Assignment problem: Difference between revisions

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Revision as of 01:36, 24 November 2005

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:There are a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any task, incurring some ''cost'' that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task in such a way that the ''total cost'' of the assignment is minimized.

If the numbers of agents and tasks are equal and the total cost of the assignment for all tasks is equal to the sum of the costs for each agent (or the sum of the costs for each task, which is the same thing in this case), then the problem is called the ''Linear assignment problem''. Commonly, when spokenspoking of the ''Assignment problem'' without any additional qualification, then the ''Linear assignment problem'' is meant.

Other kinds are the [[quadratic assignment problem]], [[bottleneck assignment problem]].

The assignment problem is a special case of another optimization problem known as the [[transportation problem]], which is a special case the [[maximal flow problem]], which in turn is a special case of a [[linear program]]. While it is possible to solve any of these problems using the [[simplex algorithm]], each problem has more efficient algorithms designed to take advantage of its special structure. AlgorithmAlgorithms arehave knownbeen devised that solve the linear assignment problem within time bounded by a polynomial expression of the number of agents.

The restrictions on agents, tasks and cost in the (linear) assignment problem could be relaxed, as shown in the example below.