Order-first split-second methods for vehicle routing problems: A review
TL;DR: In this paper, the authors consider an ordering of customers instead of building a giant tour, and propose an ordering-first split-second approach for vehicle routing. But this approach can be declined for different vehicle routing problems and reviews the associated literature.
Abstract: Cluster-first route-second methods like the sweep heuristic (Gillett and Miller, 1974) are well known in vehicle routing. They determine clusters of customers compatible with vehicle capacity and solve a traveling salesman problem for each cluster. The opposite approach, called route-first cluster-second, builds a giant tour covering all customers and splits it into feasible trips. Cited as a curiosity for a long time but lacking numerical evaluation, this technique has nevertheless led to successful metaheuristics for various vehicle routing problems in the last decade. As many implementations consider an ordering of customers instead of building a giant tour, we propose in this paper the more general name of ordering-first split-second methods. This article shows how this approach can be declined for different vehicle routing problems and reviews the associated literature, with more than 70 references.
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TL;DR: Two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery are provided, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels.
Abstract: Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.
851 citations
Cites background from "Order-first split-second methods fo..."
...…(2009), the book on the VRP and its extensions by Toth and Vigo (2002), the survey on the multiple TSP (mTSP) provided by Bektas (2006), the survey on automated guided vehicles provided by Vis (2006), and the review of order-first split-second heuristic approaches presented by Prins et al. (2014)....
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TL;DR: This classification is the first to categorize the articles of the VRP literature to this level of detail and is based on an adapted version of an existing comprehensive taxonomy.
800 citations
TL;DR: In this article, the authors provide a framework to classify various new transportation planning problems that arise in truck platooning, surveys relevant operations research models for these problems in the literature and identifies directions for future research.
Abstract: A truck platoon is a set of virtually linked trucks that drive closely behind one another using automated driving technology. Benefits of truck platooning include cost savings, reduced emissions, and more efficient use of road capacity. To fully reap these benefits in the initial phases of technology deployment, careful planning of platoons based on trucks’ itineraries and time schedules is required. This paper provides a framework to classify various new transportation planning problems that arise in truck platooning, surveys relevant operations research models for these problems in the literature and identifies directions for future research.
182 citations
TL;DR: In this paper, a two-phase heuristic is proposed to tackle the green vehicle routing problem (Green VRP) in which routes may visit alternative fuel stations (AFSs) en-route.
Abstract: The green vehicle routing problem (Green VRP) is an extension of the VRP in which routes are performed using alternative fuel vehicles (AFVs). AFVs have limited tank capacity, so routes may visit alternative fuel stations (AFSs) en-route. We propose a simple yet effective two-phase heuristic to tackle the Green VRP. In the first phase our heuristic builds a pool of routes via a set of randomized route-first cluster-second heuristics with an optimal AFSs insertion procedure. In the second phase our approach assembles a Green VRP solution by solving a set partitioning formulation over the columns (routes) stored in the pool. To test our approach, we performed experiments on a set of 52 instances from the literature. The results show that our heuristic is competitive with state-of-the-art methods. Our heuristic unveiled 8 new best-known solutions, matched another 40, and delivered solutions with an average gap of 0.14% for the 4 remaining instances.
148 citations
TL;DR: In this paper, the authors defined the main actors involved in urban parcel delivery, and then analyzed their business models and the interactions between them, in order to identify synergies, conflicts, and the operational and economic consequences of adopting green vehicles.
Abstract: In recent years, the role of freight transportation and parcel delivery in urban areas has increased, supporting the economic and social development of cities. At the same time, the industry is affected by various issues, inefficiencies, and externalities, particularly in the last-mile segment. As such, there is an emerging awareness of a need to improve urban mobility and transportation, making them more sustainable and competitive by mixing traditional and emerging technologies, such as cargo bikes, autonomous vehicles, and drones. In contrast, the complexity of the overall system, characterized by multiple actors with conflicting goals, requires a strategy that harmonizes these actors’ business and operational models. This study contributes in this direction along three axes. First, it defines the main actors involved in urban parcel delivery, and then analyzes their business models and the interactions between them. Second, it investigates the integration of traditional and green logistics (mainly cycle-logistics), from both business and operational perspectives, in order to identify synergies, conflicts, and the operational and economic consequences of adopting green vehicles. Third, it introduces a simulation-optimization decision support system tool capable of assessing mixed-fleet policies for the management of parcel delivery in urban areas. Finally, the decision support system is tested using real data of the city of Turin.
114 citations
Cites background from "Order-first split-second methods fo..."
...decade, including multi-tier transportation ([10, 11, 26, 38]), rich vehicle routing methods ([31, 44, 55]), and capacity planning problems ([40, 51])....
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References
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Book•
01 Jan 2001
TL;DR: This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.
Abstract: From the Publisher:
Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run. · Comprehensive coverage of this growing area of research · Carefully introduces each algorithm with examples and in-depth discussion · Includes many applications to real-world problems, including engineering design and scheduling · Includes discussion of advanced topics and future research · Features exercises and solutions, enabling use as a course text or for self-study · Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.
12,134 citations
TL;DR: The sweep algorithm generally produces results that are significantly better than those produced by Gaskell's savings approach and are generally slightly better than Christofides and Eilon's results; however, the sweep algorithm is not as computationally efficient as Gaskell’s and is slightly less so than Christ ofides andEilon's.
Abstract: This paper introduces and illustrates an efficient algorithm, called the sweep algorithm, for solving medium-as well as large-scale vehicle-dispatch problems with load and distance constraints for each vehicle. The locations that are used to make up each route are determined according to the polar-coordinate angle for each location. An iterative procedure is then used to improve the total distance traveled over all routes. The algorithm has the feature that the amount of computation required increases linearly with the number of locations if the average number of locations for each route remains relatively constant. For example, if the average number of locations per route is 7.5, the algorithm takes approximately 75 seconds to solve a 75-location problem on an IBM 360/67 and approximately 115 seconds to solve a 100-location problem. In contrast, the time to solve a problem with a fixed number of locations increases quadratically with the average number of locations per route. The sweep algorithm generally produces results that are significantly better than those produced by Gaskell's savings approach and are generally slightly better than Christofides and Eilon's results; however, the sweep algorithm is not as computationally efficient as Gaskell's and is slightly less so than Christofides and Eilon's.
1,168 citations
TL;DR: This paper presents a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost and shows that it has outperformed the best existing heuristics on a sample of standard test problems.
Abstract: : We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used to optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.
1,050 citations
"Order-first split-second methods fo..." refers methods in this paper
...Two good examples are the sweep algorithm, commonly attributed to Gillett and Miller (1974), and the Fisher and Jaikumar (1981), where clusters are obtained solving a generalized assignment problem....
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TL;DR: A GA without trip delimiters, hybridized with a local search procedure is proposed, which outperforms most published TS heuristics on the 14 classical Christofides instances and becomes the best solution method for the 20 large-scale instances generated by Golden et al.
974 citations
"Order-first split-second methods fo..." refers background or methods in this paper
...Prins (2004) proposed for the CVRP a similar method which was the first genetic algorithm able to compete with the best methods available at that time, tabu search heuristics....
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...Algorithm 1 is a compact version where the auxiliary graph is not generated explicitly (Prins, 2004)....
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...Concerning metaheuristics, the memetic algorithms from Lacomme et al. (2001, 2004) for the CARP and from Prins (2004) for the CVRP were the first genetic methods to outperform state of the art tabu search algorithms....
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...This test can be added to the if statement line 14 in Algorithm 1, like in Prins (2004)....
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TL;DR: The metaheuristic combines the exploration breadth of population-based evolutionary search, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and advanced population-diversity management schemes and proves extremely competitive for the capacitated VRP.
Abstract: We propose an algorithmic framework that successfully addresses three vehicle routing problems: the multidepot VRP, the periodic VRP, and the multidepot periodic VRP with capacitated vehicles and constrained route duration. The metaheuristic combines the exploration breadth of population-based evolutionary search, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and advanced population-diversity management schemes. Extensive computational experiments show that the method performs impressively in terms of computational efficiency and solution quality, identifying either the best known solutions, including the optimal ones, or new best solutions for all currently available benchmark instances for the three problem classes. The proposed method also proves extremely competitive for the capacitated VRP.
545 citations
"Order-first split-second methods fo..." refers methods in this paper
...Vidal et al. (2012) elaborate a powerful memetic algorithm for the PVRP, based on the chromosome encoding used in Lacomme et al....
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...The memetic algorithm proposed by Vidal et al. (2012) for the periodic and multi-depot VRP with limited fleet (see Section 5.1) was extended to time windows in Vidal et al. (2013a)....
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...Vidal et al. (2012) elaborate a powerful memetic algorithm for the PVRP, based on the chromosome encoding used in Lacomme et al. (2005) for the PCARP....
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