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.

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In the field of shipbuilding, there is a growing demand for faster and more efficient production processes, along with a need for swift adoption of new technologies. Modular production emerges as a potential solution, involving the development of a product family with a base platform and various modules. Instead of designing and producing each product individually, modular production allows for the combination of modules to create diverse products. Despite the recognized potential of this approach, there is a lack of quantitative results, and scheduling challenges in modular shipbuilding need to be addressed for its successful implementation. This dissertation focuses on identifying and resolving three key challenges related to scheduling in modular production. The first challenge revolves around the definition and utilization of modules. Factors such as resource requirements, project sequencing influenced by module size, and project-specific variations in module usage are crucial considerations. The second challenge pertains to inventory management, where reduced production time increases the impact of long lead times, and standardized components spread inventory costs across multiple projects. The third challenge involves stochastic scheduling, leveraging the structural similarities among products in a modular production system to optimize schedules for future projects. To address these challenges, the dissertation explores the Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS). It introduces a Mixed Integer Linear Programming (MILP) model and a solution method, demonstrating its superiority over existing methods. Given the NP-hardness of the problem, heuristic methods, including group graphs, hybrid differential evolution, and ant colony optimization algorithms, are proposed to quickly find feasible solutions. The scope expands to the production of a product family through the Resource Constrained Project Scheduling Problem with Modular construction and new Project arrivals (RCPSPMP). This extended problem incorporates stochastic project arrivals and inventory allocation, modeling the pre-assembly of modules. A Progressive Hedging (PH) algorithm is introduced to consider future project arrivals, ultimately aiming to create a profitable product family rather than individual products. Finally, stochastic project arrivals are considered for the standard Resource Constrained Project Scheduling Problem (RCPSP). Simulation optimization is initially employed, but a data-assisted method using neural networks is introduced to significantly reduce computational costs while maintaining solution quality. In conclusion, this dissertation presents comprehensive methods for scheduling in modular shipbuilding, addressing challenges related to flexible project structures, nonrenewable resources, resource allocation, and stochastic project arrivals. The versatility of these methods extends their applicability beyond shipbuilding to various industries.@en

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.

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The Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS) is a generalization of the Resource Constrained Project Scheduling Problem (RCPSP). The objective of the RCPSP-PS is to find a minimal makespan schedule subject to precedence and resource constraints, while only having to execute a subset of all activities. We present a general model, which is based on a precedence graph and a task selection graph. Furthermore, we introduce an exact solution method including procedures for generating cutting planes and variable reduction. It is shown that both the lower bound obtained from the linear relaxation, and the computation time needed to obtain integer solutions are improved using these procedures.@en

The primary drivers for buying a ship from a certain yard are price, delivery time and quality. In order to decrease construction time and costs, shipbuilding companies are exploring the development of product-families to include family wide modularity and cross family standardization. Standardization is the use of identical components across multiple products, while modularity combines parts to create 'building-blocks'. This creates an opportunity for less inventory, a more efficient supply chain and shorter delivery times. Considering a network of suppliers and shipyards, the shipbuilder has to answer the following question: Which components and pre-assembled modules should be available in which inventory? Since the exact ship orders are not known, this can be seen as an optimization problem with uncertainty. To solve it, it is formulated as an integer linear program (ILP), and to handle the uncertainty, the Sampling Average Approximation (SAA) method is used. Several smaller instances are solved to optimality by Gurobi optimization software and the performance of this approach is evaluated along with the convergence of the SAA method. The results show convergence of the SAA method although only relatively small instances can be solved to optimality by the ILP.@en