4
.
2010
4
.
: ..,
,
.., ..,
1. .. . .: , 1986.
2. .. - . , , 1998.
:
1. . . . .: , 1981.
2. .. : , , . .: , 1988.
3. .., .. : . . .: - .., 2002.
4. .. . : . . .: , 2005.
5. .., .. : . .: , - , 2006.
:
1. . - .., .., .. .: . , 1984.
2. .. . , 1982.
3. .. . , 1991.
4. .. 6 ( ). , 1988.
1.
.
1. .
, . i, i = 1, 2, 3, j, j = 1, 2, 3, ( ) i j .
| 1 | 2 | 3 | |
| 1 | 0,05 | 0,04 | 0,03 |
| 2 | 0,025 | 0,02 | 0,04 |
| 3 | 0,03 | 0,03 | 0,03 |
1, 2, 3 40, 36 40 . , 1, 2, 3, 5, 3, 4 . , , .
2. , , .
| . , ./. | ||||
| . , ./. | 0,5 | |||
| , /. | ||||
| , ./. |
, 10 . ., 90 . , 110 . .
|
|
|
, , 2000, 1300, 1500 1000 ?
3. .
() 0,03%, (S) 0,1% (Z) 3%. N1, N2, N3, . P, S Z ( %) N1, N2, N3 .
| P | S | Z | |
| N1 | 0,04 | 0,05 | 3,5 |
| N2 | 0,02 | 0,1 | 2,8 |
| N3 | 0,03 | 0,08 | 2,5 |
N1, N2, N3 150, 160, 200 . ( %) N1, N2, N3 , 1 ?
4. 5; 2,8 6,4 3: 5: 4 , ?
5. . . ( . -), ( . ), ( /), ( 1000).
| I | ||||
| II | ||||
, 2:1:3, , .
. . . , , .
| (-) 1 2 | ||||
| () 1 2 | ||||
| (.) | ||||
| () |
, , .
|
|
|
. . , 1 1- , 2 2- 3 3- .
.
,
:
,
,
:
,
,
:
, 
, 
.
POM WIN 1-3 (.19‑20).
1 3 , 10 1- , 33 2- 45 3- . 1495 . 1 (slack 1 = 0), 316 2 (slack 2 = 316). 1- (slack 3 = 0), 2- 2415 (slack 4 = 2415).
, , 2. , , .
( 3) 
, 
, 
, slack 2 ( 2 ), slack 4 ( 2- ), slack 6, slack 8, slack 10 ( 1-, 2- 3- ), surplus7, surplus 9 ( ), .
,
,
,
,
, (1)
,
,
,
,
.
, , 2, , (1) .
( 1 2) , 1- ( ), ( ). , 2- , 2 , , .
2.
. , , . ( ) :
| 4 . | 6 . |
, 45, 10, 60 , 25 , 30 . , .
. . , 
, . :
,
:
.
. , . CDEFGH .
x2
D E
C
 |
H
|
|
|
0 G x1 
F
. (4;6).
, . (4;6) , .
H. H
, 12 A 3 B 66 .
1. , , 6 , 12 4 , . 1 :
| I | II | |
I 0,5 1 , II 0,6 1 . , .
2. 8 9 . ( ):
| I | II | |
1 2,5 ., 1 1,4 .
, , 150 220 ?
3. : , , . : 900, 400 300 . ( ), 10 , , , .
| 10 . ( ) | |||
, .
3.
I. :
1. 
2. 
II. , :
1. 
2. 
3. 
4. 
. , :
. :
:
:
:
.
, 
.
, : 
.
, (1, 0, 0, 4) .
4.
.
5.
|
|
|
. ,
.
I. :
1. 
2. 
3. 
II. :
1. 
2. 
3. 
4. 
5. 
6.
. , 
(
= 1, 2, 3, 4; 
= 1, 2, 3, 4, 5). 
, 
. .
7.
. ,
8.
I. , , .
II. . , .
III. (), :
IV. A : 
, i= 1 ,,m, j= 1 ,,n. , () kl.
V. , .. :
1. 
2. 
4. 
3. 
5. 
6. 
7. 
9. 
10. 
8. 
11. 
.
Results
| X1 | X2 | X3 | RHS | Dual | ||
| Maximize | ||||||
| Constraint1 | <= | |||||
| Constraint2 | <= | |||||
| Constraint3 | <= | 1 495 | ||||
| Constraint4 | <= | 4 500 | ||||
| Constraint5 | >= | |||||
| Constraint6 | <= | |||||
| Constraint7 | >= | |||||
| Constraint8 | <= | |||||
| Constraint9 | >= | |||||
| Constraint10 | <= | |||||
| Solution | 1 495 |
Ranging
| Variable | Value | Reduced Cost | Original Value | Lower Bound | Upper Bound |
| X1 | -Infinity | ||||
| X2 | 0, 0 | ||||
| X3 | Infinity | ||||
| Constraint | Dual Value | Slack/ Surplus | Original Value | Lower Bound | Upper Bound |
| Constraint1 | |||||
| Constraint2 | Infinity | ||||
| Constraint3 | 1 495 | 1 300 | 1 600 | ||
| Constraint4 | 2 415 | 4 500 | 2 085 | Infinity | |
| Constraint5 | |||||
| Constraint6 | Infinity | ||||
| Constraint7 | - Infinity | ||||
| Constraint8 | Infinity | ||||
| Constraint9 | - Infinity | ||||
| Constraint10 | Infinity |
Solution list
| Variable | Status | Value |
| X1 | Basic | |
| X2 | Basic | |
| X3 | Basic | |
| slack 1 | NON Basic | |
| slack 2 | Basic | |
| slack 3 | NON Basic | |
| slack 4 | Basic | 2 415 |
| surplus 5 | NON Basic | |
| slack 6 | Basic | |
| surplus 7 | Basic | |
| slack 8 | Basic | |
| surplus 9 | Basic | |
| slack 10 | Basic | |
| Z | Optimal | 1 495 |
