Solving min-max multi-depot vehicle routing problem

Abstract

The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of the Single-Depot Vehicle Routing Problem (SDVRP) in which vehicle(s) start from multiple depots and return to their depots of origin at the end of their assigned tours. The traditional objective in MDVRP is to minimize the sum of all tour lengths, and existing literature handles this problem with a variety of assumptions and constraints. In this paper, we explore the notion of minimizing the maximal length of a tour in MDVRP ("min-max MDVRP"). We present two heuristics in the paper. The first heuristic is a linear programming-based approach with global improvement. The second one, the region partition heuristic, is proved to be asymptotically optimal and is potentially useful for general network applications. A comparison of the computational implementations for different heuristics is presented.

A Gossip Algorithm for Heterogeneous Multi-Vehicle Routing Problems

“…Similar problems have been recently addressed in the literature, see e.g. Carlsson et al [2009], but to the best of our knowledge, never under the assumption of heterogeneous agents and tasks.…”

“…In this paper we extend the result in Carlsson et al [2009] by considering execution times instead of tour lengths to This work has been partially supported by the European Community's Seventh Framework Programme under project HYCON2 (Grant Agreement n. FP7- ICT-2009-5/N.257462. ) and in part by account for vehicles of different speeds, tasks with arbitrary execution cost and vehicles with different task execution speeds.…”

“…Interesting examples can be found in Toth and Vigo [2002], Laporte [1992b]. Several extensions to this problem have been proposed by considering at first more than one salesman as in Carlsson et al [2009], then introducing several additional constraints and objectives to better suit practical applications such as the multi-vehicle routing problem (MVRP) with a variable number of vehicles, finite load capacity, service time windows and several more as in Bektas [2006], Pisinger and Ropke [2007]. Finally, several extensions explore a dynamic setting in which multiple vehicles serve a dynamic number of tasks as discussed in Bullo et al [2011b].…”

“…It has been shown in Carlsson et al [2009] that when comparing the length of the optimal tour of one vehicle that visits all tasks locations with the multiple vehicle case, the maximum length of the tours for the multiple vehicle case is proportional to the tour length of the single vehicle case and proportionally inverse to the number of vehicles. Both upper and lower bounds with such scaling were given.…”

“…• We formalize the centralized problem in terms of a mixed integer linear programming (MILP) problem and extend the bounds in Carlsson et al [2009] for the multi TSP to the HMVRP.…”