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- A genetic algorithm for the resource-constrained project scheduling problem with alternative subgraphs using a boolean satisfiability solverPublication . Servranckx, Tom; Coelho, José; Vanhoucke, MarioThis study evaluates a new solution approach for the Resource-Constrained Project Scheduling with Alternative Subgraphs (RCPSP-AS) in case that complex relations (i.e. nested and linked alternatives) are considered. In the RCPSP-AS, the project activity structure is extended with alternative activity sequences. This implies that only a subset of all activities should be scheduled, which corresponds with a set of activities in the project network that model an alternative execution mode for a work package. Since only the selected activities should be scheduled, the RCPSP-AS comes down to a traditional RCPSP problem when the selection subproblem is solved. It is known that the RCPSP and, hence, its extension to the RCPSP-AS is NP-hard. Since similar scheduling and selection subproblems have already been successfully solved by satisfiability (SAT) solvers in the existing literature, we aim to test the performance of a GA-SAT approach that is derived from the literature and adjusted to be able to deal with the problem-specific constraints of the RCPSP-AS. Computational results on small and large-scale instances (both artificial and empirical) show that the algorithm can compete with existing metaheuristic algorithms from the literature. Also, the performance is compared with an exact mathematical solver and learning behaviour is observed and analysed. This research again validates the broad applicability of SAT solvers as well as the need to search for better and more suited algorithms for the RCPSP-AS and its extensions.
- A prediction model for ranking branch-and-bound procedures for the resource-constrained project scheduling problemPublication . Guo, Weikang; Vanhoucke, Mario; Coelho, JoséThe branch-and-bound (B&B) procedure is one of the most widely used techniques to get optimal solutions for the resource-constrained project scheduling problem (RCPSP). Recently, various components from the literature have been assembled by Coelho and Vanhoucke (2018) into a unified search algorithm using the best performing lower bounds, branching schemes, search strategies, and dominance rules. However, due to the high computational time, this procedure is only suitable to solve small to medium-sized problems. Moreover, despite its relatively good performance, not much is known about which components perform best, and how these components should be combined into a procedure to maximize chances to solve the problem. This paper introduces a structured prediction approach to rank various combinations of components (configurations) of the integrated B&B procedure. More specifically, two regression methods are used to map project indicators to a full ranking of configurations. The objective is to provide preference information about the quality of different configurations to obtain the best possible solution. Using such models, the ranking of all configurations can be predicted, and these predictions are then used to get the best possible solution for a new project with known network and resource values. A computational experiment is conducted to verify the performance of this novel approach. Furthermore, the models are tested for 48 different configurations, and their robustness is investigated on datasets with different numbers of activities. The results show that the two models are very competitive, and both can generate significantly better results than any single-best configuration.
- New resource-constrained project scheduling instances for testing (meta-)heuristic scheduling algorithmsPublication . Coelho, José; Vanhoucke, MarioThe resource-constrained project scheduling problem (RCPSP) is a well-known scheduling problem that has attracted attention since several decades. Despite the rapid progress of exact and (meta-)heuristic procedures, the problem can still not be solved to optimality for many problem instances of relatively small size. Due to the known complexity, many researchers have proposed fast and efficient meta-heuristic solution procedures that can solve the problem to near optimality. Despite the excellent results obtained in the last decades, little is known why some heuristics perform better than others. However, if researchers better understood why some meta-heuristic procedures generate good solutions for some project instances while still falling short for others, this could lead to insights to improve these meta-heuristics, ultimately leading to stronger algorithms and better overall solution quality. In this study, a new hardness indicator is proposed to measure the difficulty of providing near-optimal solutions for meta-heuristic procedures. The new indicator is based on a new concept that uses the 𝜎 distance metric to describe the solution space of the problem instance, and relies on current knowledge for lower and upper bound calculations for problem instances from five known datasets in the literature. This new indicator, which will be called the 𝜎𝐷 indicator, will be used not only to measure the hardness of existing project datasets, but also to generate a new benchmark dataset that can be used for future research purposes. The new dataset contains project instances with different values for the 𝜎𝐷 indicator, and it will be shown that the value of the 𝜎 distance metric actually describes the difficulty of the project instances through two fast and efficient meta-heuristic procedures from the literature.
- Project management and scheduling 2022Publication . Servranckx, Tom; Coelho, José; Vanhoucke, MarioThis article summarises the research studies published in the special issue on Project Management and Scheduling devoted to the 18th International Conference on Project Management and Scheduling (PMS). The special issue contains state-of-the art research in the field of (non-)robust project and machine scheduling and the contribution of each individual study to the academic literature are discussed. We notice that there is a growing interest in the research community to investigate robust scheduling approaches and optimisation problems observed in real-life business settings. This allows us to derive some interesting future research directions for the project and machine scheduling community.
- An approach using SAT solvers for the RCPSP with logical constraintsPublication . Vanhoucke, Mario; Coelho, JoséThis paper presents a new solution approach to solve the resource-constrained project scheduling problem in the presence of three types of logical constraints. Apart from the traditional AND constraints with minimal time-lags, these precedences are extended to OR constraints and bidirectional (BI) relations. These logical constraints extend the set of relations between pairs of activities and make the RCPSP definition somewhat different from the traditional RCPSP research topics in literature. It is known that the RCPSP with AND constraints, and hence its extension to OR and BI constraints, is NP-hard. The new algorithm consists of a set of network transformation rules that removes the OR and BI logical constraints to transform them into AND constraints and hereby extends the set of activities to maintain the original logic. A satisfiability (SAT) solver is used to guarantee the original precedence logic and is embedded in a metaheuristic search to resource feasible schedules that respect both the limited renewable resource availability as well as the precedence logic. Computational results on two well-known datasets from literature show that the algorithm can compete with the multi-mode algorithms from literature when no logical constraints are taken into account. When the logical constraints are taken into account, the algorithm can report major reductions in the project makespan for most of the instances within a reasonable time.
- Automatic detection of the best performing priority rule for the resource-constrained project scheduling problemPublication . Guo, Weikang; Vanhoucke, Mario; Coelho, José; Luo, JingyuPriority rules are applied in many commercial software tools for scheduling projects under limited resources because of their known advantages such as the ease of implementation, their intuitive working, and their fast speed. Moreover, while numerous research papers present comparison studies between different priority rules, managers often do not know which rules should be used for their specific project, and therefore have no other choice than selecting a priority rule at random and hope for the best. This paper introduces a decision tree approach to classify and detect the best performing priority rule for the resource-constrained project scheduling problem (RCPSP). The research relies on two classification models to map project indicators onto the performance of the priority rule. Using such models, the performance of each priority rule can be predicted, and these predictions are then used to automatically select the best performing priority rule for a specific project with known network and resource indicator values. A set of computational experiment is set up to evaluate the performance of the newly proposed classification models using the most well-known priority rules from the literature. The experiments compare the performance of multi-label classification models with multi-class classification models, and show that these models can outperform the average performance of using any single priority rule. It will be argued that this approach can be easily extended to any extension of the RCPSP without changing the methodology used in this study.
- A tool to test and validate algorithms for the resource-constrained project scheduling problemPublication . Vanhoucke, Mario; Coelho, JoséIn a paper written by by Vanhoucke et al. (2016), an overview of artificial and empirical project databases has been given for integrated project management and control. These databases are collections of the most well-known and widespread data instances available in literature for the construction of a baseline schedule, the analysis of schedule risk or the use for project control. The current paper serves as a follow-up study to further elaborate on the use of these data instances, and to give researchers an incentive to use these datasets for their research on the development and validation of new algorithms for project scheduling. Therefore, unlike the general focus of the previous paper on baseline scheduling, schedule risk analysis and project control, the focus on the current paper is restricted to resource-constrained project scheduling. The intention of this follow-up overview is fourfold. First and foremost, a procedure is proposed to facilitate the reporting of best known solutions for the well-known single- and multi-mode resource-constrained project scheduling problem to minimize the project makespan. Secondly, the paper reports our best known solutions we obtained so far, and reflects on the network and resource parameters that increase the project complexity. In doing so, areas to focus on for future research are detected, and an attempt to define hard problem instances is given. Thirdly, a new dataset is presented for the resource-constrained project scheduling problem that is much more diverse in both the network topology and resource scarceness and will enable the future researcher to develop algorithms to solve a wider range of project problems. Finally, the paper also adds some links to tutorials and other relevant information to stimulate researchers to download the data and update best known solutions once available.
- A new approach to minimize the makespan of various resource-constrained project scheduling problemsPublication . Coelho, José; Vanhoucke, MarioThis abstract presents a new solution approach to solve the resource-constrained project scheduling problem in the presence of multiple modes with mode identity constraints and two types of logical constraints. Apart from the traditional AND constraints with minimal time-lags, these precedences are extended to OR constraints. These logical constraints extend the set of relations between pairs of activities and make the RCPSP definition somewhat different from the traditional RCPSP research topics in literature. It is known that the RCPSP with AND constraints, and hence its extension to OR constraints, is NP-hard.
- Going to the core of hard resource-constrained project scheduling instancesPublication . Coelho, José; Vanhoucke, MarioThe resource-constrained project scheduling problem (RCPSP) is one of the most studied problems in the project scheduling literature, and aims at constructing a project schedule with a minimum makespan that satisfies both the precedence relations of the network and the limited availability of the renewable resources. The problem has attracted attention due to its NP hardness status, and different algorithms have been proposed that solve a wide variety of RCPSP instances to optimality or near-optimality. In this paper, we analyse the hardness of this problem from an experimental point-of-view by testing different algorithms on a huge set of existing instances and detect which ones are difficult to solve. To that purpose, we propose a three-phased approach that makes use of five elementary blocks, well-performing algorithms and a huge amount of computational power to transform easy RCPSP instances into very hard ones. The purpose of this study is to create insight and understanding into what makes an RCPSP instance hard, and propose a new dataset that consists of a small set of instances that are impossible to solve with the algorithms currently existing in the literature. These instances should be as small as possible in terms of number of activities and resources, and should be as diverse as possible in terms of network structure and resource strictness. Such a dataset should enable researchers to focus their attention on the development of radically new algorithms to solve the RCPSP rather than gradually improving current algorithms that can solve the existing RCPSP instances only slightly better.
- A study of the critical chain project management method applied to a multiproject systemPublication . Ordoñez, Robert Eduardo Cooper; Vanhoucke, Mario; Coelho, José; Anholon, Rosley; Novaski, OlívioIn 1997, Eliyahu Goldratt proposed a method called Critical Chain Project Management (CCPM) to minimize the inefficiencies identified in traditional project management. The project management community accepted the proposed method as a viable alternative. However, to allow its implementation with a multiproject system, more research was necessary. Seeking to identify the key factors that influence the performance of the multiproject system applying the CCPM method, we performed a case study. Logistic regression analysis showed that applying the CCPM method in a multiproject system allows for better time estimation of activities and facilitates the allocation of critical resources.
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