Models and Methods for Merge - in - Transit Operations

We develop integer programming formulations and solution methods for addressing operational issues in merge-in-transit distribution systems. The models account for various complex problem features including the integration of inventory and transportation decisions, the dynamic and multimodal components of the application, and the non-convex piecewise linear structure of the cost functions. To accurately model the cost functions, we introduce disaggregation techniques that allow us to derive a hierarchy of linear programming relaxations. To solve these relaxations, we propose a cutting-plane procedure that combines constraint and variable generation with rounding and branch-and-bound heuristics. We demonstrate the e ectiveness of this approach on a large set of test problems with instances with up to almost 500,000 integer variables derived from actual data from the computer industry.