests, said input data, and said current pilot training and transition plan, for generating variables and constraints therefrom, and for generating an MIP (mixed integer programming) Model from said variables and said constraints to provide said recall of said furloughed pilots in seniority order and before hiring of new pilots, and provide a limit to deviating start bid periods for training assignments with respect to a bid period of said current pilot training and transition plan; and
means for solving said MIP Model with said variables and said constraints to generate said multiple alternative pilot training and transition plans with cost optimization,
wherein said MIP Model includes a following objective function:
Minimize
PNH
∑
t
∑
h
NH
Cost
ht
y
NHht
+
PNA
∑
t
∑
i
∈
NA
NA
Cost
it
y
it
+
PF
∑
t
∑
i
∈
F
F
Cost
it
y
it
+
Ppay
(
∑
i
∈
λ
1
a
i
R
i
+
∑
i
∈
58
Y
a
i
R
58
i
+
∑
i
∈
λ
2
a
i
M
i
)
+
PS
*
PBH
∑
h
∑
t
S
ht
/
Blockhrs
ht
+
PE
*
PBH
*
(
1
/
3
)
∑
h
∑
t
E
ht
/
Blockhrs
ht
+
PF
∑
t
∑
i
∈
λ
FR
FR
Cost
it
y
FRit
wherein PNH is Level of importance of New Hire Cost in the solution;
NHCos ht is Cost per new hire advanced to position h in period t (computed as the number of month between t and the end of the planning horizon, times the pay rate, times the average pay hours);
PNA is Level of importance of no-awards cost in the solution;
NACost it is Cost if pilot iεNA is released in bid period t (computed as the number of months between t and the beginning of the planning horizon, times the pay rate, times the average pay hours);
FCost it is Cost if pilot iεF is furloughed in bid period t (computed as the number of months between t and the beginning of the planning horizon, times the pay rate, times the average pay hours);
Ppay is Level of importance of pay protection cost in the solution;
PS is Level of importance of shortages in block hours in the solution;
PE is Level of importance of excess in block hours in the solution;
PF is Level of importance of furloughs cost in the solution;
PBH is Cost associated to each block hour missed due lack of crews; and
Block ht is Business plan block hours for position h in bid period t.
19. The optimizer system of claim 18 , wherein said limit is applied to a percentage of pilots whose start bid periods for training assignments occur outside of said bid period.
20. The optimizer system of claim 18 , wherein said limit is applied to a total percentage of said furloughed pilots whose start date for training assignments is changed to occur within said bid period, and of said furloughed pilots whose start date for training assignments is changed to occur outside of said bid period.