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How does Integer Linear Programming differ from traditional Linear Programming?
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Integer Linear Programming (ILP) differs from traditional Linear Programming (LP) in that ILP involves finding the optimal solution to a linear function under a set of linear constraints over integer variables. In contrast, LP involves choosing the best result of a linear function through a procedure called linear programming, without the additional constraint of integer variables.

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ILP is a more specific kind of LP that is applied when variables must have integer values. It is more difficult than LP and requires specialist strategies to solve, but it has several uses in many different industries and may be applied to a variety of optimization issues.


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LP is used for problems where continuous decisions are appropriate, such as production planning, resource allocation, and portfolio optimization. ILP is used when decisions must be discrete, such as in problems involving integer quantities (e.g., selecting the number of products to manufacture, assigning tasks to workers, or scheduling activities).

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LP problems are typically easier to solve because they involve continuous variables. The simplex method and interior-point methods are commonly used to find optimal solutions efficiently.  ILP problems are generally more complex due to the inclusion of integer constraints. Finding the optimal integer solution is NP-hard, which means that solving larger ILP problems can become computationally challenging.

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