MIP Model for Inventory Routing in Industrial Gases Supply Chain

A mixed-integer programming (MIP) model is developed to address inventory routing in industrial gases supply chains. First, we propose a discrete-time approach to address the basic problem, with both anticipatable and order-only customers, heterogeneous vehicles, and time-varying consumption rates. Valid inequalities are also presented to tighten the formulation. Second, drivers are modeled explicitly, to account for driver working and resting time constraints. Finally, we show how this model can be extended to handle other important restrictions that may appear in practice. The proposed model is the first to address the inventory routing problem with crew restrictions modeled in detail.