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Branchandbound
is essentially a strategy of ‘‘divide and conquer.’’ The idea is to partition the feasible
region into more manageable subdivisions and then, if required, to further partition the subdivisions. In
general, there are a number of ways to divide the feasible region, and as a consequence there are a number
of
branchandbound algorithms. We shall consider one such technique, for problems with only binary
variables,
in Section 9.7. For historical reasons, the technique that will be described next usually is referred to as
the
branchandbound procedure.
Basic Procedure
An integer linear program is a linear program further constrained by the integrality restrictions. Thus, in a
maximization problem, the value of the objective function, at the linearprogram optimum, will always be
an
upper bound on the optimal integerprogramming objective. In addition, any integer feasible point is
always
a lower bound on the optimal linearprogram objective value.
The idea of branchandbound is to utilize these observations to systematically subdivide the
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This note was uploaded on 10/15/2011 for the course MBAHRM 565 taught by Professor Profbhattacharya during the Spring '11 term at IIT Kanpur.
 Spring '11
 ProfBhattacharya

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