The value function of a transportation problem |
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Institution: | 1. St. Petersburg Institute for Economics and Mathematics RAS, Saint Petersburg, Russia;2. Institute for Regional Economic Studies RAS, Saint Petersburg, Russia;3. National Research University Higher School of Economics, St.Petersburg, Russia |
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Abstract: | We investigate the value of an optimal transportation problem with the maximization objective as a function of costs and vectors of production and consumption. The value is concave in production. For generic costs, the numbers of linearity domains and peak points are independent of costs and consumption. The peak points are determined by an auxiliary assignment problem. The volumes of the linearity domains are independent of costs while their dependence on consumption can be expressed via the multinomial distribution. |
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Keywords: | Transportation problem Transportation polytope Assignment problem Optimal plan Extreme points Multinomial distribution |
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