An exact approach for cyclic inbound inventory routing in a level production system

We study an inbound inventory routing problem concerned with the minimal-cost collection of distinct components from a network of suppliers and subsequent delivery to a manufacturing plant. We assume known and constant production of end products at the plant that generates a synchronized production of components at each supplier. The lean production philosophy motivates two distinctive features of our formulation. To facilitate standardized work, we consider inventory collection plans that are cyclic and repeatable into the near future. To support the notion of level production planning, we consider inventory collection plans such that the pickup amount at each supplier is a multiple of the daily demand and in exact proportion to the number of days since the last pickup. We study the polyhedron of the convex hull of our mathematical formulation and define new valid inequalities that we implement within our branch-and-cut algorithm for the problem. As our computational experiments confirm, our cyclic formulation is significantly more difficult to solve to optimality than the standard non-cyclic formulation. Regardless, our three-phase approach obtains competitive results for one-, two-, and three-vehicle instances over three- and six-period planning horizons.