A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints

This article presents an exact algorithm for the multi-depot vehicle routing problem (MDVRP) under capacity and route length constraints. The MDVRP is formulated using a vehicle-flow and a set-partitioning formulation, both of which are exploited at different stages of the algorithm. The lower bound computed with the vehicle-flow formulation is used to eliminate non-promising edges, thus reducing the complexity of the pricing subproblem used to solve the set-partitioning formulation. Several classes of valid inequalities are added to strengthen both formulations, including a new family of valid inequalities used to forbid cycles of an arbitrary length. To validate our approach, we also consider the capacitated vehicle routing problem (CVRP) as a particular case of the MDVRP, and conduct extensive computational experiments on several instances from the literature to show its effectiveness. The computational results show that the proposed algorithm is competitive against stateof-the-art methods for these two classes of vehicle routing problems, and is able to solve to optimality some previously open instances. Moreover, for the instances that cannot be solved by the proposed algorithm, the final lower bounds prove stronger than those obtained by earlier methods

On the heterogeneous vehicle routing problem under demand uncertainty

In this paper we study the heterogeneous vehicle routing problem under demand uncertainty, on which there has been little research to our knowledge. The focus of the paper is to provide a strong formulation that also easily allows tractable robust and chance-constrained counterparts. To this end, we propose a basic Miller-Tucker-Zemlin (MTZ) formulation with the main advantage that uncertainty is restricted to the right-hand side of the constraints. This leads to compact and tractable counterparts of demand uncertainty. On the other hand, since the MTZ formulation is well known to provide a rather weak linear programming relaxation, we propose to strengthen the initial formulation with valid inequalities and lifting techniques and, furthermore, to dynamically add cutting planes that successively reduce the polyhedral region using a branch-and-cut algorithm. We complete our study with extensive computational analysis with different performance measures on different classes of instances taken from the literature. In addition, using simulation, we conduct a scenario-based risk level analysis for both cases where either unmet demand is allowed or not

A two-level local search heuristic for pickup and delivery problems in express freight trucking

We consider a multiattribute vehicle routing problem inspired by a freight transportation company operating a fleet of heterogeneous trucks. The company offers an express service for requests including multiple pickup and multiple delivery positions spread in a regional area, with associated soft or hard time windows often falling in the same working day. Routes are planned on a daily basis and reoptimized on-the-fly to fit new requests, taking into account constraints and preferences on capacities, hours of service, route termination points. The objective is to maximize the difference between the revenue from satisfied orders and the operational costs. The problem mixes attributes from both intercity less-than-truckload and express couriers operations, and we propose a two-level local search heuristic. The first level assigns orders to vehicles through a variable neighborhood stochastic tabu search; the second level optimizes the route service sequences. The algorithm, enhanced by neighborhood filtering and parallel exploration, is embedded in a decision support tool currently in use in a small trucking company. Results have been compared to bounds obtained from a mathematical programming model solved by column generation. Experience on the field and test on literature instances attest to the quality of results and the efficiency of the proposed approach

Thirty years of heterogeneous vehicle routing

It has been around thirty years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems

A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70\% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments

The Plug-In Hybrid Electric Vehicle Routing Problem with Time Windows

There is an increasing interest in sustainability and a growing debate about environmental policy measures aiming at the reduction of green house gas emissions across di erent economic sectors worldwide. The transportation sector is one major greenhouse gas emitter which is heavily regulated to reduce its dependance on oil. These regulations along with the growing customer awareness about global warming has led vehicle manufacturers to seek di erent technologies to improve vehicle e ciencies and reduce the green house gases emissions while at the same time meeting customer's expectation of mobility and exibility. Plug-in hybrid electric vehicles (PHEV) is one major promising solution for a smooth transition from oil dependent transportation sector to a clean electric based sector while not compromising the mobility and exibility of the drivers. In the medium term, plug-in hybrid electric vehicles (PHEV) can lead to signi cant reductions in transportation emissions. These vehicles are equipped with a larger battery than regular hybrid electric vehicles which can be recharged from the grid. For short trips, the PHEV can depend solely on the electric engine while for longer journeys the alternative fuel can assist the electric engine to achieve extended ranges. This is bene cial when the use pattern is mixed such that and short long distances needs to be covered. The plug-in hybrid electric vehicles are well-suited for logistics since they can avoid the possible disruption caused by charge depletion in case of all-electric vehicles with tight time schedules. The use of electricity and fuel gives rise to a new variant of the classical vehicle routing with time windows which we call the plug-in hybrid electric vehicle routing problem with time windows (PHEVRPTW). The objective of the PHEVRPTW is to minimize the routing costs of a eet of PHEVs by minimizing the time they run on gasoline while meeting the demand during the available time windows. As a result, the driver of the PHEV has two decisions to make at each node: (1) recharge the vehicle battery to achieve a longer range using electricity, or (2) continue to the next open time window with the option of using the alternative fuel. In this thesis, we present a mathematical formulation for the plug-in hybrid-electric vehicle routing problem with time windows. We solve this problem using a Lagrangian relaxation and we propose a new tabu search algorithm. We also present the rst results for the full adapted Solomon instances