# The Optimal Assignment Problem for a Countable State Space

@article{Akian2008TheOA, title={The Optimal Assignment Problem for a Countable State Space}, author={Marianne Akian and St{\'e}phane Gaubert and Vassili N. Kolokoltsov}, journal={arXiv: Optimization and Control}, year={2008} }

Given a n × n matrix B = (bij) with real entries, the optimal assignment problem is to find a permutationof {1,...,n} maximising the sum P n=1 bi�(i). In discrete optimal control and in the theory of discrete event systems, one often encounters the problem of solving the equation Bf = g for a given vector g, where the same symbol B denotes the corresponding max- plus linear operator, (Bf)i := max1≤j≤n bij + fj. The matrix B is said to be strongly regular when there exists a vector g such that…

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