An exact solution approach for vehicle routing and scheduling problems with soft time windows

A new column generation based exact optimization approach for the vehicle routing and scheduling problem with semi soft time windows (VRPSSTW) is presented. Elementary shortest path problem with resource constraints and late arrival penalties is solved as a subproblem, which rises from the Dantzig–Wolfe decomposition method. Exact solutions of VRPSSTW and hard time windows variant are compared on Solomon’s benchmark instances as well as on an instance based on Tokyo road network. It was found that the VRPSSTW solution results in fewer routes thus overall costs are reduced and late arrival penalties contribute only a small fraction to total cost.     

A spatiotemporal partitioning approach for large-scale vehicle routing problems with time windows

For VRP with time windows (VRPTW) solved by conventional cluster-first and route-second approach, temporal information is usually considered with vehicle routing but ignored in the process of clustering. We propose an alternative approach based on spatiotemporal partitioning to solving a large-scale VRPTW, considering jointly the temporal and spatial information for vehicle routing. A spatiotemporal representation for the VRPTW is presented that measures the spatiotemporal distance between two customers. The resulting formulation is then solved by a genetic algorithm developed for k-medoid clustering of large-scale customers based on the spatiotemporal distance. The proposed approach showed promise in handling large scale networks.     

The time constrained multi-commodity network flow problem and its application to liner shipping network design

The multi-commodity network flow problem is an important sub-problem in several heuristics and exact methods for designing route networks for container ships. The sub-problem decides how cargoes should be transported through the network provided by shipping routes. This paper studies the multi-commodity network flow problem with transit time constraints which puts limits on the duration of the transit of the commodities through the network. It is shown that for the particular application it does not increase the solution time to include the transit time constraints and that including the transit time is essential to offer customers a competitive product.     

The trade-off between fixed vehicle costs and time-dependent arrival penalties in a routing problem

This paper introduces the vehicle routing problem with soft time windows (VRPSTW) in which problem definition differs from ones previously defined in literature. Branch-and-price approach is employed, resulting in a set partitioning master problem and its new subproblem. Novel techniques are consequently developed to solve this new subproblem. Experimental results report the comparisons of these solution techniques under the branch-and-price framework. The VRPSTW solutions have further been compared to the state-of-the-art literature, signifying the superiority of the VRPSTW on this issue.     

A reactive tabu search algorithm for the multi-depot container truck transportation problem

A container truck transportation problem that involves multiple depots with time windows at both origins and destinations, including the reposition of empty containers, is formulated as a multi-traveling salesman problem with time windows (m-TSPTW) with multiple depots. Since the problem is NP-hard, a cluster method and a reactive tabu search (RTS) algorithm are developed to solve the problem. The two methods are compared with the mixed integer program which can be used to find optimum solutions for small size problems. The computational results show that the developed methods, particularly the RTS algorithm, can be efficiently used to solve the problem.     

Vehicle routing optimization with soft time windows in a fuzzy random environment

This paper is concerned with a vehicle routing problem with soft time windows (VRPSTW) in a fuzzy random environment. Two objectives are considered: (1) minimize the total travel cost and (2) maximize the average satisfaction level of all customers. After setting up the model for the VRPSTW in a fuzzy random environment, the fuzzy random expected value concept is used to deal with the constraints and its equivalent crisp model is derived. The global–local–neighbor particle swarm optimization with exchangeable particles (GLNPSO-ep) is employed to solve the equivalent crisp model. A case study is also presented to illustrate the effectiveness of the proposed approach.     

An exact algorithm for the multi-trip vehicle routing and scheduling problem of pickup and delivery of customers to the airport

Door-to-Door service of Pickup and Delivery of Customers to the Airport (D2PDCA) is a new service provided by certain Airline Ticket Sales Agencies (ATSAs) in China. This new service provides an attractive alternative way by picking up customer at this/her specified position and at any time he/she preferred and delivering to the airport more conveniently than airport shuttle and thus earn high customer service quality. Compared with the single-trip mode, the multi-trip mode of D2PDCA (MTM-D2PDCA) service can reduce travel distances, the number of vehicles required and the operating cost. To obtain the exact solution of the MTM-D2PDCA problem, we propose a novel, exact algorithm based on the trip-chain-oriented set-partitioning (TCO-SP) model, where a trip-chain represents multiple trips made by a specific vehicle. In the exact algorithm, we propose an improved label-correcting method to remove infeasible trip-chains quickly and thus speed the search process. Based on the feasible trip-chains, the MTM-D2PDCA problem is formulated as the novel TCO-SP model, which can be solved exactly by the optimization software CPLEX. In addition, we present several mathematical insights into the relationship between the number of trip-chains and the number of local optimal trips that are applicable in both theory and practice. Extensive experiments are conducted to illustrate the application of the model and demonstrate the cost savings of the MTM-D2PDCA mode over the single-trip mode and provide managerial insights into successfully operating a MTM-D2PDCA service.     

The time dependent vehicle routing problem with time windows: Benchmark problems, an efficient solution algorithm, and solution characteristics

An algorithm that can tackle time dependent vehicle routing problems with hard or soft time windows without any alteration in its structure is presented. Analytical and experimental results indicate that average computational time increases proportionally to the number of customers squared. New replicable test problems that capture the typical speed variations of congested urban settings are proposed. Solution quality, time window perturbations, and computational time results are discussed as well as a method to study the impact of perturbations by problem type. The algorithm efficiency and simplicity is well suited for urban areas where fast running times may be required.     

An integer programming approach to the bloodmobile routing problem

Every day, a blood center must determine a set of locations among a group of potential sites to route their vehicles for blood collection so as to avoid shortfalls. In this study, a vehicle routing problem is modeled using an integer programming approach to simultaneously identify number of bloodmobiles to operate and minimize the distance travelled. Additionally, the model is extended to incorporate uncertainty in blood potentials and variable durations in bloodmobile visits. Optimal routings are determined using CPLEX solver and branch-and-price algorithm. Results show that proposed algorithm solve the problem to optimality up to 30 locations within 3600 s.     

Solving an integrated operational transportation planning problem with forwarding limitations

In integrated operational transportation planning (IOTP) problems, the traditional vehicle routing problem is extended by using external resources for the fulfillment of transportation requests. IOTP is getting more complex when the choice of the fulfillment mode is limited for some requests. In this paper, an existing column generation-based heuristic for IOTP is extended by two strategies for handling forwarding limitations. The computational experiments indicate that one of the extended versions of the heuristic outperforms all previous approaches in literature. Further on, the impact of forwarding limitations on different location structures and on the size of the private fleet is analyzed.     

Accounting for population exposure to vehicle-generated pollutants and environmental equity in the toll design problem

The emissions generated by motor vehicles remain a major source of air pollutants that affect public health and contribute to anthropogenic climate change. These negative externalities can be reduced, in part, with the implementation of environmentally oriented road pricing schemes, which can be designed using optimization-based approaches. In this paper, a toll design problem is proposed for determining toll locations and levels that minimize the expected human exposure to air pollutants and the related environmental inequalities, subject to constraints on pollutant concentration levels and implementation costs. The practical use of the proposed problem is hindered in most real-world applications by the computational costs associated with the evaluation of candidate solutions, as is common for network design problems. Furthermore, the problem cannot be expressed analytically given the multiple types of models (e.g., traffic assignment, emissions, air dispersion models) that would be required to evaluate a single design alternative. For these reasons, a derivative-free surrogate-based solution algorithm is proposed for mixed integer problems like the ones considered here. Numerical examples are used to illustrate possible applications of the proposed model and to test the performance of the surrogate-based algorithm. Relative to a joint simulated annealing-genetic algorithm heuristic and a genetic algorithm-based approach, the proposed algorithm found better solutions in fewer function evaluations.     

A robust optimization approach for the road network daily maintenance routing problem with uncertain service time

This paper studies the robust optimization approach for the routing problem encountered in daily maintenance operations of a road network. The uncertainty of service time is considered. The robust optimization approach yields routes that minimize total cost while being less sensitive to substantial deviations of service times. A robust optimization model is developed and solved by the branch-and-cut method. In computational experiments, the behavior of the robust solutions and their performance are analyzed using Monte Carlo simulation. The robust optimization model is also compared with a classic chance-constrained programming model. The experimental analysis provides managerial insights for decision makers to determine an appropriate routing strategy.     

A combinatorial benders’ cuts algorithm for the quayside operation problem at container terminals

The quayside operation problem is one of the key components in the management system for a container terminal. In this paper, the integrated models proposed in the previous studies to address the quayside operation problem are examined and one of the potential frameworks is identified. A new method called combinatorial benders’ cuts algorithm is developed to solve the berth-level model in the framework. The computational experiment conducted in this research shows that the proposed approach is more efficient than the branch and cut algorithm embedded in CPLEX.