A location-routing problem for the conversion to the “click-and-mortar” retailing: The static case

The static conversion from brick-and-mortar retailing to the hybrid click-and-mortar business model is studied from the perspective of distribution logistics. Retailers run warehouses and brick-and-mortar stores to meet the demand of their walk-in customers. When they decide to operate on the Web as an e-tailer, also click-and-mortar stores are needed which can serve both walk-in and online customers. While the distance between home and the nearest open store is used as a proxy measure for walk-in customers, a quality of service (QoS) guarantee for online customers is timely delivery of their orders. We describe and solve a static location-routing based problem for companies that embrace the clicks-and-bricks strategy in their retail operations. An augmented Lagrangian relaxation method embedded in a subgradient optimization procedure generates lower bounds, whereas a heuristic method finds feasible solutions. The performance of the Lagrangian-based solution method is tested on a number of randomly generated test problems.