In modular shipbuilding, modules are used to lower construction costs and decrease lead times. Achieving these decreases in both costs and time requires making the right choices in material use and activity planning. Therefore, we introduce the Resource Constrained Project Scheduling Problem with Modular Production in which decisions are made for the inventory level of resources, activity selection and activity scheduling, in order to maximize profit minus inventory costs. Since these decisions have to be made before uncertain project arrival information is revealed, a scenario-tree based approach is used that optimizes over multiple scenarios simultaneously. An Integer Linear Programming formulation is introduced for this problem and a Progressive Hedging algorithm to find good solutions to this problem, along with two extensions to this algorithm. A computational study is performed, where the activity selection decisions are used to model choices in modular production and outsourcing. The basic PH algorithm outperforms using a commercial solver to find feasible solutions to the ILP model, in terms of both solution quality and computing time. However, the basic PH algorithm still has a hard time converging to an implementable solution, which makes the algorithm rely heavily on a repair step. The introduced extensions improve the convergence properties significantly, and can also be used to prioritize solution quality and/or computing time.

Benders is a household name in optimization, but as a person he was hardly known beyond his circle of colleagues and students. In this brief paper, we review his life and work.

In large modular construction projects, such as shipbuilding, multiple similar projects arrive stochastically. At project arrival, a schedule has to be created, in which future modifications are difficult and/or undesirable. Since all projects use the same set of shared resources, current scheduling decisions influence future scheduling possibilities. To model this problem, we introduce the Dynamic Resource Constrained Multi-project Scheduling Problem with Static project Schedules. To find schedules, both a greedy approach and simulation-based approach with varying scenarios are introduced. Although the simulation-based approach schedules projects proactively, the computing times are long, even for small instances. Therefore, a method is introduced that learns from schedules obtained in the simulation-based method and uses a neural network to estimate the objective function value. It is shown that this method achieves a significant improvement in objective function value over the greedy algorithm, while only requiring a fraction of the computation time of the simulation-based method.

The Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS) is a generalization of the Resource Constrained Project Scheduling Problem (RCPSP). In the RCPSP, the goal is to determine a minimal makespan schedule subject to precedence and resource constraints. The generalization introduced in the RCPSP-PS is that, instead of executing all activities, only a subset of all activities has to be executed. We present a model that is based on two graphs: one representing precedence relations and one representing the activity selection structure. The latter defines which subset of activities has to be executed. Additionally, we present theoretical properties of this model and give an exact solution method that makes use of these properties by generating cutting planes and setting bounds on variables. Furthermore, three problem properties are introduced to classify problems in the literature. We compare our model to a model from literature on instances that possess a subset of these three problem properties and find a reduction in computing time. Furthermore, by comparing results on instances that possess all problem properties, it is shown that the computing times are decreased and better lower bounds are found by the cutting planes and variable bounds presented in this paper.

Branch-and-bound for integer optimization typically uses single-variable disjunctions. Enumerative methods for integer optimization with theoretical guarantees use a non-binary search tree with general disjunctions based on lattice structure. These disjunctions are expensive to compute and challenging to implement. Here we compare two lattice reformulations that can be used to heuristically obtain general disjunctions in the original space, we develop a new lattice-based variant, and compare the derived disjunctions computationally with those produced by the algorithm of Lovász and Scarf.

The resource constrained project scheduling problem with a flexible project structure and consumption and production of resources, involves making a selection of activities and scheduling these activities in order to minimize the makespan, subject to precedence and resource constraints. Since finding a feasible selection of activities is NP-hard, we introduce the concept of group graphs and restrict ourselves to instances with an acyclic group graph. For these instances, which represent many practical cases, we show how to make a feasible selection of activities in polynomial time and use this concept to schedule the selected activities using a hybrid differential evolution algorithm. We compare this algorithm with an algorithm from the literature on special cases of instances without consumption and production of resources, and show that our algorithm creates solutions of higher quality. Furthermore, to compare general instances, we develop an ant colony optimization algorithm that performs slightly better on special cases than the algorithm from literature and show that the hybrid differential evolution algorithm outperforms the ant colony optimization algorithm on general instances.

Background Ambulance services play a crucial role in providing pre-hospital emergency care. In order to ensure quick responses, the location of the bases, and the distribution of available ambulances among these bases, should be optimized. In mixed urban-rural areas, this optimization typically involves a trade-off between backup coverage in high-demand urban areas and single coverage in rural low-demand areas. The aim of this study was to find the optimal distribution of bases and ambulances in the Vestfold region of Norway in order to optimize ambulance coverage. Method The optimal location of bases and distribution of ambulances was estimated using the Maximum Expected Covering Location Model. A wide range of parameter settings were fitted, with the number of ambulances ranging from 1 to 15, and an average ambulance utilization of 0, 15, 35 and 50%, corresponding to the empirical numbers for night, afternoon and day, respectively. We performed the analysis both conditioned on the current base structure, and in a fully greenfield scenario. Results Four of the five current bases are located close to the mathematical optimum, with the exception of the northernmost base, in the rural part of the region. Moving this base, along with minor changes to the location of the four other bases, coverage can be increased from 93.46% to 97.51%. While the location of the bases is insensitive to the workload of the system, the distribution of the ambulances is not. The northernmost base should only be used if enough ambulances are available, and this required minimum number increases significantly with increasing system workload. Conclusion As the load of the system increases, focus of the model shifts from providing single coverage in low-demand areas to backup coverage in high-demand areas. The classification rule for urban and rural areas significantly affects results and must be evaluated accordingly.

Background: Helicopter emergency medical services are important in many health care systems. Norway has a nationwide physician manned air ambulance service servicing a country with large geographical variations in population density and incident frequencies. The aim of the study was to compare optimal air ambulance base locations using both population and incident data. Methods: We used municipality population and incident data for Norway from 2015. The 428 municipalities had a median (5-95 percentile) of 4675 (940-36,264) inhabitants and 10 (2-38) incidents. Optimal helicopter base locations were estimated using the Maximal Covering Location Problem (MCLP) optimization model, exploring the number and location of bases needed to cover various fractions of the population for time thresholds 30 and 45 min, in green field scenarios and conditioned on the existing base structure. Results: The existing bases covered 96.90% of the population and 91.86% of the incidents for time threshold 45 min. Correlation between municipality population and incident frequencies was -0.0027, and optimal base locations varied markedly between the two data types, particularly when lowering the target time. The optimal solution using population density data put focus on the greater Oslo area, where one third of Norwegians live, while using incident data put focus on low population high incident areas, such as northern Norway and winter sport resorts. Conclusion: Using population density data as a proxy for incident frequency is not recommended, as the two data types lead to different optimal base locations. Lowering the target time increases the sensitivity to choice of data.

We consider the Maximum Weighted Coverage problem (MCP). We can relate the MCP to optimisation problems using submodular functions. Performance guarantees of the Swap Local Search algorithm are known for these problems, but can be improved for the MCP. Our main contribution is a constructive proof of tight performance guarantees for Swap Local Search applied to the MCP, which provides insight into the structure of worst-case MCP instances, and has the potential to be applicable to other optimisation problems.