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