Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Consider the following ILP:
max z = 14x, + 6x2 + 18x3
s.t.
11x, + 44x, + 22x3 < 143
27x1 + 9x2 + 18x, < 171
6x, - 3x, - 3x, >9
X1, X2, X3 2 0 and integer
Solve the ILP using Branch and Bound method. Use the following strategy:
Node selection: Best bound (i.e., select the active node with best objective function value).
• Variable selection: Highest fraction (i.e., select the variable with highest fraction value).
• Branch selection: Branch-up (i.e., at each node start with 2 branch first).
Termination criteria: Solve maximum of 10 nodes.
Note: Draw the < branch at the left. Record at each node its number and the objective function value. Record on
each branch the branching variable constraint. Show on the tree the nodes that are: DIS/fathom, IFS/Incumbent,
NFS/Infeasible. Do not write/explain anything else on the tree. Make sure your writing is clear and visible. In
order to solve the LPs at each node, you can use any linear programming solver.
2
Transcribed Image Text:Consider the following ILP: max z = 14x, + 6x2 + 18x3 s.t. 11x, + 44x, + 22x3 < 143 27x1 + 9x2 + 18x, < 171 6x, - 3x, - 3x, >9 X1, X2, X3 2 0 and integer Solve the ILP using Branch and Bound method. Use the following strategy: Node selection: Best bound (i.e., select the active node with best objective function value). • Variable selection: Highest fraction (i.e., select the variable with highest fraction value). • Branch selection: Branch-up (i.e., at each node start with 2 branch first). Termination criteria: Solve maximum of 10 nodes. Note: Draw the < branch at the left. Record at each node its number and the objective function value. Record on each branch the branching variable constraint. Show on the tree the nodes that are: DIS/fathom, IFS/Incumbent, NFS/Infeasible. Do not write/explain anything else on the tree. Make sure your writing is clear and visible. In order to solve the LPs at each node, you can use any linear programming solver. 2
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