Inventory Allocation in Multi-period Multi-echelon Logistics Networks of Modular Products

In this study, inventory planning in logistics networks of modular products is investigated in a multi-period and multi-echelon setting. It is shown that this optimization problem can be converted to another problem which is briefly called modular proportional flow problem. This later problem is a minimum cost network flow problem with side constraints. The whole network consists of several disjoint subnetworks requiring the flows in some given sets of arcs to be proportional. Building efficient solution methods to this problem is important since it can be addressed several times as a subproblem. First, we show that the bases of this problem are good forests, and then design a network simplex algorithm that exploits this special structure. Finally, an illustrative example is supplied to demonstrate the algorithm.