Maximum Flow and the Linear Assignment Problem

Here’s a problem: Your business assigns contractors to fulfill contracts. You look through your rosters and decide which contractors are available for a one-month engagement and you look through your available contracts to see which of them are for one month long tasks. Given that you know how effectively each contractor can fulfill each contract, how do you assign contractors to maximize the overall effectiveness for that month? This is an example of the assignment problem, and the problem can be solved with the classical Hungarian algorithm.

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