(a) Perform a row and column reduction. (b) Perform any additional steps required to complete the Hungarian Algorithm.
The assignement problem of workers to jobs is a classical problem in the field of operations research.
The problem can be about finding an optimal assignment of workers to jobs so as to minimize the total cost. The objective function is defined as the sum of the times taken by each worker (in hours) multiplied by his or her hourly wage, minus the total cost of assigning all workers to their respective jobs.
The assignement problem can be solved using linear programming. This can be done by solving a sequence of smaller problems and then aggregating them back together into one solution.
In practice, it is often more efficient to use heuristics such as "greedy" algorithms or simulated annealing instead of linear programming, since these are often faster and easier to implement than linear programming.
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