An Exact algorithm to minimize the makespan in project scheduling with scarce resources and feeding precedence relations

In this paper we study an extension of the Resource-Constrained Project Scheduling Problem (RCPSP) with minimum makespan objective by introducing as precedence constraints the so called “Feeding Precedences” (FP). For the RCPSP with FP we propose a new mathematical formulation and a branch and bound algorithm exploiting the latter formulation. The exact algorithm takes advantage also of a lower bound based on a Lagrangian relaxation of the same formulation. A computational experimentation on randomly generated instances and a comparison with the results achieved by a commercial solver, show that the proposed approach is able to behave satisfactorily

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

The Fuzzy Project Scheduling Problem with Minimal Generalized Precedence Relations

In scheduling, estimations are affected by the imprecision of limited information on future events, and the reduction in the number and level of detail of activities. Overlapping of processes and activities requires the study of their continuity, along with analysis of the risks associated with imprecision. In this line, this paper proposes a fuzzy heuristic model for the Project Scheduling Problem with flows and minimal feeding, time and work Generalized Precedence Relations with a realistic approach to overlapping, in which the continuity of processes and activities is allowed in a discretionary way. This fuzzy algorithm handles the balance of process flows, and computes the optimal fragmentation of tasks, avoiding the interruption of the critical path and reverse criticality. The goodness of this approach is tested on several problems found in the literature; furthermore, an example of a 15-story building was used to compare the better performance of the algorithm implemented in Visual Basic for Applications (Excel) over that same example input in Primavera© P6 Professional V8.2.0, using five different scenarios.This research was supported by the FAPA program of Universidad de Los Andes, Colombia. The authors would like to thank the research group of Construction Engineering and Management (INgeco) of Universidad de Los Andes, and the five anonymous referees for their helpful and constructive suggestions.Ponz Tienda, JL.; Pellicer Armiñana, E.; Benlloch Marco, J.; Andrés Romano, C. (2015). The Fuzzy Project Scheduling Problem with Minimal Generalized Precedence Relations. Computer-Aided Civil and Infrastructure Engineering. 30(11):872-891. doi:10.1111/mice.12166S8728913011Adeli, H., & Park, H. S. (1995). Optimization of space structures by neural dynamics. 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Minimizing the completion time of a project under resource constraints and feeding precedence relations: a Lagrangian relaxation based lower bound

In this paper we study an extension of the classical Resource-Constrained Project Scheduling Problem (RCPSP) with minimum makespan objective by introducing a further type of precedence constraints denoted as “Feeding Precedences” (FP). This kind of problem happens in that production planning environment, like make-to-order manufacturing, when the effort associated with the execution of an activity is not univocally related to its duration percentage and the traditional finish-to-start prece- dence constraints or the generalized precedence relations cannot completely represent the overlapping among activities. In this context we need to introduce in the RCPSP the FP constraints. For this problem we propose a new mathematical formulation and define a lower bound based on a resource constraints Lagrangian relaxation. A computational experimentation on randomly generated instances of sizes of up to 100 activities show a better performance of this lower bound with respect to others. More- over, for the optimally solved instances, its value is very close to the optimal one

04231 Abstracts Collection -- Scheduling in Computer and Manufacturing Systems

During 31.05.-04.06.04, the Dagstuhl Seminar 04231 "Scheduling in Computer and Manufacturing Systems" was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A three-phase approach for robust project scheduling: an application for R&D project scheduling

During project execution, especially in a multi-project environment unforeseen events arise that disrupt the project process resulting in deviations of project plans and budgets due to missed due dates and deadlines, resource idleness, higher work-in-process inventory and increased system nervousness. In this thesis, we consider the preemptive resource constrained multi-project scheduling problem with generalized precedence relations in a stochastic and dynamic environment and develop a three-phase model incorporating data mining and project scheduling techniques to schedule the R&D projects of a leading home appliances company in Turkey. In Phase I, models classifying the projects with respect to their resource usage deviation levels and an activity deviation assignment procedure are developed using data mining techniques. Phase II, proactive project scheduling phase, proposes two scheduling approaches using a bi-objective genetic algorithm (GA). The objectives of the bi-objective GA are the minimization of the overall completion time of projects and the minimization of the total sum of absolute deviations for starting times for possible realizations leading to solution robust baseline schedules. Phase II uses the output of the first phase to generate a set of non-dominated solutions. Phase III, called the reactive phase, revises the baseline schedule when a disruptive event occurs and enables the project managers to make “what-if analysis” and thus to generate a set of contingency plans for better preparation

Using Deep Neural Networks for Scheduling Resource-Constrained Activity Sequences

Eines der bekanntesten Planungsprobleme stellt die Planung von Aktivitäten unter Berücksichtigung von Reihenfolgenbeziehungen zwischen diesen Aktivitäten sowie Ressourcenbeschränkungen dar. In der Literatur ist dieses Planungsproblem als das ressourcenbeschränkte Projektplanungsproblem bekannt und wird im Englischen als Resource-Constrained Project Scheduling Problem oder kurz RCPSP bezeichnet. Das Ziel dieses Problems besteht darin, die Bearbeitungszeit einer Aktivitätsfolge zu minimieren, indem festgelegt wird, wann jede einzelne Aktivität beginnen soll, ohne dass die Ressourcenbeschränkungen überschritten werden. Wenn die Bearbeitungsdauern der Aktivitäten bekannt und deterministisch sind, können die Startzeiten der Aktivitäten à priori definiert werden, ohne dass die Gefahr besteht, dass der Zeitplan unausführbar wird. Da jedoch die Bearbeitungsdauern der Aktivitäten häufig nicht deterministisch sind, sondern auf Schätzungen von Expertengruppen oder historischen Daten basieren, können die realen Bearbeitungsdauern von den geschätzten abweichen. In diesem Fall ist eine reaktive Planungsstrategie zu bevorzugen. Solch eine reaktive Strategie legt die Startzeiten der einzelnen Aktivitäten nicht zu Beginn des Projektes fest, sondern erst unmittelbar an jedem Entscheidungspunkt im Projekt, also zu Beginn des Projektes und immer dann wenn eine oder mehrere Aktivitäten abgeschlossen und die beanspruchten Ressourcen frei werden. In dieser Arbeit wird eine neue reaktive Planungsstrategie für das ressourcenbeschränkte Projektplanungsproblem vorgestellt. Im Gegensatz zu anderen Literaturbeiträgen, in denen exakte, heuristische und meta-heuristische Methoden zur Anwendung kommen, basiert der in dieser Arbeit aufgestellte Lösungsansatz auf künstlichen neuronalen Netzen und maschinellem Lernen. Die neuronalen Netze verarbeiten die Informationen, die den aktuellen Zustand der Aktivitätsfolge beschreiben, und erzeugen daraus Prioritätswerte für die Aktivitäten, die im aktuellen Entscheidungspunkt gestartet werden können. Das maschinelle Lernen und insbesondere das überwachte Lernen werden für das Trainieren der neuronalen Netze mit beispielhaften Trainingsdaten angewendet, wobei die Trainingsdaten mit Hilfe einer Simulation erzeugt wurden. Sechs verschiedene neuronale Netzwerkstrukturen werden in dieser Arbeit betrachtet. Diese Strukturen unterscheiden sich sowohl in der ihnen zur Verfügung gestellten Eingabeinformation als auch der Art des neuronalen Netzes, das diese Information verarbeitet. Es werden drei Arten von neuronalen Netzen betrachtet. Diese sind neuronale Netze mit vollständig verbundenen Schichten, 1- dimensionale faltende neuronale Netze und 2-dimensionale neuronale faltende Netze. Darüber hinaus werden innerhalb jeder einzelnen Netzwerkstruktur verschiedene Hyperparameter, z.B. die Lernrate, Anzahl der Lernepochen, Anzahl an Schichten und Anzahl an Neuronen per Schicht, mittels einer Bayesischen Optimierung abgestimmt. Während des Abstimmens der Hyperparameter wurden außerdem Bereiche für die Hyperparameter identifiziert, die zur Verbesserung der Leistungen genutzt werden sollten. Das am besten trainierte Netzwerk wird dann für den Vergleich mit anderen vierunddreißig reaktiven heuristischen Methoden herangezogen. Die Ergebnisse dieses Vergleichs zeigen, dass der in dieser Arbeit vorgeschlagene Ansatz in Bezug auf die Minimierung der Gesamtdauer der Aktivitätsfolge die meisten Heuristiken übertrifft. Lediglich 3 Heuristiken erzielen kürzere Gesamtdauern als der Ansatz dieser Arbeit, jedoch sind deren Rechenzeiten um viele Größenordnungen länger. Eine Annahme in dieser Arbeit besteht darin, dass während der Ausführung der Aktivitäten Abweichungen bei den Aktivitätsdauern auftreten können, obwohl die Aktivitätsdauern generell als deterministisch modelliert werden. Folglich wird eine Sensitivitätsanalyse durchgeführt, um zu prüfen, ob die vorgeschlagene reaktive Planungsstrategie auch dann kompetitiv bleibt, wenn die Aktivitätsdauern von den angenommenen Werten abweichen