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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- Fall '08
- TODD
- Operations Research, Linear Programming, Optimization, LP, integer program, LP Optimum
-
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