Direct k-routing versus cross-docking: worst-case results

We consider a firm that devises outbound routes from its plant to satisfy daily demand of the set of its n customers at minimum cost. While routes can vary daily based on demand, we assume that the firm must commit long-term to a routing strategy. We consider the following routing strategies: (i) the direct delivery of products to customers from the plant on a k-route, where a k-route is a vehicle route with at most k customers on the route, and (ii) the use of a cross-dock as an intermediate transit point by first consolidating customer demand on vehicles traveling on mainline routes, which travel from the plant to the cross-dock, and then shipping demand from the cross-dock to customers on a set of n-routes. We examine the worst-case behavior for these routing strategies and their managerial implications.