A column generation-based matheuristic for an inventory-routing problem with driver-route consistency

This paper investigates a variant of an inventory-routing problem (IRP) that enforces two conditions on the structure of the solution: time-invariant routes, and a fixed, injective (i.e., one-to-one) assignment of routes to vehicles. The practical benefits of concurrent route invariance and driver assignments are numerous. Fixed routes reduce the solution space of the problem and improve its tractability; they simplify operations; and they increase the viability of newer delivery technologies like drones and autonomous vehicles. Consistency between driver and customer is linked to improved service, driver job satisfaction and delivery efficiency, and is also an important consideration in certain contexts like home healthcare. After formulating the problem as a mixed integer-linear program, we recast it as a set partitioning problem whose linear relaxation is solved via column generation. Due to the prohibitively expensive nature of the pricing problem that generates new columns, we present a novel column generation-based heuristic for it that relies on decoupling routing and inventory management decisions. We demonstrate the effectiveness of the proposed method via a numerical study.