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 generaes 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.