NASA's astronaut crew currently includes 10 mission specialists who hold a doctoral degree in either astrophysics or astromedicine. One of these specialists will be assigned to each of the 10 flights scheduled for the upcoming nine months. Mission specialists are responsible for carrying out scientific and medical experiments in space or for launching, and repairing satellites. The chief of astronaut personnel, himself a former crew member with three missions under his belt must decide who should be assigned and trained for each of the very different missions. Clearly. astronauts with medical educations are more suited to missions involving biological or medical experiments, whereas those with engineering~ or physics-oriented degrees are best suited to other types of missions. The chief assigns each astronaut a rating on a scale of 1 to 10 for each possible mission, with a 10 being a perfect match for the task at hand and a 1 being a mismatch. Only one specialist is assigned to each flight, and none is reas signed until all others have flown at least once (a) Who should be assigned to which flight to maximize ratings? (b) NASA has just been notified that Anderson is getting married in February and has been granted a highly sought publicity tour in Europe that month. (He intends to take his wife and let the trip double as a honeymoon.) How does this change the final schedule? (c) Certo has complained that he was misrated on his January missions. Both ratings should be 10s, he claims to the chiet, who agrees and recomputes the schedule. Do any over the schedule set in part (b)? (d) What are the strengths and weaknesses of this approach to scheduling?
NASA's astronaut crew currently includes 10 mission specialists who hold a doctoral degree in either astrophysics or astromedicine. One of these specialists will be assigned to each of the 10 flights scheduled for the upcoming nine months. Mission specialists are responsible for carrying out scientific and medical experiments in space or for launching, and repairing satellites. The chief of astronaut personnel, himself a former crew member with three missions under his belt must decide who should be assigned and trained for each of the very different missions. Clearly. astronauts with medical educations are more suited to missions involving biological or medical experiments, whereas those with engineering~ or physics-oriented degrees are best suited to other types of missions. The chief assigns each astronaut a rating on a scale of 1 to 10 for each possible mission, with a 10 being a perfect match for the task at hand and a 1 being a mismatch. Only one specialist is assigned to each flight, and none is reas signed until all others have flown at least once
(a) Who should be assigned to which flight to maximize ratings?
(b) NASA has just been notified that Anderson is getting married in February and has been granted a highly sought publicity tour in Europe that month. (He intends to take his wife and let the trip double as a honeymoon.) How does this change the final schedule?
(c) Certo has complained that he was misrated on his January missions. Both ratings should be 10s, he claims to the chiet, who agrees and recomputes the schedule. Do any over the schedule set in part (b)?
(d) What are the strengths and weaknesses of this approach to
![A
1
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3 Decision Variables
4
5
6
7
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9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24 Objective Function Coefficient
25 Constraints:
26 Constraint #1 Vienze
27 Constraint #2 Veit
28 Constraint #3 Anderson
29 Constraint #4 Herbert
30 Constraint #5 Schatz
31 Constraint #6 Plane
32 Constraint #7 Certo
33 Constraint #8 Moses
34 Constraint #9 Brandon
35 Constraint #10 Drtina
36 Constraint #11
37 Constraint #12
38
39
B
JAN-12.
60 ANO CO
9
8
2
10
9
3
лс
5
10
C
JAN-27.
7
8
1
4
10
3
9
2
4
+9
10
D
23 0 10
-999587
10
FEB-5. FEB-26. MAR-26. APR-12.
9
5
E
8
7
5
9
LO
1
4
10
10
F
5
9
10
7
1
9
8
9
G
9
4
10
6
9
9
4
9
9
7
1
3
10
N
7
H
MAY-1. JUN-9.
8
7
7
1
1
10
1
- 0
9
5
5
9
7
6
2
1
10
2
VN
7
4
4
AUG-20.
2
4
6
3
1
9
2
7
9
8
K
SEP 19.
6
4
7
4
1
2
9
9
8
8
L
LHS
M
N
Sign RHS
O
P
Q
i 1 to 10 for 10 astronauts
k = a to j for the 10 projects
R
S
Let
Xik = 1 if the astronaut ith is assigned to project kth, otherwise its va
is 0.
Objective function is given as:
Max Z = Cik x Xik
T
The objective of the assignment of the astronauts is to maximize the
total rating while assigning astronauts to projects.
Let Cik represents rating of astronaut i is assigned for assigning to
project k
Subject to:
Assignment of astronaut Vincze to the projects:
X1a + X1b + X1c + X1d + X1e + X1f + X1g + X1h + X1i + X1j = 1
Similarly other astronaut assignment constraints are:
[X2k = 1, [X3k = 1, [X4k = 1, [X5k = 1, [X6k = 1, [X7k = 1, [X8k = 1,
>X9k = 1, and [X10k = 1
Assignment of project on 12-Jan to the astronauts:
X1a + X2a + X3a + X4a + X5a + X6a + X7a + X8a + X9a + X10a = 1
Similarly other astronaut assignment constraints are:
[Xib = 1, [Xic = 1, [Xid = 1, [Xie = 1, [Xif = 1, [Xig = 1, [Xih = 1, {Xii
and ΣXij = 1
Non-negativity constraint, Xik >= 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6a844b1-7148-4511-97e9-e9e80ac1a339%2F16197a1d-fab7-453e-b15c-1688f3e1431a%2F8ootq3d_processed.png&w=3840&q=75)
![Data for Problem 9-31
ASTRONAUT
Vincze
Veit
Anderson
Herbert
Schatz
Plane
Certo
Moses
Brandon
Drtina
JAN.
12
9
8
2
4
10
1
9
3
5
10
JAN.
27
7
8
1
4
10
3
9
2
4
10
FEB.
5
2
3
10
10
9
5
8
7
5
9
FEB.
26
1
4
10
9
9
7
8
6
9
7
MISSION
MAR.
26
10
7
1
9
8
9
9
4
10
6
APR.
12
9
9
4
9
9
7
1
3
10
7
MAY
8
7
7
1
1
10
1
9
5
5
JUN.
9
9
7
6
2
1
10
2
7
4
4
AUG.
20
2
4
6
3
1
9
2
7
9
8
SEP.
19
6
4
7
4
1
2
9
9
8
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6a844b1-7148-4511-97e9-e9e80ac1a339%2F16197a1d-fab7-453e-b15c-1688f3e1431a%2Fyitnpvv_processed.png&w=3840&q=75)
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