A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables

We show that the production-transportation problem involving an arbitrary fixed number of factories with concave production cost is solvable in strongly polynomial time. The algorithm is based on a parametric approach which takes full advantage of the specific structure of the problem: monotonicity of the objective function along certain directions, small proportion of nonlinear variables and combinatorial properties implied by transportation constraints.

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