An improved Lagrangian relaxation-based heuristic for a joint location-inventory problem

We consider a multi-echelon joint inventory-location (MJIL) problem that makes location, order assignment, and inventory decisions simultaneously. The model deals with the distribution of a single commodity from a single manufacturer to a set of retailers through a set of sites where distribution centers can be located. The retailers face deterministic demand and hold working inventory. The distribution centers order a single commodity from the manufacturer at regular intervals and distribute the product to the retailers. The distribution centers also hold working inventory representing product that has been ordered from the manufacturer but has not been yet requested by any of the retailers. Lateral supply among the distribution centers is not allowed. The problem is formulated as a nonlinear mixed-integer program, which is shown to be NP-hard. This problem has recently attracted attention, and a number of different solution approaches have been proposed to solve it. In this paper, we present a Lagrangian relaxation-based heuristic that is capable of efficiently solving large-size instances of the problem. A computational study demonstrates that our heuristic solution procedure is efficient and yields optimal or near-optimal solutions.