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I am trying to implement a paper, and one of the problems that I need to solve is the following:

The domain is $$\Pi(\pi_0, \pi_1)=\{w\in\mathcal M_{K_0,\,K_1}(\mathbb R^+) : w1_{K_1}=\pi_0 \text{ and }1_{K_0}^tw=\pi_1\}$$

and I want to find $$\min_{w\in\Pi(\pi_0,\pi_1)}\sum_{k,\,l}w_{kl}f(k,l)$$

where $f(k, l)$ is completely determined (plug and chug given $k$ and $l$).

Any help is welcome!

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1 Answer 1

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This is the transportation problem and can be solved via linear programming or a specialized network algorithm.

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