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Assignment Problem with Distributional Constraints

Student: Anastasiya Sidneva

Supervisor: Sergey Ketkov

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2021

The assignment problem is one of the most well-known combinatorial optimization problems and has many ways to be useful in practice. Depending on the constraints, the objective function and the type of optimization, the assignment problem can be useful in the allocation of resources in production, logistics tasks, tasks related to human resources, in various economic tasks, as well as in scheduling tasks. Solving the assignment problem is part of the optimization under uncertainty. Since our goal is to find the best solution without knowing the exact parameters of the problem, we consider a robust assignment problem with distributional constraints. This version of the problem can estimate the worst case, because it can represent possible real situations when we do not know the exact distribution of the problem parameters, but can only talk about a certain family of distributions. The risk measure Conditional Value-at-Risk (CVaR) was chosen as the objective function, since this risk measure is coherent, and therefore more reliable for estimation. In this paper, we formulate using duality theory a one-level assignment problem with distributional constraints, and computational experiments were conducted using the CPLEX software package. Computational experiments made it possible to reveal the relationship between the value of the objective function and the parameters (level of confidence, deviation of values).

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