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Partial linear relaxation yields an integer solution

Consider a binary integer program \begin{align} \min \quad &\sum _{j \in J}f_j x_j +\sum _{i \in I} c_i y_i \notag \\ \mbox{s.t.} \quad &\sum _{j \in N_i} x_j \ge 1-y_i, \quad \forall i\in I ...
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Differential rents problem solving for transport problem

Sorry if question was asked, but I was unable to find the exact duplicate. Let's assume that we have transport problem. Will optimal plan for transport problem be the same regardless the method I ...