capitulo-9- solucionario de taha

7/25/2019 CAPITULO-9- Solucionario de Taha

1/22


2/22


3/22


4/22


5/22


6/22


7/22


8/22


9/22


10/22


11/22


12/22


13/22

Set 9.1d

1. Straightforward formulation:

7777Letxit= 1 if load i is assigned to trailer t, o otherwiseLi= linear feet of load iri= revenue from load i

10 2

1 1

10

1

2

1

M aximize subject to

36, 1, 2

1, 1, ...,10, (0,1), 1, 2, ...10

i it

i t

i it

i

it it

t

z r x

L x t

x i x i

= =

=

=

=

=

= = =

2. Formulation using if-then:

Let xit= feet in trailertassigned to load iyi = (0, 1), i= 1, 2, , 10, wit= (0, 1), i = 1, 2, ..., 10, t = 1, 2

10 2

1 1

10

1

1 2

1 2

Maximize subject to

36, 1,2

, (1 ), 1,2,...,10

(above constraint is not as efficient as 1, 1, 2,...,10 in formulation 1)

(if 0 then ) translat

i it

i t

it

i

i i i i i i

i i

it it i

z r x

x t

x L y x L y i

x x i

x x L

= =

=

=

=

=

+ =

> =

es to

(1 ), , , 1, 2,...,10, 1, 2

, , (0,1), 1,2,...,10, 1, 2

it it i it it i it it

it it i

x M w L x Mw L x Mw i t

x w y i t

+ = =

= = =

Solution:z= $7929. Problem has several alternative optima. (See file ampl9.1d-7.txt.)

Solution 1 Solution 2

Trailer Load Feet Load Feet

1 1 5 1 55 7 2 116 9 6 98 14 9 10

Total 35 ft Total 35 ft2 2 11 4 15

4 15 5 79 10 8 14

Total 36 ft Total 36 ft

9-14


14/22


15/22


16/22


17/22


18/22


19/22


20/22


21/22


22/22

capitulo-9- solucionario de taha

Documents