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

Multi-objective Vehicle Routing Problem with Cost and Emission Functions

AbstractAmong the logistics activities, transportation, is presented as a major source of air pollution in Europe, generating harmful levels of air pollutants and is responsible for up to 24% of greenhouse gases (GHGs) emissions in the European Union. The growing environmental concern related to the economic activity has been transferred to the field of transport and logistics in recent decades. Therefore, environmental targets are to be added to economic targets in the decision-making, to find the right balance between these two dimensions. In real life, there are many situations and problems that are recognized as multi-objective problems. This type of problems containing multiple criteria to be met or must be taken into account. Often these criteria are in conflict with each other and there is no single solution that simultaneously satisfies everyone. Vehicle routing problems (VRP) are frequently used to model real cases, which are often established with the sole objective of minimizing the internal costs. However, in real life other factors could be taken into account, such as environmental issues. Moreover, in industry, a fleet of vehicles is rarely homogeneous. The need to be present in different segments of the market, forcing many companies to have vehicles that suit the type of goods transported. Similarly, to have vehicles of different load capacities enables a better adaptation to the customer demand. This paper proposes a multi-objective model based on Tchebycheff methods for VRP with a heterogeneous fleet, in which vehicles are characterized by different capacities, costs and emissions factors. Three objective functions are used to minimize the total internal costs, while minimizing the CO2 emissions and the emission of air pollutants such as NOx. Moreover, this study develops an algorithm based on C&W savings heuristic to solve the model when time windows are not considered. Finally, a real case application is analyzed to confirm the practicality of the model and the algorithm

Solving Rich Vehicle Routing Problem Using Three Steps Heuristic

Vehicle Routing Problem (VRP) relates to the problem of providing optimum service with a fleet of vehicles to customers. It is a combinatorial optimization problem. The objective is usually to maximize the profit of the operation. However, for public transportation owned and operated by government, accessibility takes priority over profitability. Accessibility usually reduces profit, while increasing profit tends to reduce accessibility. In this research, we look at how accessibility can be increased without penalizing the profitability. This requires the determination of routes with minimum fuel consumption, maximum number of ports of call and maximum load factor satisfying a number of pre-determined constraints: hard and soft constraints. To solve this problem, we propose a heuristic algorithm. The results from this experiment show that the algorithm proposed has better performance compared to the partitioning set

A GRASPxELS with Depth First Search Split Procedure for the HVRP

Split procedures have been proved to be efficient within global framework optimization for routing problems by splitting giant tour into trips. This is done by generating optimal shortest path within an auxiliary graph built from the giant tour. An efficient application has been introduced for the first time by Lacomme et al. (2001) within a metaheuristic approach to solve the Capacitated Arc Routing Problem (CARP) and second for the Vehicle Routing Problem (VRP) by Prins (2004). In a further step, the Split procedure embedded in metaheuristics has been extended to address more complex routing problems thanks to a heuristic splitting of the giant tour using the generation of labels on the nodes of the auxiliary graph linked to resource management. Lately, Duhamel et al. (2010) defined a new Split family based on a depth first search approach during labels generation in graph. The efficiency of the new split method has been first evaluated in location routing problem with a GRASP metaheuristic. Duhamel et al. (2010) provided full numerical experiments on this topic

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

Mixed Integer Programming Model for open Vehicle Routing Problem with Fleet and driver Scheduling Considering Delivery and Pick-Up Simultaneously

Vehicle Routing Problem (VRP) is a key element of many logistic systems which involve routing and scheduling of vehicles from a depot to a set of customers node. This is a combinatorial optimization problem with the objective to find an optimal set of routes used by a fleet of vehicles to serve a set of customers It is required that these vehicles return to the depot after serving customers’ demand. This paper investigates a variant of VRP, in which the vehicles do not need to return to the depot, called open vehicle routing problem (OVRP). The problem incorporates time windows, fleet and driver scheduling, pick-up and delivery in the planning horizon. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling of fleet and driver and routing policies of the vehicles. The objective is to minimize the sum of the costs of all routes over the planning horizon. We model the problem as a linear mixed integer program. We develop a combination of heuristics and exact method for solving the model

A GRASPxELS with Depth First Search Split Procedure for the HVRP

Split procedures have been proved to be efficient within global framework optimization for routing problems by splitting giant tour into trips. This is done by generating optimal shortest path within an auxiliary graph built from the giant tour. An efficient application has been introduced for the first time by Lacomme et al. (2001) within a metaheuristic approach to solve the Capacitated Arc Routing Problem (CARP) and second for the Vehicle Routing Problem (VRP) by Prins (2004). In a further step, the Split procedure embedded in metaheuristics has been extended to address more complex routing problems thanks to a heuristic splitting of the giant tour using the generation of labels on the nodes of the auxiliary graph linked to resource management. Lately, Duhamel et al. (2010) defined a new Split family based on a depth first search approach during labels generation in graph. The efficiency of the new split method has been first evaluated in location routing problem with a GRASP metaheuristic. Duhamel et al. (2010) provided full numerical experiments on this topic

Optimal Routing for Heterogeneous Fixed Fleets of Multicompartment Vehicles

We present a metaheuristic called the reactive guided tabu search (RGTS) to solve the heterogeneous fleet multicompartment vehicle routing problem (MCVRP), where a single vehicle is required for cotransporting multiple customer orders. MCVRP is commonly found in delivery of fashion apparel, petroleum distribution, food distribution, and waste collection. In searching the optimum solution of MCVRP, we need to handle a large amount of local optima in the solution spaces. To overcome this problem, we design three guiding mechanisms in which the search history is used to guide the search. The three mechanisms are experimentally demonstrated to be more efficient than the ones which only apply the known distance information. Armed with the guiding mechanisms and the well-known reactive mechanism, the RGTS can produce remarkable solutions in a reasonable computation time