Assignment Problem

TRAVELLING SALESMAN PROBLEM |

QTBD II |

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Submitted By:

Section: A

Aakash Tyagi................2010002

Aakreeti Jindal..............2010003

Aditya Kumar Singh......2010019

Amruta Neve.................2010027

Anmol Agarwal.............2010040

Anubhav Sharma..........2010041

ASSIGNMENT PROBLEM

The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. It consists of finding a maximum weight matching in a weighted bipartite graph.

In its most general form, the problem is as follows:

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 speaking of the Assignment problem without any additional qualification, then the Linear assignment problem is meant.

ALGORITHMS AND GENERALIZATIONS

The Hungarian algorithm is one of many algorithms that have been devised that solve the linear assignment problem within time bounded by a polynomial expression of the number of agents.

The assignment problem is a special case of the transportation problem, which is a special case of the minimum cost 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 specialization has more efficient algorithms designed to take advantage of its special structure. If the cost function involves quadratic...