Optimal expansion of capacitated transshipment networks

In this paper, we address the problem of allocating a given budget to increase the capacities of arcs in a transshipment network to minimize the cost of flow in the network. The capacity expansion costs of arcs are assumed to be piecewise linear convex functions. We use properties of the optimum solution to convert this problem into a parametric network flow problem. The concept of optimum basis structure is used which allows us to consider piecewise linear convex functions without introducing additional arcs. The resulting algorithm yields an optimum solution of the capacity expansion problem for all budget levels less than or equal to the given budget. For integer data, the algorithm performs almost all computations in integers. Detailed computational results are also presented.