  The two-echelon inventory-routing problem (2E-IRP) addresses the coordination
of inventory management and freight transportation throughout a two-echelon
supply network. The latter consists of geographically widespread customers
whose demand over a discrete planning horizon can be met from either their
local inventory or intermediate facilities' inventory. Intermediate facilities
are located in the city outskirt and are supplied from distant suppliers. The
2E-IRP aims to minimize transportation costs and inventory costs while meeting
customers' demand. A route-based formulation is proposed and a branch-and-price
algorithm is developed for solving the 2E-IRP. A labeling algorithm is used to
solve several pricing subproblems associated with each period and intermediate
facility. We generate 400 instances and obtain optimal solutions for 116
instances, and good upper bounds for 60 instances with a gap of less than 5%
(with an average of 2.8%). Variations of the algorithm could solve 7 more
instances to optimality. We provide comprehensive analyses to evaluate the
performance of our solution approach.
