Vehicle routing

The vehicle routing problem (VRP) plays a central role in the optimization of distribution networks. Since some classical instances with 75 nodes resist the best exact solution methods, most researchers concentrate on metaheuristics for solving real-life problems. Contrary to the VRP with time windows, no genetic algorithm (GA) can compete with the powerful tabu search (TS) methods designed for the VRP. This paper bridges the gap by presenting a relatively simple but e ective hybrid GA. In terms of average solution cost, this algorithm outperforms most published TS heuristics on the 14 classical Christoÿdes instances and becomes the best solution method for the 20 large-scale instances generated by Golden et al.

The present paper approaches the loading distribution of trucks for Product Transportation as a rich problem. This is formulated with the classic Bin Packing Problem and five variants associated with a real case of study. A state of the art review reveals that related work deals with three variants at the most. Besides, they do not consider its relation with the vehicle routing problem. For the solution of this new rich problem a heuristic-deterministic algorithm was developed. It works together with a metaheuristic algorithm to assign routes and loads. The results of solving a set of real world instances show an average saving of three vehicles regarding their manual solution; this last needed 180 minutes in order to solve an instance and the actual methodology takes two minutes. On average, the demand was satisfied in 97.45%. As future work the use of a non deterministic algorithm is intended.

This paper focuses on an integrated optimization problem that is designed to improve productivity in printed circuit board (PCB) manufacturing. We examine the problems of allocating the components to feeders and sequencing the placement of these components on the PCBs, populated by a rotary head machine with surface mount technology. While previous research focuses on sequencing the placement and only considers this subproblem as part of an interrelated set of problems, we provide an integrated approach which tackles all subproblems simultaneously as a single problem. Given an e-approximation algorithm for the vehicle routing problem we present a solution with an e-error gap for the

The basic Vehicle Routing and Scheduling Problem (VRSP) is described followed by an outline of solution approaches. Different variations of the basic VRSP are examined that involve the consideration of additional constraints or other changes in the structure of the appropriate model. An introduction is provided to Green Logistics issues that are relevant to vehicle routing and scheduling including discussion of the environmental objectives that should be considered. Particular consideration is given to VRSP models that relate to environmental issues including the timedependent VRSP, the transportation of hazardous materials and dynamic VRSP models. Finally some conclusions are drawn about further research needs in this area and the relation to road pricing.

We present an integrated model for simultaneous optimization of the loading and routing decisions associated with an automotive supplier's outbound supply chain. The supplier, Webb Wheel (WW), is a manufacturer of brake drums, rotors, hubs, and spoke wheels. WW accepts new orders from customers each day. Given sufficient inventory, it combines these orders into loads, releases them based on various dispatch criteria (e.g., truck-utilization, route-utilization, or penalty-based dispatch policies) and due-date considerations, and ships them in truckloads, less-than-truckloads, and containers. Dynamically changing demand information, inventory rationing, inventory interactions among orders, and lead-time considerations are some of the challenging aspects of the problem. Our optimization model is based on the decomposition of the problem into assignment and routing subproblems. The assignment subproblem determines the transportation mode and carrier choices, while considering total transportation costs. These costs depend on a variety of factors, including destination, number of drop locations on the route, and needs of customers on the route. Given the customer clusters and transportation modes from the assignment subproblem, the routing subproblem determines the sequence of drops and the true cost of the shipment using a modified traveling salesman problem. A scalable database with a graphical user interface supports the optimization model. We test our algorithm using four months of WW data and compare these data to the company's practice. Our results demonstrate the impact of transportation mode-specific capacities, customer locations, inventory availabilities, and due-date restrictions on outbound logistics costs. Since implementing our load-planning algorithm, WW has achieved cost savings of 4.4 percent over its previous load-planning process.

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This paper describes an integrated location-distribution model for coordinating logistics support and evacuation operations in disaster response activities. Logistics planning in emergencies involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas and evacuation and transfer of wounded people to emergency units. During the initial response time it is also necessary to set up temporary emergency centers and shelters in affected areas to speed up medical care for less heavily wounded survivors. In risk mitigation studies for natural disasters, possible sites where these units can be situated are specified according to risk based urban structural analysis. Logistics coordination in disasters involves the selection of sites that result in maximum coverage of medical need in affected areas. Another important issue that arises in such emergencies is that medical personnel who are on duty in nearby hospitals have to be re-shuffled to serve both temporary and permanent emergency units. Thus, an optimal medical personnel allocation must be determined among these units. The proposed model also considers this issue.

In real-time fleet management, vehicle routes are built in an on-going fashion as vehicle locations, travel times and customer requests are revealed over the planning horizon. To deal with such problems, a new generation of fast on-line algorithms capable of taking into account uncertainty is required. Although several articles on this topic have been published, the literature on real-time vehicle routing is still disorganized. In this paper the research in this field is reviewed and some issues that have not received attention so far are highlighted. A particular emphasis is put on parallel computing strategies.

This paper describes a tabu search heuristic for the vehicle routing problem with soft time windows. This problem allows lateness at customer locations although a penalty is then incurred and added to the objective value. By adding large penalty values, the vehicle routing problem with hard time windows can be addressed as well. In the tabu search, a neighborhood of the current solution is created through an exchange procedure that swaps sequences of consecutive customers (or segments) between two routes. The tabu search also exploits an adaptive memory that contains the routes of the best previously visited solutions. New starting points for the tabu search are produced through a combination of routes taken from different solutions found in this memory. Many best know solutions are reported on classical test problems.

We consider a combination of the capacitated vehicle routing problem and a class of additional loading constraints involving a parallel machine scheduling problem. The work is motivated by a real-world transportation problem occurring to a wood-products retailer, which delivers its products to a number of customers in a specific region. We solve the problem by means of two different metaheuristics algorithms: a Tabu Search and an Ant Colony Optimization. Extensive computational results are given for both algorithms, on instances derived from the vehicle routing literature and on real-world instances.

An algorithm for the distribution of fresh vegetables in which the perishability represents a critical factor was developed. This particular problem was formulated as a vehicle routing problem with time windows and time-dependent travel-times (VRPTWTD) where the travel-times between two locations depends on both the distance and on the time of the day. The model considers the impact of the perishability as part of the overall distribution costs and a heuristic approach, based on the tabu search is used to solve the problem. The performance of the algorithm was verified using modified Solomon's problems. Using parameters typical of the Slovenian food market, different schedules were achieved, giving improvements of up to 47% reduction in perished goods.

This paper presents a review on design and control of automated guided vehicle systems. We address most key related issues including guide-path design, estimating the number of vehicles, vehicle scheduling, idle-vehicle positioning, battery management, vehicle routing, and conflict resolution. We discuss and classify important models and results from key publications in literature on automated guided vehicle systems, including often-neglected areas, such as idlevehicle positioning and battery management. In addition, we propose a decision framework for design and implementation of automated guided vehicle systems, and suggest some fruitful research directions.

The vehicle routing problem (VRP) under capacity and distance restrictions involves the design of a set of minimum cost delivery routes, originating and terminating at a central depot, which services a set of customers. Each customer must be supplied exactly once by one vehicle route. The total demand of any vehicle must not exceed the vehicle capacity. The total length of any route must not exceed a pre-speeified bound. Approximate methods based on descent, hybrid simulated annealing/tabu search, and tabu search algorithms are developed and different search strategies are investigated. A special data structure for the tabu search algorithm is implemented which has reduced notably the computational time by more than 50%. An estimate for the tabu list size is statistically derived. Computational results are reported on a sample of seventeen bench-mark test problems from the literature and nine randomly generated problems. The new methods improve significantly both the number of vehicles used and the total distances ~avelled on all results reported in the literature.

This paper considers a relaxation of the classical vehicle routing problem (VRP), in which split deliveries are allowed. As the classical VRP, this problem is NP-hard, but nonetheless it seems more difficult to solve exactly. It is first formulated as an integer linear program. Several new classes of valid constraints are derived, and a hierarchy between these is established. A constraint relaxation branch and bound algorithm for the problem is then described. Computational results indicate that by using an appropriate combination of constraints, the gap between the lower and upper bounds at the root of the search tree can be reduced considerably. These results also confirm the quality of a previously published heuristic for this problem.

In this paper, we formulate the elevator dispatching problem as a stochastic bilevel optimization problem, where a group of elevators serves a set of transportation requests. In the upper level, the requests are assigned to the elevators. In the lower level, the route for each elevator is solved separately. The lower level problem predicts the optimal system state for a finite planning horizon according to stochastic demand. The demand affects the cost of traveling, capacity constraints, and the upper level payoff function. To solve the problem in real time, we use a genetic algorithm to optimize the upper level assignments. In the lower level optimization, we use the certainty equivalent control scheme, where stochastic quantities are replaced by their expected values. Extensive numerical simulations carried out in this paper, together with commercial installations, verify the applicability of our new on-line optimization algorithm.

The collection of waste is a highly visible and important municipal service that involves large expenditures. Waste collection problems are, however, one of the most difficult operational problems to solve. This paper describes the optimization of vehicle routes and schedules for collecting municipal solid waste in Eastern Finland. The solutions are generated by a recently developed guided variable neighborhood thresholding metaheuristic that is adapted to solve real-life waste collection problems. Several implementation approaches to speed up the method and cut down the memory usage are discussed. A case study on the waste collection in two regions of Eastern Finland demonstrates that significant cost reductions can be obtained compared with the current practice. q

This paper presents a review on design and control of automated guided vehicle systems. We address most key related issues including guide-path design, estimating the number of vehicles, vehicle scheduling, idle-vehicle positioning, battery management, vehicle routing, and conflict resolution. We discuss and classify important models and results from key publications in literature on automated guided vehicle systems, including often-neglected areas, such as idlevehicle positioning and battery management. In addition, we propose a decision framework for design and implementation of automated guided vehicle systems, and suggest some fruitful research directions.

We consider a pickup and delivery vehicle routing problem commonly encountered in real-world logistics operations. The problem involves a set of practical complications that have received little attention in the vehicle routing literature. In this problem, there are multiple carriers ...

Forty five years ago, an academic and practitioner from the north of England published a method of tackling the vehicle routing problem (VRP) in an American journal. Little could they have realised how the method they devised would still be a significant part of the research agenda nearly half a century later. Adaptations of their method are significant components in the analysis of the many different extensions to the problem that have been investigated. This paper provides the historical background to the development of the savings method and subsequent proposed variations to the basic savings formula and other improvements, and then charts the role the savings method has played in the investigation of VRPs with additional constraints. Some interesting examples of practical applications of the savings method are reported. Finally, comments are made on the use of the savings method in commercial routing packages.

Transportation is a main component of supply chain competitiveness since it plays a major role in the inbound, inter-facility, and outbound logistics. In this context, assigning and scheduling vehicle routing is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic nature of travel times in this problem. In this paper, a vehicle routing problem with time windows and stochastic travel times due to potential ...

Waste Management (WM) obtains one third of its revenue from landfill disposals and two-thirds from wastecollection services. As most of the revenue comes from collecting trash, improving efficiency in operating the fleet improves the bottom line. After a flurry of acquisitions and a merger with USA Waste, WM found itself with a large fleet of vehicles whose routing, dispatching, maintenance, and management were decentralized. WM recognized that it could reduce operating costs by improving its use of assets. It contracted with the Institute of Information Technology to develop WasteRoute, a comprehensive route-management system that took into account WM's specific routing concerns and provided broad benefits. Initially, the target audience of the system was the dispatchers and indirectly the drivers. Sales and customer service also benefited because WasteRoute integrated the sales, customer service, and operations departments. The system reduced operating costs, provided better customer service, and determined appropriate prices. WM deployed WasteRoute across the nation beginning in March 2003. By the end of 2003, WM had 984 fewer routes, saving $18 million. It estimated that its savings for 2004 due to the reduction will be $44 million. As it extends the system to additional areas, it expects additional route reductions.

In this paper, we study an extension of the PVRP where the vehicles can renew their capacity at some intermediate facilities. Each vehicle returns to the depot only when its work shift is over. For this problem we propose a tabu search (TS) algorithm and present computational results on a set of randomly generated instances and on a set of PVRP instances taken from the literature. Ó

This paper is a survey of location-routing: a relatively new branch of locational analysis that takes into account vehicle routing aspects. We propose a classification scheme and look at a number of problem variants. Both exact and heuristic algorithms are investigated. Finally, some suggestions for future research are presented.

In 2004 and 2005, Coca-Cola Enterprises (CCE)-the world's largest bottler and distributor of Coca-Cola products-implemented ORTEC's vehicle-routing software. Today, over 300 CCE dispatchers use this software daily to plan the routes of approximately 10,000 trucks. In addition to handling nonstandard constraints, the implementation is notable for its progressive transition from the prior business practice. CCE has realized an annual cost saving of $45 million and major improvements in customer service. This approach has been so successful that Coca-Cola has extended it beyond CCE to other Coca-Cola bottling companies and beer distributors.

... JfB (2008) 58: 81–117 A survey on pickup and delivery problems Part II: Transportation between pickup and delivery locations ... Keywords Pickup and delivery vehicle routing · Pickup and delivery problem · Dial-a-ride problem · Transportation · Survey ...

The aim of this chapter is to survey the state of the art in location-routing. The location-routing problem (LRP) is a research area within location analysis, with the distinguishing property of paying special attention to underlying issues of vehicle routing. Since the Vehicle-Routing Problem (VRP), which is a complex problem itself, is known as a basic component of LRPs, the main concepts of VRP are introduced in the first section. In the second section, the definition, applications and classifications of LRP are discussed. The next section is dedicated to the LRP models and introduces some basic mathematical models of this field. Solution techniques are presented in the fourth section. Finally, three case studies regarding applications of LRP in real world are briefly reviewed.

Assigning and scheduling vehicle routes in a dynamic environment is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic and dynamic nature of travel times. In this paper, a vehicle routing problem with time-dependent travel times due to potential traffic congestion is considered. The approach developed introduces the traffic congestion component based on queueing theory. This is an innovative modelling scheme to capture the stochastic behavior of travel times as it generates an analytical expression for the expected travel times as well as for the variance of the travel times. Routing solutions that perform well in the face of the extra complications due to congestion are developed. These more realistic solutions have the potential to reduce real operating costs for a broad range of industries which daily face routing problems. A number of datasets are used to illustrate the appropriateness of the novel approach. Moreover it is shown that static (or time-independent) solutions are often infeasible within a congested traffic environment which is generally the case on European road networks. Finally, the effect of travel time variability (obtained via the queueing approach) is quantified for the different datasets.

This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.

In the vehicle routing problem with time window (VRPTW), the objective is to minimize the number of vehicles and then minimize the total time travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. An effective tabu search for vehicle routing with time window (TSTS-VRPTW) heuristic for this problem is proposed. The TSTS-VRPTW is based on three function MOVE, EXCHANGE, SWAP. Computational results on Solomon ′ s benchmarks that consist of six different datasets show that the proposed TSTS-VRPTW is comparable in terms of solution quality to the best performing published heuristics.

The aim of this chapter is to survey the state of the art in location-routing. The location-routing problem (LRP) is a research area within location analysis, with the distinguishing property of paying special attention to underlying issues of vehicle routing. Since the Vehicle-Routing Problem (VRP), which is a complex problem itself, is known as a basic component of LRPs, the main concepts of VRP are introduced in the first section. In the second section, the definition, applications and classifications of LRP are discussed. The next section is dedicated to the LRP models and introduces some basic mathematical models of this field. Solution techniques are presented in the fourth section. Finally, three case studies regarding applications of LRP in real world are briefly reviewed.

In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants. This chapter proposes a classification and a generic formulation for the SPPRCs, briefly discusses complex modeling issues involving resources, and presents the most commonly used SPPRC solution methods. First and foremost,

A number of technological advances have led to a renewed interest on dynamic vehicle routing problems. This survey classifies routing problems from the perspective of information quality and evolution. After presenting a general description of dynamic routing, we introduce the notion of degree of dynamism, and present a comprehensive review of applications and solution methods for dynamic vehicle routing problems.

This scientific report summarizes the results of a literature review on dynamic vehicle routing problems. After a brief description of vehicle routing problems in general, a classification is introduced to distinguish between static and dynamic problems. Then a more precise definition of dynamism is presented, supported by example of real-world applications of such problems. Finally, a detailed study of the current state of the art in dynamic vehicle routing optimization is drawn.

The paper addresses the problem of multi-depot vehicle routing in order to minimize the delivery time of vehicle objective. Three hybrid heuristics are presented to solve the multi-depot vehicle routing problem. Each hybrid heuristic combines elements from both constructive heuristic search and improvement techniques. The improvement techniques are deterministic, stochastic and simulated annealing (SA) methods. Experiments are run on a number of randomly generated test problems of varying depots and customer sizes. Our heuristics are shown to outperform one of the best-known existing heuristic. Statistical tests of significance are performed to substantiate the claims of improvement.

The globalisation of the economy leads to a rapidly growing exchange of goods on our planet. Limited commodities and transportation resources, high planning complexity and the increasing cost pressure through the strong competition between logistics service providers make it essential to use computer-aided systems for the planning of the transports. An important subtask in this context is the operational planning of trucks or other specialized transportation vehicles. These optimization tasks are called Vehicle Routing Problems (VRP). Over 1000 papers about a huge variety of Vehicle Routing Problems indicate the practical and theoretical importance of this NP-hard optimization problem. Therefore, many specific solvers for different Vehicle Routing Problems can be found in the literature. The drawback is that most of these solvers are high specialized and inflexible and it needs a lot of effort to adapt them to modified problems. Additionally, most real world problems are often much more complex than the idealized problems out of literature and they also change over time. To face this issue, we present an integrated modelling and optimization framework for solving complex and practical relevant Vehicle Routing Problems. The modular structure of the framework, a script based modelling language, a library of VRP related algorithms and a graphical user interface give the user both reusable components and high flexibility for rapid prototyping of complex Vehicle Routing Problems.

This paper presents an exact solution framework for solving some variants of the vehicle routing problem (VRP) that can be modeled as set partitioning (SP) problems with additional constraints. The method consists in combining different dual ascent procedures to find a near optimal dual solution of the SP model. Then, a column-and-cut generation algorithm attempts to close the integrality gap left by the dual ascent procedures by adding valid inequalities to the SP formulation. The final dual solution is used to generate a reduced problem containing all optimal integer solutions that is solved by an integer programming solver. In this paper, we describe how this solution framework can be extended to solve different variants of the VRP by tailoring the different bounding procedures to deal with the constraints of the specific variant. We describe how this solution framework has been recently used to derive exact algorithms for a broad class of VRPs such as the capacitated VRP, the VRP with time windows, the pickup and delivery problem with time windows, 123 230 R. Baldacci et al. all types of heterogeneous VRP including the multi depot VRP, and the period VRP. The computational results show that the exact algorithm derived for each of these VRP variants outperforms all other exact methods published so far and can solve several test instances that were previously unsolved.

Taniguchi defines City Logistics as "the process of totally optimising the logistics and transport activities by private companies in urban areas while considering the traffic environment, traffic congestion and energy consumption within the framework of a market economy". The distribution of goods based on road services in urban areas contribute to traffic congestion, generates environmental impacts and in some cases incurs in high logistics costs. On the other hand the various stakeholders involved in the applications may have possibly conflicting objectives. Industrial firms, shippers, freight carriers, have individually established to meet consumer demands looking to maximize the company effectiveness and as a consequence from a social point of view the resulting logistics system is inefficient from the point of view of the social costs and environmental impacts. As a consequence the design and evaluation of City Logistics applications requires an integrated framework in which all components could work together. Therefore City Logistics models must be models that, further than including the main components of City Logistics applications, as vehicle routing and fleet management models, should be able of including also the dynamic aspects of the underlying road network, namely if ICT applications are taken into account. Some of the methodological proposals made so far are based on an integration of vehicle routing models and, dynamic traffic simulation models that emulate the actual traffic conditions providing at each time interval the estimates of the current travel times, queues, etc. on each link of the road network, that is, the information that will be used by the logistic model (i.e. a fleet management system identifying in real-time the positions of each vehicle in the fleet and its operational conditions -type of load, available capacity, etc. -to determine the optimal dynamic routing and scheduling of the vehicle. This paper reports on the modeling framework developed and tested in the European Project MEROPE of the INTERREG IIIB Programme, and in the national project SADERYL, sponsored by the Spanish DGCYT. The modeling framework is supported by a Computer Decision Support System which core architecture consists of the following main components: A Data Base, to store all the data required by the implied models: locations of logistic centres and customers, capacities of warehouses and depots, transportation costs, operational costs, fleet data, etc.; a Data Base Management System, for the updating of the information stored in the data base; a Model Base, containing the family of models and algorithms to solve the related problems, discrete location, network location, street vehicle routing and scheduling, to account explicitly with the asymmetry of costs typical of urban applications etc.; a Model Base Management System, to update, modify, add or delete models from the Model Base; a Graphic User Interface, GUI, supporting the windows based dialogues to define and update data, select the model suited to the intended problem, apply the corresponding algorithm, visualize the problem and the results, etc.

The technician routing and scheduling problem consists in routing and scheduling a crew of technicians in order to attend a set of service requests, subject to skill, tool, and spare part constraints. In this study we propose a formal definition of the problem and present a constructive heuristic and a large neighborhood search optimization algorithm.