The Travelling Salesman Problem is a classical problem used to illustrate the benefits of implementing mathematical programming algorithms to solve transportation routing problems. In particular, this case is called the Assignment Problem.
The Assignment problem is a particular case of a transportation problem that considers the number of origins to be equal to the number of destinations (m = n), as well as the fact that each origin has a supply of 1 unit and each destination has a demand of 1 unit.
When solving the assignment problem, the main objective is to optimise the number of resources for a number of activities so that the cost is minimised.
In this case, two approaches are compared:
- The Assignment Problem Relaxation
- Dantzig, Fulkerson and Johnson Elimination Constraints (DFJ)
Whereas the Assignment Problem Relaxation allows for subtours to be created, the DFJ algorithm constraints the creation of subtours, building a full solution to the problem.
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