Integer Programming HW# 6
ORI 391Q
Implicit Enumeration
1. Solve the following 0-1 ILP using the additive (Balas) algorithm:
min z = 5x1 + 6x2 + 7x3 + 8x4 + 9x5
subject to 3x1 – x2 + x3 + x4 – 2x5≥ 2
x1 + 3x2 – x3 – 2x4 + x5≥ 0
–x1 – x2 + 3x3 + x4 + x5≥ 1
xj binary, j = 1,...,5
2. Find an upper bound for the integer variables in the following ILP and then convert it to a 0-1
problem. Solve the resultant 0-1 ILP using the additive algorithm.
max z = 3x1 + 4x2 + 2x3 + x4 + 2x5
subject to 2x1 – x2 + x3 + x4 + x5≤ 3
–x1 + 3x2 + x3 – x4 – 2x5≤ 2
2x1 + x2 – x3 + x4 + 3x5≤ 1
xj ≥ 0, j = 1,...,5
xj binary, j = 1,...,3
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