An Inventory-Distribution System with LTL Deliveries – Mixed Integer Approach

The paper concerns a class of supply chain management problems called Joint Transportation-and-Inventory Problems (JTIPs). These problems are characterized by the presence of both transportation and inventory considerations, either as policy-variables or constraints. The research presented in this paper aims at determining an optimal joint inventory/transportation policy. Mathematical modeling is applied to find the optimal solution to JTIPs thus defined. The set partitioning formulation for solving the vehicle routing problem is incorporated into a discrete time, finite-horizon inventory planning problem. Two models will be discussed: time-discretized integer programming and the new approach with predefined quantities of delivery. As is shown in this paper, the approach allows us to use a column generation technique.