A Simplicial Branch-and-bound Algorithm for Production-transportation Problems with Inseparable Concave Production Cost

In this paper, we develop a branch-and-bound algorithm to solve a network flow problem of optimizing production and transportation simultaneously. The production cost is assumed to be a concave function in light of scale economy. The proposed algorithm generates a globally optimal solution to this nonconvex minimization problem in finite time, without assuming the separability of the production-cost function unlike existing algorithms. We also report some computational results, which indicate that the algorithm is fairly promising for practical use.