In this paper, we introduce a Dantzig-Wolfe reformulation to compute aircraft arrival routes in a terminal maneuvering area (TMA) where the aircraft are flying according to theoptimal continuous-descent-operation (CDO) speed profile with idle thrust. This model assumes fixed entry times for all aircraft and a single separation time that is independent of wake-turbulence categories.Preliminary experiments show that this approach leads to significantly reduced runtimes.Moreover, the results indicate the possiblity of extending the reformulation to the full model and applying it to address additional practical considerations, such as wind effects in the future.

In hospitals, the nurse schedules are sensitive to disruptions such as sick leave since the absence of nurses with the right skills can have a severe impact on healthcare quality. We consider nurse rerostering from a strategic perspective in the case of having multiple skills and varying staffing demand. Our aim is to design a decision support tool to be used on a strategic level to analyse how the distribution of skills affects the sick-leave robustness of schedules. Schedules are evaluated based on generated scenarios with sick leave and possible rerostering of tasks. We have performed a case study at a ward in a Swedish hospital, and show how our tool can be used to indicate which of the available skills can be removed, with only a small impact on the understaffing in the nominal scenario and in scenarios with sick leave.

The elementary shortest path problem with resource constraints (ESPPRC) is a common problem that often arises as a pricing problem when solving vehicle routing problems with a column generation approach. One way of solving the ESPPRC is to use a labeling algorithm. In this paper, we focus on how different bounding strategies for labeling algorithms can be adapted and strengthened for the ESPPRC that arises from the Electric Vehicle Routing Problem with Time Windows and Piecewise Linear Recharging function (EVRPTW-PLR). We present a new completion bound method that takes charging times into account, and show how the completion bound can be combined with ng-routes. Computational experiments show that the new completion bound combined with ng-routes significantly improves the performance compared to a basic labeling algorithm.

The solution to a job scheduling problem that involves humans as well some other shared resource has to consider the humans’ availability times. For practical acceptance of a scheduling tool, it is crucial that the interaction with the humans is kept simple and to a minimum. It is rarely practical to ask users to fully specify their availability times or to let them enumerate all possible starting times for their jobs. In the scenario we are considering, users initially only propose a single starting time for each of their jobs and a feasible and optimized schedule shall then be found within a small number of interaction rounds. In each such interaction round, our scheduling approach may propose each user a small number of alternative time intervals for scheduling the user’s jobs, and then the user may accept or reject these. To make the best out of these limited interaction possibilities, we propose an approach that utilizes integer linear programming and an exact and computationally efficient probability calculation for the users’ availabilities assuming two different stochastic models. In this way, educated proposals of alternative time intervals for performing the jobs are determined based on the computed availability probabilities and the improvements these time intervals would enable. The approach is experimentally evaluated on a variety of artificial benchmark scenarios, and different variants are compared with each other and to diverse baselines. Results show that an initial schedule can usually be quickly improved over few interaction rounds even when assuming a quite simple stochastic model, and the final schedule may come close to the solution of the full-knowledge case despite the strongly limited interaction.

Logic-based Benders decomposition is a technique to solve optimization problems to optimality. It works by splitting the problem into a master problem, which neglects some aspects of the problem, and a subproblem, which is used to iteratively produce cuts for the master problem to account for those aspects. It is critical for the computational performance that these cuts are strengthened, but the strengthening of cuts comes at the cost of solving additional subproblems. In this work we apply a graph neural network in an autoregressive fashion to approximate the compilation of an irreducible cut, which then only requires few postprocessing steps to ensure its validity. We test the approach on a job scheduling problem with a single machine and multiple time windows per job and compare to approaches from the literature. Results show that our approach is capable of considerably reducing the number of subproblems that need to be solved and hence the total computational effort.

Cut-strengthening techniques have a significant impact on the computational effectiveness of the logic-based Benders’ decomposition (LBBD) scheme. While there have been numerous cut-strengthening techniques proposed, very little is understood about which techniques achieve the best computational performance for the LBBD scheme. This is typically due to implementations of LBBD being problem specific, and thus, no systematic study of cut-strengthening techniques for both feasibility and optimality cuts has been performed. This paper aims to provide guidance for future researchers with the presentation of an extensive computational study of five cut-strengthening techniques that are applied to three different problem types. The computational study involving 3000 problem instances shows that cut-strengthening techniques that generate irreducible cuts outperform the greedy algorithm and the use of no cut strengthening. It is shown that cut strengthening is a necessary part of the LBBD scheme, and depth-first binary search and deletion filter are the most effective cut-strengthening techniques.

Large-neighbourhood search (LNS) heuristics are important mathematical programming techniques that search for primal feasible solutions by solving an auxiliary problem with a restricted feasible region. Extending such powerful generic LNS heuristics to the branch-and-price context is inherently challenging. The most prominent challenges arise from the fact that in branch-and-price algorithms, columns are generated with the sole aim to solve linear programming relaxations. Hence, the ability to form integer feasible solutions is not considered during the generation of columns. Without any changes to the standard pricing schemes, the potential of deploying generic LNS heuristics within a branch-and-price procedure is severely limited. This paper proposes a matheuristic, based on an LNS heuristic framework, where the novelty is a customised pricing scheme for generating columns to solve an auxiliary problem. The theoretical foundation for this pricing scheme is a set of optimality conditions for integer programs. From this foundation, a column generation strategy is developed for finding columns that are likely to be of use in high-quality primal feasible solutions for the original problem. The proposed matheuristic is implemented in the generic branch-price-and-cut solver GCG. On a broad test set comprising classical block diagonal structured instances and general instances from the MIPLIB 2017 Collection, the computational results show a significant improvement to the solving performance of GCG.

When solving a job scheduling problem that involves humans, the times in which they are available must be taken into account. For practical acceptance of a scheduling tool, it is further crucial that the interaction with the humans is kept simple and to a minimum. Requiring users to fully specify their availability times is typically not reasonable. We consider a scenario in which initially users only suggest single starting times for their jobs and an optimized schedule shall then be found within a small number of interaction rounds. In each round users may only be suggested a small set of alternative time intervals, which are accepted or rejected. To make the best out of these limited interaction possibilities, we propose an approach that utilizes integer linear programming and a theoretically derived probability calculation for the users’ availabilities based on a Markov model. Educated suggestions of alternative time intervals for performing jobs are determined from these acceptance probabilities as well as the optimization’s current state. The approach is experimentally evaluated and compared to diverse baselines. Results show that an initial schedule can be quickly improved over few interaction rounds, and the final schedule may come close to the solution of the full-knowledge case despite the limited interaction.

To effectively solve challenging staff rerostering problems, we propose to enhance a large neighborhood search (LNS) with a machine learning guided destroy operator. This operator uses a conditional generative model to identify variables that are promising to select and combines this with the use of a special sampling strategy to make the actual selection. Our model is based on a graph neural network (GNN) and takes a problem-specific graph representation as input. Imitation learning is applied to mimic a time-expensive approach that solves a mixed-integer program (MIP) for finding an optimal destroy set in each iteration. An additional GNN is employed to predict a suitable temperature for the destroy set sampling process. The repair operator is realized by solving a MIP. Our learning LNS outperforms directly solving a MIP with Gurobi and yields improvements compared to a well-performing LNS with a manually designed destroy operator, also when generalizing to schedules with various numbers of employees.

Here lies the raw dataset for the publication "Instance dataset for a multiprocessor scheduling problem with multiple time windows and time lags: Similar instances with large differences in difficulty" (In revision). A version-controlled repository hosting the dataset is available at https://gitlab.liu.se/eliro15/multiprocessor_scheduling_inst