Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table

Multi-skill resource-constrained project scheduling problems : models and algorithms

Tese de doutoramento, Estatística e Investigação Operacional (Otimização), Universidade de Lisboa, Faculdade de Ciências, 2018In this dissertation, project scheduling problems with multi-skill resources are investigated. These problems are commonly found in companies making use of human resources or multi-purpose machinery equipment. The general problem consists of a single project comprising a set of activities. There are precedence relations between the activities. Each activity requires one or several skills for being processed and for each of these skills, more than one resource may be needed. The resources have a unitary capacity per time unit and may master more than one skill. The resources can contribute with at most one skill to at most one activity that requires it, in each time unit. It is usually assumed that the resources are homogeneous, i.e., the proficiency at which each skill is performed is the same across all resources that master that skill. Preemption is not allowed, which implies that once an activity starts being processed it cannot be interrupted. When a resource is assigned to perform a skill for an activity, it remains in that status for the whole processing time of the activity. The objective of the problem is to schedule all the activities, satisfying all constraints such that the makespan of the project is minimized. After introducing a framework to the realm of project scheduling problems with multi-skill resources and highlighting the main objectives and contributes of this thesis, a state-of the-art review on the topic is presented. The particular problem investigated in this document is then described in detail and its specific features are discussed. To that end, a continuous-time mathematical formulation from the literature is revisited, an example of the problem is presented and some aspects related to the computation of feasible solutions are discussed. This last topic is of major relevance when dealing with problems that combine personnel staffing with project scheduling. In order to properly assess the quality of solutions obtained by the methodological developments proposed in this thesis, it became necessary to develop an instance generator to build a set of instances larger than those existing in the literature. After formally proposing such generator, we detail the characteristics of the two sets of instances considered for the computational experiments to be performed. In the next sections of the document, the solution methodologies developed within the scope of this thesis are presented and thoroughly discussed. A wide range of mathematical formulations is studied, two of which are first proposed in this document. From the assessment of their ability both to compute feasible and possibly optimal solutions and to derive good lower bounds (stemming from their linear programming relaxations) to the problem, it will become clear that the so-called discrete-time formulations yield the strongest lower bounds whereas a continuous-time formulation from the literature proved to be the most suitable for solving instances of the problem to optimality. This trend is observed for both sets of instances considered. Two constructive lower bound mechanisms proposed for the resource-constrained project scheduling problem are extended to account for the existence of multi-skill resources and multi skill requirements of the activities. The results reveal that such methods improve the lower bounds achieved by the studied mathematical formulations for some instances. Real-world project scheduling problems usually involve a large number of activities, resources and skills. Hence, the use of exact methods such as the standard techniques for tackling the aforementioned mathematical models, is often impractical. When faced with this kind of situations, a project manager may consider preferable to have a good feasible solution, not necessarily an optimal one, within an admissible time, by means of an approximate method. A close look into the problem being investigated in this thesis reveals that it has some features that are not present in some well-studied particular cases of it, namely the notion of skill—multi skill resources and skill requirements of the activities. Hence, with the objective of developing approximate solution methodologies that better exploit the specific characteristics of the problem at hand, two new concepts are introduced: activity grouping and resource weight. The well-known parallel and serial scheduling schemes, proposed originally for the class of resource-constrained project scheduling problems, are extended to our problem setting and the two above-mentioned concepts are incorporated into these two new frameworks. Such frameworks use well-known activity priority rules for defining the order by which the activities are selected to be scheduled and resource weight rules to determine a set of resources that meets the requirements of all the activities to be scheduled at each time with the least total cost (weight). Thereafter, two heuristic procedures making use of those schedule generation schemes are proposed, namely a multi-pass heuristic built upon the parallel scheduling scheme and a biased random-key genetic algorithm. The idea of computing a feasible solution using the so-called backward planning is also considered in both methods. The multi-pass heuristic retrieves the solution with the minimum makespan after performing a specific number of passes, each associated with a unique combination of the considered activity priority rules, the developed resource weight rules and the two precedence networks: forward and backward. The biased random-key genetic algorithm is a metaheuristic whose developed chromosome structure encodes information related to: (i) the priority values of the activities; (ii) the weights of the resources; (iii) how a chromosome is decoded, i.e., the scheduling scheme and precedence network scheme to be used for computing the associated makespan. By embedding all this information into the chromosomes, it becomes possible to take advantage of the evolutionary framework of the biased random-key genetic algorithm, which tends to allow the evolution of such data (change in their values) over time, towards better makespan valued solutions. Three variants of the biased random-key genetic algorithm are considered with regard to the type of scheduling generation scheme to be used for decoding its chromosomes: (i) all chromosomes are decoded with the parallel scheduling scheme; (ii) all chromosomes are decoded with the serial scheduling scheme; (iii) the scheduling scheme to be used for decoding each chromosome depends on the value of the associated parameter which is embedded in the chromosome. The computational results revealed that the proposed multi-pass heuristic is an efficient algorithm for computing feasible solutions of acceptable quality within a small computational time whereas the biased random-key genetic algorithm is a robust algorithm and a more competitive approximate approach for computing feasible solutions of higher quality, especially for harder instances such as those of medium and large dimensions. We conclude this thesis with an overview of the work done and with some directions for further research in terms of methodological developments and of some potentially interesting extensions of the addressed problem

An integrated approach for requirement selection and scheduling in software release planning

It is essential for product software companies to decide which requirements should be included in the next release and to make an appropriate time plan of the development project. Compared to the extensive research done on requirement selection, very little research has been performed on time scheduling. In this paper, we introduce two integer linear programming models that integrate time scheduling into software release planning. Given the resource and precedence constraints, our first model provides a schedule for developing the requirements such that the project duration is minimized. Our second model combines requirement selection and scheduling, so that it not only maximizes revenues but also simultaneously calculates an on-time-delivery project schedule. Since requirement dependencies are essential for scheduling the development process, we present a more detailed analysis of these dependencies. Furthermore, we present two mechanisms that facilitate dynamic adaptation for over-estimation or under-estimation of revenues or processing time, one of which includes the Scrum methodology. Finally, several simulations based on real-life data are performed. The results of these simulations indicate that requirement dependency can significantly influence the requirement selection and the corresponding project plan. Moreover, the model for combined requirement selection and scheduling outperforms the sequential selection and scheduling approach in terms of efficiency and on-time delivery. \u

Méthodes exactes et approchées pour le problème de gestion de projet à contraintes de ressources

Le problème de gestion de projet à contraintes de ressources est un des problèmesles plus étudiés dans la littérature. Il consiste à planifier des activités soumises à desrelations de précédence, et nécessitant des ressources renouvelables. L objectif est deminimiser la durée du projet, soit le makespan. Nous étudions le problème de gestion deprojet à contraintes de ressources. Nous nous sommes intéressées à la résolution exactedu problème. Dans la première partie de la thèse, nous élaborons une série de bornesinférieures basées sur le raisonnement énergétique et des formulations mathématiques.Les résultats montrent que les bornes proposées surpassent ceux de la littérature. Dansla deuxième partie, nous proposons des procédures par séparation et évaluation utilisantles bornes inférieures dévelopées dans la première partie.Resource Constrained Project Scheduling Problem is one of the most studied schedulingproblems in the literature. It consists in scheduling activities, submitted to precedencerelationship, and requiring renewable resources to be processed. The objective isto minimize the project duration, i.e., the makespan. We study the Resource ConstrainedProject Scheduling Problem. We are interested on the exact resolution of the problem.In the first part of the thesis, we develop a series of lower bounds based on energeticreasoning and mathematical formulations. The computational results show that theproposed lower bounds outperform the ones of the literature. In the second part, wepropose Branch-and-Bound procedures using the lower bounds developed on the firstpart.TOURS-Bibl.électronique (372610011) / SudocSudocFranceF

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the classical simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.Comment: 18 pages, 1 figur