Comparing Integer Programming and Linear Programming

Explain how the applications of Integer programming differ from those of linear programming.

Integer programming regards problems optimization where some variables are needed to employ discrete values, instead of permitting variables to suppose all real values in a certain range. Models with integer variables are very essential since they can easily model situation which cannot be modeled by linear programming. One can model a binary decision with variables ranging between 0 and 1, however, integer programming does not work with fraction and instead it demands that decision variables be either 1 or 0, but not any value in between them. Beside this, practical size integer programming model are frequently impossible or very difficult to solve. However, linear programming techniques can handle problems order of magnitude greater that of integer programming technique (Jense, 2004).

The Integer Programming Model

Why is “rounding-down” an LP solution a suboptimal way to solve Integer programming problems?

This is because it can results to fatal errors such as constraints violation and thus, rounding –down of LP solution should not be used in solving integer programming methods

Explain the characteristics of integer programming problems.

Some of the integer programming problems characteristics include that all of the variables value of the models are integers, and thus it does not accommodate fractions in its decision model. In addition, integer programming problems normally involve linear objective function optimization subject to linear constraints, integer value condition and nonnegative conditions. Integer programming problems are classified based on the type of variables employed, a problem with only integer variable is call pure integer IP problem, with some continuous variables and integers is mixed-integer IP problem, and with variable restricted to zero or one is known as zero-one IP problem  (McCarl & Spreen, 1997) .

Give specific instances in which you would use an integer programming model rather than an LP model. Provide real-world examples.

Integer programming model can be employed in one area where linear programming will never be able to function. This is in binary decisions that include invest-not invest, build-on build or yes-no. This is because integer programming is very discrete and always produce clear result that ease decision making. In real life situation, integer programming application in include airline crew scheduling, warehouse management among others (Larsen, n.d.).

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