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assignment12_ProblemSet

assignment12_ProblemSet - ORIE 3300/5300 Individual work...

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ORIE 3300/5300 ASSIGNMENT 12 Fall 2008 Individual work. Due: noon, Friday December 5. 1. You wish to apply branch-and-bound to a maximization integer pro- gram with binary variables (that is, the variables are restricted to be either 0 or 1). (a) When you solve a linear programming relaxation and branch on some variable x , what restrictions do you place on each of the two branches? (b) Now suppose that you are interested in solving one of these in- teger programs (with binary variables) in which there are three variables. (Clearly, this is just to illustrate the ideas behind the algorithms, since for a problem this small, one can easily check all eight possible solutions, and find the optimal one.) For each node of the branch-and-bound procedure, we have to compute the optimal value of the LP relaxation with some of the variables fixed. To simplify things, the table below contains the optimal value of every LP that we might encounter. For any solution, we let z denote the objective function value; all objective function coefficients are integer. In this table,
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