Solving a Family of Multi-Depot Vehicle Routing and Location-Routing Problems

Abstract

This paper examines a class of asymmetrical multi-depot vehicle routing problems and location-routing problems, under capacity or maximum cost restrictions. By using an appropriate graph representation, and then a graph extension, the problems are transformed into equivalent constrained assignment problems. Optimal solutions are then found by means of a branch and bound tree. Problems involving up to 80 nodes can be solved without difficulty.

On the impact of real-time information on field service scheduling

“…These problems are NP-hard and can only be solved exactly for rather small instances, as has been shown in experimental analyses ( [23], [24], [1]). The FSSP has a number of notable differences to the MDVRP.…”

Solving the Multi-Depot Location-Routing Problem with Lagrangian Relaxation

“…However, due to the complexity of both location and routing problems, these two have been traditionally solved separately. In the literature there exist heuristic solution methods -for example; Tüzün and Burke (1999), Wu et al (2002), Albareda-Sambola et al (2005) -as well as exact methods -for example; Laporte et al (1988) proposed for solving the LRP as a whole.…”

“…They recommend solving the subproblems of the LRP concurrently in order to be able to analyze the tradeoffs between location and routing factors at the same level of decision hierarchy. Among the exact solution methods developed for the LRP is Laporte et al's (1988) method which transforms the Multi-Depot Vehicle Routing Problem (MDVRP) and LRP into a constrained assignment problem solved by branch and bound. Ambrosino and Scutellà (2005) attribute the significance of strategic decisions like facility locations, transportation and inventory levels in the distribution network design problem (DNDP) to an article by Crainic and Laporte (1997), along with an extensive literature review of the LRP and DNDP.…”

“…Ambrosino and Scutellà (2005) attribute the significance of strategic decisions like facility locations, transportation and inventory levels in the distribution network design problem (DNDP) to an article by Crainic and Laporte (1997), along with an extensive literature review of the LRP and DNDP. Ambrosino and Scutellà adopt Laporte's (1988) classification of LRPs. Their proposed integrated DNDP can be formulated as an LRP of category 4/R/T/T involving facility, warehousing and transportation as well as inventory decisions.…”

“…According to Laporte's (1988) classification of LRPs, our problem is 2/T. It means there exist 2 layers; namely, depots and customers where the transportation between these layers is realized via tours (vehicle routes).…”