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The aim of this erratum is to correct an error in the computer implementation of the algorithm proposed by Dabia, Ropke, and van Woensel [Dabia S, Ropke S, van Woensel T (2013) Branch and price for the time-dependent vehicle routing problem with time windows. Transportation Sci. 47(3):295–454]. Section 6, "Computational Results," from the original paper is rewritten to reflect the corrected implementation, the new computational setup, and the updated results. [ABSTRACT FROM AUTHOR]

This paper describes an exact branch-and-cut (B&C) algorithm for the split delivery vehicle routing problem. The underlying model is based on a previously proposed two-index vehicle flow formulation that models a relaxation of the problem. We dynamically separate two well-known classes of valid inequalities, namely capacity and connectivity cuts, and use an in-out algorithm to improve the convergence of the cutting phase. We generate no-good cuts from feasible integer solutions to the relaxation using a recently proposed single-commodity flow formulation in the literature. The exact methodology is complemented by a very effective adaptive large neighborhood search (ALNS) heuristic that provides high-quality upper bounds to initiate the B&C algorithm. Key ingredients in the design of the heuristic include the use of a tailored construction algorithm, which can exploit the situation in which the ratio of the number of customers to the minimum number of vehicles needed is low, and the use of a route-based formulation to improve the solutions found before, during, and after the ALNS procedure. An earlier version of this work was submitted to the DIMACS (Center for Discrete Mathematics and Theoretical Computer Science) implementation challenge, where it placed third. On sets of well-known benchmark instances for limited and unlimited fleet variants of the problem, we demonstrate that the heuristic provides very competitive solutions, with respective average gaps of 0.19% and 0.18% from best-known values. Furthermore, the exact B&C framework is also highly competitive with state-of-the-art methods, providing solutions with an average optimality gap of 1.82%. History: This paper has been accepted for the Transportation Science Special Section on DIMACS Implementation Challenge: Vehicle Routing Problems. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0353. [ABSTRACT FROM AUTHOR]

We consider a variant of the berth allocation problem—that is, the multiport berth allocation problem—aimed at assigning berthing times and positions to vessels in container terminals. This variant involves optimizing vessel travel speeds between multiple ports, thereby exploiting the potentials of a collaboration between carriers (shipping lines) and terminal operators. Using a graph representation of the problem, we reformulate an existing mixed-integer problem into a generalized set partitioning problem, in which each variable refers to a sequence of feasible berths in the ports that the vessel visits. By integrating column generation and cut separation in a branch-and-cut-and-price procedure, our proposed method is able to outperform commercial solvers in a set of benchmark instances and adapt better to larger instances. In addition, we apply cooperative game theory methods to efficiently distribute the savings resulting from a potential collaboration and show that both carriers and terminal operators would benefit from collaborating. [ABSTRACT FROM AUTHOR]

In global liner shipping networks, a large share of transported cargo is transshipped at least once between container vessels, and the total transportation time of these containers depends on how well the corresponding services are synchronized. We propose a problem formulation that integrates service scheduling into the liner shipping network design problem. Furthermore, the model incorporates many industry-relevant modeling aspects: it allows for leg-based sailing speed optimization, it is not limited to simple or butterfly-type services, and it accounts for service-level requirements such as cargo transit time limits. The classic liner shipping network design problem is already a hard problem, and to solve the extended version, we propose a column-generation matheuristic that uses advanced linear programming techniques. The proposed method solves LINER-LIB instances of up to 114 ports and, if applied to the classic liner shipping network design problem, finds new best solutions to all instances, outperforming existing methods reported in the literature. Additionally, we analyze the relevance of scheduling for liner shipping network design. The results indicate that neglecting scheduling and approximating transshipments instead may result in the design of liner shipping networks that underestimate cargo transit times and their implications. [ABSTRACT FROM AUTHOR]

This paper introduces the vehicle routing problem with time windows and shifts (VRPTWS). At the depot, several shifts with nonoverlapping operating periods are available to load the planned trucks. Each shift has a limited loading capacity. We solve the VRPTWS exactly by a branch-and-cut-and-price algorithm. The master problem is a set partitioning with an additional constraint for every shift. Each constraint requires the total quantity loaded in a shift to be less than its loading capacity. For every shift, a pricing subproblem is solved by a label-setting algorithm. Shift capacity constraints define knapsack inequalities; hence we use valid inequalities inspired from knapsack inequalities to strengthen the linear programming relaxation of the master problem when solved by column generation. In particular, we use a family of tailored robust cover inequalities and a family of new nonrobust cover inequalities. Numerical results show that nonrobust cover inequalities significantly improve the algorithm. [ABSTRACT FROM AUTHOR]