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¶ … integer programming differ from those of linear programming.
(LP), is a type of convex programming, studies the case in which the objective function f is linear and the set of constraints is specified using only linear equalities and inequalities. Integer programming is the same thing, but with whole numbers. So integer programming is used with real life solutions that must be whole numbers that cannot be broken up.
Why is "rounding-down" an LP solution a suboptimal way to solve Integer programming problems?
It may create a solution that is very far away from the original solution. For example, consider:
max (2x + 3z)
where x and y are both integers above
the LP solution is
x= 4.5, y= 0.75
rounding down yields
x=4, y=0, with optimal objective value z=
but the optimal solution is actually x=4, y=1, with optimal objective value z=
So, if you were trying to find a value for something in the 10,000 units scale, the difference between 110,000 and 80,000 may be intolerably large.
3. Explain the characteristics of integer programming problems.
Give specific instances in which you would use an integer programming model rather than an LP model. Provide real-world examples.
Integer programming problems use whole numbers. So for example, you have a bunch of packages you want to ship. You have a truck that has 1000 cubic feet of space. You have packages that are 13 and 17 cubic feet. How do you pack the truck so you can waste the least amount of space, while also shipping the packages you need to? If you treat it as a linear programming problem, for any value of x < 1000/13, we can find a value of y so that f (x, y) = 1000, but you'll find partial packages. If you were shipping tons of grains and rice, you can split the tons into pieces, so it could fit. (This also gives another answer to #2 -- the linear programming
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