BIT2506 Exam 2
Chapter 5 Integer Programming
Total integer model all values must be integers (things that must be whole numbers cats, cars)
1.
integer model all values must be either zero or one
•
Can construct
Swimming pool (x1) and tennis court(x2) built on same parcel of land constraint looks like
x1+x2<= 1
•
If it said
either
the swimming pool or the tennis court x1+x2=1
•
Types of constraints
o
Mutually exclusive either zero or one and only one but not both.
x
1
+ x
2
≤
1 – either one of the two variables can be 1 or they can both be zero, but they cannot
both be 1. (contingent)
o
Multiplechoiceone (or some specified number) must be included.
x
1
+ x
2
= 1 – one of the variables has to be 1 but not both and both cannot be zero
can build 2 of 4 facilities x1+x2+x3+x4<=2
o
ConditionalOne choice depends on another.
x
2
≤
x
1
– if x
1
is not chosen then neither is x
2
, but x
1
can be chosen with or without x
2
o
Corequisite if one is chosen then the other must be (both or neither must be chosen).
x
1
= x
2
– both variables have to be 0 or both variables have to be 1
o
be careful: things like land do not need to be integers
o
Rounding noninterger solution values up can result in an infeasible solution
o
Rounding noninterger values down can resuly in a less than optimal (suboptimal) solution.
o
When inputting 01 constraint: simply put CELL <=1 and CELL = integer also assume non
negativity to assure only 0 or 1 can be allowed
Capital budgeting example
•
You can use the BIN constraint to represent 01
•
Tech adding bookstore, bank, clothing dept
Fixed charge and facility location
o
Which farm to buy and which plants to send it to
o
Const: amt shipped must be less than or equal to harvest projection
o
X1a+x1b+x1c<=11.2 y1
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X1a+x1b+x1c11.2ya<=0
Basically saying can only ship product if you select that facility
Set covering example:
o
Constructing new hubs to ship items
o
The constraints are sum of hubs >=1 saying that
at least
one hub must be within the 300 miles
Mixed integer modelOnly sum of the values must be integers
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 '07
 LLClark
 Project Management, Shortest path problem, Flow network, maximal flow, permanent set

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