Assignment Problem Algorithm

Because each worker has different skills, the time required to perform a job depends on the worker who is assigned to it.The matrix below shows the time required (in minutes) for each combination of a worker and a job.

Assume for example that we have four jobs that need to be executed by four workers.The assignment problem deals with assigning machines to tasks, workers to jobs, soccer players to positions, and so on.The goal is to determine the optimum assignment that, for example, minimizes the total cost or maximizes the team effectiveness.And we might naturally just go with Susan, since she’s giving us the best overall price.However, another solution might be to break down what we need done into individual items.Naturally, you go out and get quotes on remodeling and repairing what needs to be done.Let’s assume the four quotes you received look like this: This would seem pretty reasonable, all things considered.Now, we will subtract the lowest value, which we’ve converted to zero, from the remaining column values.Here, I’ve updated column 1, subtracting the lowest value, 70, from the remaining column values, leaving us with 15, 30, and 80: Now, we’ll notice that each column contains a zero.All other assignments lead to a larger amount of time required.The Hungarian algorithm can be used to find this optimal assignment.


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