A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.Vehicle routing; branch-and-cut; separation

Minimum cost VRP with time-dependent speed data and congestion charge

A heuristic algorithm, called LANCOST, is introduced for vehicle routing and scheduling problems to minimize the total travel cost, where the total travel cost includes fuel cost, driver cost and congestion charge. The fuel cost required is influenced by the speed. The speed for a vehicle to travel along any road in the network varies according to the time of travel. The variation in speed is caused by congestion which is greatest during morning and evening rush hours. If a vehicle enters the congestion charge zone at any time, a fixed charge is applied. A benchmark dataset is designed to test the algorithm. The algorithm is also used to schedule a fleet of delivery vehicles operating in the London area

Minimizing CO2e emissions by setting a road toll

The main purpose of this paper is to develop a bi-level pricing model to minimize the CO2e emissions and the total travel time in a small road network. In the lower level of the model, it is assumed that users of the road network find a dynamic user equilibrium which minimises the total costs of those in the system. For the higher level of the model, different road toll strategies are applied in order to minimize the CO2e emissions. The model has been applied to an illustrative example. It shows the effects on traffic flows, revenues, total time and CO2e emissions for different numbers of servers collecting tolls and different pricing strategies over a morning peak traffic period. The results show that the CO2e emissions produced can be significantly affected by the number of servers and the type of toll strategy employed. The model is also used to find the best toll strategy when there is a constraint on the revenue that is required to be raised from the toll and how this affects the emissions produced. Further runs compare strategies to minimize the CO2e emissions with those that minimize total travel time in the road system. In the illustrative example, the results for minimizing CO2e emissions are shown to be similar to the results obtained from minimizing the total travel time

The Relationship between Vehicle Routing & Scheduling and Green Logistics - A Literature Survey

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

The potential use of e-procurement in the Malaysian palm oil industry supply chain

E-procurement is electronic methods of conducting business transactions particularly purchasing activities. Many companies around the world have started to apply the technologies though there are still some which refuse to utilize them. The objective of this paper was to investigate the application of e-procurement technologies in managing purchasing activities among the Malaysian Palm Oil Industry (MPOI) supply chain players. Responses from the representative player of each stage of the MPOI supply chain were gathered via in-depth interviews using an open ended questionnaire. A detailed analysis based on content analysis from the responses revealed that e-procurement technologies could be a potential tool to increase the efficiency of purchasing activities, enhance purchasing and searching processes, as well as providing relevant information on materials, and aid in the reduction of human error. Certain products for example fresh fruit bunch (FFB), crude palm oil (CPO), crude palm kernel oil (CPKO) and palm kernel however were found to be impractical to use e-procurement tools due to several reasons. These products were commonly supplied by very established suppliers who are quite conventional in their business. Thus e-procurement tools are not often used in their purchasing activities. This paper concluded that e-procurement technologies were not 'really' available in the MPOI supply chain

The Time-Dependent Multiple-Vehicle Prize-Collecting Arc Routing Problem

In this paper, we introduce a multi vehicle version of the Time-Dependent Prize-Collecting Arc Routing Problem (TD-MPARP). It is inspired by a situation where a transport manager has to choose between a number of full truck load pick-ups and deliveries to be performed by a fleet of vehicles. Real-life traffic situations where the travel times change with the time of day are taken into account. Two metaheuristic algorithms, one based on Variable Neighborhood Search and one based on Tabu Search, are proposed and tested for a set of benchmark problems, generated from real road networks and travel time information. Both algorithms are capable of finding good solutions, though the Tabu Search approach generally shows better performance for large instances whereas the VNS is superior for small instances. We discuss the structural differences of the implementation of the algorithms which explain these results

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers’ demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles’ capacities. In this paper, its features are analyzed. A mathematical model and Tabu Search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature

Fuel emissions optimization in vehicle routing problems with time-varying speeds

The problem considered in this paper is to produce routes and schedules for a fleet of delivery vehicles that minimize the fuel emissions in a road network where speeds depend on time. In the model, the route for each vehicle must be determined, and also the speeds of the vehicles along each road in their paths are treated as decision variables. The vehicle routes are limited by the capacities of the vehicles and time constraints on the total length of each route. The objective is to minimize the total emissions in terms of the amount of Greenhouse Gas (GHG) produced, measured by the equivalent weight of CO2 (CO2e). A column generation based tabu search algorithm is adapted and presented to solve the problem. The method is tested with real traffic data from a London road network. The results are analyzed to show the potential saving from the speed adjustment process. The analysis shows that most of the fuel emissions reduction is able to be attained in practice by ordering the customers to be visited on the route using a distance-based criterion, determining a suitable path between customers for each vehicle and travelling as fast as is allowed by the traffic conditions up to a preferred speed

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

Optimal location and size of logistics parks in a regional logistics network with economies of scale and CO2 emission taxes

This paper proposes a model to address the design problem of a regional logistics network. In the proposed model, the decision variables include the location and size of logistics parks. The interaction between the logistics authority and logistics users as well as the effects of economies of scale and CO2 emission taxes on the logistics network design are explicitly considered. The proposed model is formulated as a bi-level formulation, in which the upper level aims to maximize total social welfare of the system by determining the optimal location and size of logistics parks with CO2 emission taxes consideration, whereas the lower level describes the logistics users’ choices for service routes. A heuristic solution algorithm is presented to solve the proposed model, and a numerical example is given to illustrate the applications of the proposed model and solution algorithm. The findings show that the optimal location and size of logistics parks depend on the realized logistics demand and the level of the economies of scale. The CO2 emission taxation can help to improve the total social welfare of the system and drive the logistics users to choose greener transportation modes. First published online 28 January 201