Set 9.1d
7
1. Straightforward formulation:
Let xit = 1 if load i is assigned to trailer t , o otherwise Li = linear feet of load i r i = revenue from load i M aximize z =
10
2
i =1
t =1
∑ ∑ ri x it
subject to
10
∑ Li xit ≤ 36, t = 1, 2 i =1
2
∑ x it
i = 1, 2, ...10 ≤ 1, i = 1, ...,10, x it = (0,1),
t =1
2. Formulation using if-then: Let xit = feet in trailer t assigned to load i yi = (0, 1), i = 1, 2, …, 10, wit = (0, 1), i = 1, 2, ..., 10, t = 1, 2 10
2
Maximize z = ∑ ∑ ri xit subject to i =1 t =1
10
∑ xit ≤ 36, t = 1, 2 i =1
xi1 ≤ Li yi , xi 2 ≤ Li (1 − yi ), i = 1, 2,...,10
(above constraint is not as efficient as xi1 + xi 2 ≤ 1, i = 1, 2,...,10 in formulation 1) (if xit > 0 then xit = Li ) translates to xit ≤ M (1 − wit ), Li − xit ≤ Mwit , − Li + xit ≤ Mwit , i = 1, 2,...,10, t = 1, 2 xit , wit , yi = (0,1), i = 1, 2,...,10, t = 1, 2
Solution: z = $7929. Problem has several alternative optima. (See file ampl9.1d-7.txt.)
Solution 1 Trailer 1
Load 1 5 6 8 Total
2
2 4 9 Total
Solution 2 Feet 5 7 9 14 35 ft 11 15 10 36 ft 9-14
Load 1 2 6 9 Total 4 5 8 Total
Feet 5 11 9 10 35 ft 15 7 14 36 ft
