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In this paper, we study a problem that integrates the vessel scheduling problem with the berth allocation into a collaborative problem denoted as the multi-port continuous berth allocation problem (MCBAP). This problem optimizes the berth allocation of a set of ships simultaneously in multiple ports while also considering the sailing speed of ships between ports. Due to the highly combinatorial character of the problem, exact methods struggle to scale to large-size instances, which points to exploring heuristic methods. We present a mixed-integer problem formulation for the MCBAP and introduce an adaptive large neighborhood search (ALNS) algorithm enhanced with a local search procedure to solve it. The computational results highlight the method's suitability for larger instances by providing high-quality solutions in short computational times. Practical insights indicate that the carriers' and terminal operators' operational costs are impacted in different ways by fuel prices, external ships at port, and the modeling of a continuous quay.

We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally non-uniform, periods and do not exclude all optimal solutions, but they constrain solutions to adhere to a canonical form. The new formulation has numerous variables and constraints, and hence we apply a Dantzig-Wolfe decomposition in order to compute the linear programming relaxation in reasonable time; the resulting lower bound is stronger than the bound from the classical time-indexed formulation. We develop a branch-and-price framework that solves several instances from the literature for the first time. We compare the new formulation with the time-indexed and arc-time-indexed formulation by means of a series of computational experiments.

We study a new variant of the vehicle routing problem, called the Mobile Production Vehicle Routing Problem (MoP-VRP). In this problem, vehicles are equipped with 3D printers, and production takes place on the way to the customer. The objective is to minimize the weighted cost incurred by travel and delay of service. We formulate a Mixed Integer Programming (MIP) model and develop an Adaptive Large Neighbourhood Search (ALNS) heuristic for this problem. To show the advantage of mobile production, we compare the problem with the Central Production Vehicle Routing Problem (CP-VRP), where production takes place in a central depot. We also propose an efficient ALNS for the CP-VRP. We generate benchmark instances based on Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances, and realistic instances based on real-life data provided by the Danish Company 3D Printhuset. Overall, the proposed ALNS for both problems are efficient, and we solve instances up to 200 customers within a short computational time. We test different scenarios with varying numbers of machines in each vehicle, as well as different production time. The results show that these are the key factors that influence travel and delay costs. The key advantage of mobile production is flexibility: it can shorten the time span from the start of production to the delivery of products, and at the same time lower delivery costs. Moreover, long-term cost estimations show that this technology has low operation costs and thus is feasible in real life practice., Comment: Submitted to European Journal of Operational Research (revision round)

This paper introduces a family of valid inequalities, that we term consistency cuts, to be applied to a Dantzig-Wolfe reformulation (or decomposition) with linking variables. We prove that these cuts ensure an integer solution to the corresponding Dantzig-Wolfe relaxation when certain criteria to the structure of the decomposition are met. We implement the cuts and use them to solve a commonly used test set of 200 instances of the temporal knapsack problem. We assess the performance with and without the cuts and compare further to CPLEX and other solution methods that have historically been used to solve the test set. By separating consistency cuts we show that we can obtain optimal integer solutions much faster than the other methods and even solve the remaining unsolved problems in the test set. We also perform a second test on instances from the MIPLIB 2017 online library of mixed-integer programs, showing the potential of the cuts on a wider range of problems., Comment: To appear in Operations Research

We consider a variant of the berth allocation problem-i.e., the multi-port 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., Comment: 42 pages, 9 figures

In this study, the periodic train timetabling problem is formulated using a time-space graph formulation. Three solution methods are proposed and compared where solutions are built by what we define as a dive-and-cut-and-price procedure. An LP relaxed version of the problem with a subset of constraints is solved using column generation where each column corresponds to the train paths of a line. Violated constraints are added by separation and a heuristic process is applied to help to find integer solutions. The passenger travel time is computed based on a solution timetable and Benders' optimality cuts are generated allowing the method to integrate the routing of the passengers. We propose two large neighborhood search methods where the solution is iteratively destroyed and repaired into a new one and one random iterative method. The problem is tested on the morning rush hour period of the Regional and InterCity train network of Zealand, Denmark. The solution approaches show robust performance in a variety of scenarios, being able to find good quality solutions in terms of travel time and path length relatively fast. The inclusion of the proposed Benders' cuts provides stronger relaxations to the problem. In addition, the graph formulation covers different real-life constraints and has the potential to easily be extended to accommodate more constraints.