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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.
- 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 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.
- Multi-mode resource-constrained project scheduling using RCPSP and SAT solversPublication . Coelho, José; Vanhoucke, MarioThis paper reports on a new solution approach for the well-known multi-mode resource-constrained project scheduling problem (MRCPSP). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and non-renewable) resource feasible project schedule with a minimal makespan. The problem type is known to be NP-hard and has been solved using various exact as well as (meta-)heuristic procedures. The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean non-renewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.
- On the summary measures for the resource-constrained project scheduling problemPublication . Van Eynde, Rob; Vanhoucke, Mario; Coelho, JoséThe resource-constrained project scheduling problem is a widely studied problem in the literature. The goal is to construct a schedule for a set of activities, such that precedence and resource constraints are respected and that an objective function is optimized. In project scheduling literature, summary measures are often used as a tool to evaluate the performance of algorithms and to analyze instances and datasets. They can be classified in two groups, network measures describe the precedence constraints of a project, while resource measures focus on the resource constraints of the instance. In this manuscript we make an exhaustive evaluation of the summary measures for project scheduling. We provide an overview of the most prevalent measures and also introduce some new ones. For our tests we combine different datasets from the literature and generate a new set with diverse characteristics. We evaluate the performance of the summary measures on three dimensions: consistency, instance complexity and algorithm selection. We conclude by providing an overview of which measures are best suited for each of the three investigated dimensions.
- The multi-mode resource-constrained project scheduling problemPublication . Coelho, José; Vanhoucke, MarioThis chapter reports on a new solution approach for the multi-mode resource-constrained project scheduling problem (MRCPSP, MPS | prec | C max ). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and nonrenewable) resource-feasible project schedule with a minimal makespan. The problem type is known to be NP -hard and has been solved using various exact as well as (meta-)heuristic procedures. The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean nonrenewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.
- Various extensions in resource-constrained project scheduling with alternative subgraphsPublication . Servranckx, Tom; Coelho, José; Vanhoucke, MarioIn this research, we present several extensions for the resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS). First of all, we investigate more complex variants of the alternative project structure. More precisely, we consider nested alterative subgraphs, linked alternative branches, multiple selection, caused and closed choices, and split choices. Secondly, we introduce non-renewable resources in the RCPSP-AS in order to implicitly avoid certain combinations of alternatives given a limited availability of this resource over the complete project horizon. We formulate both the basic RCPSP-AS and its extensions as an ILP model and solve it using Gurobi. The computational experiments are conducted on a large set of artificial project instances as well as three case studies. The results show the impact of the different extensions on the project makespan and the computational complexity. We observe that combinations of the proposed extensions might imply complex alternative project structures, resulting in an increasing computational complexity or even infeasible solutions. The analysis of the three case studies shows that it is hard to find feasible solutions with a small time limit or optimal solutions with a larger time limit for projects with a realistic size in terms of the number of activities or alternatives.