OR 3300/5300 Optimization I
Fall 2011
Professor Bland
Integer Linear Programming
(BHM Ch. 9, Sections 1, 3, 4, 5, 8 has more detail on the material in this handout, however,
you will not be responsible for this material on the final exam. If you take 3310/5310 in the
spring, you will study this material in depth.) See the zip file of figures that accompanies
this handout.
Minimize
n
X
j
=1
c
j
x
j
s
.
t
.
n
X
j
=1
a
ij
x
j
=
b
i
(
i
= 1
, . . . , m
)
(ILP)
x
j
≥
0 and integer
(
j
= 1
, . . . , n
)
.
(May maximize rather than minimizing, may have
≤
,
≥
, constraints, etc. May have some
variables that are required to be integervalued, others not.)
Assume
a
ij
’s,
c
j
’s
b
i
’s are integervalued (or, at least rational). If we drop the integrality
conditions from (ILP) we get the
linear programming relaxation
.
(ILP) has
very
broad applicability:
•
indivisible commodities
•
batchsizing and fixed charges
•
“go, nogo” decisions
•
logical constraints, conditional constraints
•
sequencing and precedence constraints
•
piecewiselinear approximation of nonlinear functions.
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 '08
 TODD
 Operations Research, Linear Programming, Linear Programming Relaxation, ILP, l.p. relaxation

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