Multi-mode resource-constrained project schedule problem: metaheuristic solution procedures and extensions

Operations research (OR) heeft als doel processen binnen organisaties te verbeteren of te optimaliseren met behulp van hiervoor ontwikkelde technieken en modellen. De discipline kende zijn oorsprong tijdens WOII, toen aan de hand van wiskundige modellen de logistieke bevoorrading van militair materiaal en goederen werd gepland. In de jaren na de oorlog ontwikkelde OR zich ten volle en tot op vandaag worden technieken en procedures ontwikkeld om complexe problemen in de bedrijfswereld, de maatschappij en de industrie te analyseren en te optimaliseren. Een van de onderzoeksdomeinen waarbinnen OR actief is, is project management. Project management kan omschreven worden als het geheel van kennis, vaardigheden, tools en technieken om een project te plannen, teneinde aan alle projecteisen te voldoen. Een project kan gedefinieerd worden als een tijdelijke inspanning met als doel het cre¨eren van een uniek product of een unieke service (PMBOK). De bouw van piramides in Egypte, de ontwikkeling van een iPhoneapplicatie, het schrijven van een doctoraat, de organisatie van een verkiezingscampagne of het bouwen van een huis, het zijn allen typische voorbeelden van projecten. De voorbije jaren is het belang van project management enorm toegenomen. Tientallen boeken over project management zijn verschenen en project software pakketten zijn ontwikkeld of uitgebreid met nieuwe planningsmogelijkheden. Bovendien zijn verschillende planningsproblemen reeds uitvoerig bestudeerd in de academische literatuur en zijn talloze exacte, heuristische of metaheuristische oplossingsmethodes voorgesteld. Een van die planningsproblemen is het zogenaamde ’multi-mode resourceconstrained project scheduling probleem’, waarbij getracht wordt een project in een zo kort mogelijke duurtijd te plannen, rekening houdend met de volgorderelaties tussen de verschillende activiteiten ´en met de beschikbare hernieuwbare en niet-hernieuwbare middelen. Voor elk van de activiteiten zijn er bovendien meerdere uitvoeringsmogelijkheden. Dit doctoraat is opgedeeld in twee delen. In een eerste deel worden drie metaheuristische oplossingsprocedures en een nieuwe dataset voorgesteld, terwijl in het tweede deel verschillende meer praktische concepten worden ge¨ıntroduceerd. Dit werk wordt afgesloten met een algemene conclusie en enkele suggesties voor verder onderzoek. Deel I van dit doctoraat start met een introductie van het multi-mode resourceconstrained project scheduling probleem en een overzicht van de beschikbare literatuur. Aan de hand van een voorbeeld worden enkele veelgebruikte termen in de project planning literatuur voorgesteld. Vervolgens worden drie oplossingsmethodes ontwikkeld: een genetisch algoritme (GA), een artificiel immune system algoritme (AIS) en een scatter search algoritme (SS). Het voorgestelde genetisch algoritme verschilt van andere genetische oplossingsmethodes aangezien het gebruik maakt van twee populaties, ´e´en met leftjustified schedules (waarbij alle activiteiten zo vroeg mogelijk gepland worden) en ´e´en met right-justified schedules (waarbij alle activiteiten zo laat mogelijk gepland worden). Het algoritme maakt ook gebruik van een generatieschema dat is uitgebreid met een methode die de gekozen mode van een activiteit tracht te optimaliseren door te kiezen voor de mode die resulteert in de laagst mogelijke eindtijd voor die activiteit. De artificial immune system procedure is gebaseerd op de principes van het menselijke immuun systeem. Wanneer ziektekiemen het menselijke lichaam binnendringen zullen de antigenen die in staat zijn om de ziektekiemen te bestrijden, zich vermenigvuldigen om op die manier zo snel mogelijk de ziekte te doen verdwijnen. Ditzelfde principe wordt toegepast in deze oplossingsmethode, die bovendien een procedure bevat om op een gecontroleerde manier de initi¨ele populatie te genereren. Deze procedure is gebaseerd op experimentele resultaten die een link aantonen tussen bepaalde karakteristieken van de gekozen modes en de uiteindelijke duurtijd van het project. Een laatste algoritme is een scatter search procedure. Deze procedure maakt gebruik van verschillende verbeteringsmethodes die elk aangepast zijn aan de specifieke karakteristieken van de verschillende hernieuwbare en niet-hernieuwbare middelen. De procedure wordt aan de hand van parameters die de beperktheid van de middelen aangeeft, gestuurd in de richting van de meest effici¨ente verbeteringsmethode en op die manier wordt een zo optimaal mogelijke oplossing gezocht. Elk van de voorgestelde procedures behaalde uitstekende resultaten op de bestaande benchmark datasets. Deze sets vertonen evenwel enkele beperkingen gezien de huidige evolutie in de ontwikkeling van metaheuristische oplossingsmethodes. Om die reden werd een nieuwe, verbeterde dataset ontwikkeld, die onderzoekers in staat moet stellen om hun oplossingen te vergelijken met andere procedures. Om een vergelijking te kunnen maken tussen alle bestaande oplossingsmethodes hebben we elk algoritme dat beschikbaar is in de literatuur gecodeerd en getest op de bestaande en nieuwe datasets. Door alle testen uit te voeren op eenzelfde computer en met eenzelfde stopcriterium zijn we in staat geweest een duidelijke en faire vergelijking te maken. Onze voorgestelde algoritmes performeren bovendien uitstekend. In het tweede deel van dit doctoraat worden een aantal uitbreidingen onder de loep genomen. Zo wordt in het eerste hoofdstuk van dit tweede deel de invloed nagegaan van het onderbreken van activiteiten: activiteiten kunnen dan op elke tijdstip stopgezet worden om later, zonder bijkomende kost, herstart te worden. De introductie van deze uitbreiding leidt tot een significante daling van de gemiddelde duurtijd van een project vergeleken met de situatie waarin geen onderbrekingen toegelaten worden. Een andere uitbreiding is de introductie van leereffecten in een projectomgeving. Hierbij wordt verondersteld dat een persoon effici¨enter wordt naarmate hij of zij langer aan een activiteit werkt. Dit leerconcept wordt vanuit drie verschillende zijdes bekeken. Ten eerste wordt nagegaan wat de invloed is van de introductie van het leerconcept op de totale duurtijd van een project en worden de verschillende parameters die hierop een invloed hebben geanalyseerd. Ten tweede bekijken we welke foutenmarge er moet aangenomen worden wanneer men geen rekening houdt met het leerconcept en tot slot achterhalen we dat door het tijdig incorporeren van de leereffecten significante verbeteringen kunnen gerealiseerd worden. In het laatste deel van dit doctoraat wordt het genetisch algoritme uit deel I gebruikt om de planning van een audit kantoor te optimaliseren. In deze planning dienen audit teams toegewezen te worden aan verschillende audit taken. Er kan duidelijk aangetoond worden dat met het gebruik van optimalisatietechnieken significante verbeteringen kunnen gemaakt worden in de planning van de audit teams. De bijdrage van dit doctoraat is drievoudig. Ten eerste werden drie stateof-the-art algoritmes gepresenteerd die in staat zijn om het multi-mode resourceconstrained project scheduling probleem op een heel effici¨ente manier op te lossen. Bovendien werd telkens specifieke project informatie gebruikt om de effici¨entie van de procedure te verhogen. Ten tweede werden verschillende stappen ondernomen om dit probleem uit te breiden naar meer realistische planningsproblemen. Het toelaten van het onderbreken van activiteiten en de introductie van leereffecten leidden tot nieuwe inzichten in het onderzoek van project planning. Tot slot wordt met de ontwikkeling van een nieuwe dataset onderzoekers aangemoedigd om hun resultaten te vergelijken met die van andere procedures. Met deze nieuwe dataset is tevens de basis gelegd voor verder onderzoek van dit interessante planning

Welcome to OR&S! Where students, academics and professionals come together

In this manuscript, an overview is given of the activities done at the Operations Research and Scheduling (OR&S) research group of the faculty of Economics and Business Administration of Ghent University. Unlike the book published by [1] that gives a summary of all academic and professional activities done in the field of Project Management in collaboration with the OR&S group, the focus of the current manuscript lies on academic publications and the integration of these published results in teaching activities. An overview is given of the publications from the very beginning till today, and some of the topics that have led to publications are discussed in somewhat more detail. Moreover, it is shown how the research results have been used in the classroom to actively involve students in our research activities

Time-constrained project scheduling with adjacent resources

We develop a decomposition method for the Time-Constrained Project Scheduling Problem (TCPSP) with Adjacent Resources. For adjacent resources the resource units are ordered and the units assigned to a job have to be adjacent. On top of that, adjacent resources are not required by single jobs, but by job groups. As soon as a job of such a group starts, the adjacent resource units are occupied, and they are not released before all jobs of that group are completed. The developed decomposition method separates the adjacent resource assignment from the rest of the scheduling problem. Test results demonstrate the applicability of the decomposition method. The presented decomposition forms a first promising approach for the TCPSP with adjacent resources and may form a good basis to develop more elaborated methods

Multi-Project Multi-Mode Resource Constrained Scheduling Problem with Material Ordering

In Multi–mode Project Scheduling with Resource Constrained (MPSRCP), activities are sequenced under resource limitation. In this thesis, an extension of the problem is considered. Multi-project multi-mode resource constrained scheduling problem with material ordering is studied. Bonus and penalty are taken into account in solving the considered problem as it is the case in many different industries. A literature review is presented and various solution methods for solving the considered and similar problems are studied. A new mathematical model is proposed considering a multi-project version of the problem. A new decomposition based heuristic to solve the problem is developed in this thesis. The approach is to use three separated mathematical models for each part of the problem. The developed heuristic is examined using various example problems with different features and randomly generated data. It can generate close-to-optimal solutions for all tested example problems with much reduced computational time when off-shelf optimization software was used. The developed math model and heuristic method are applied to a larger size case study based on a practical system in a manufacturing company in northern Ontario

An integer programming based algorithm for the resource constrained project scheduling problem

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 2005.Thesis (Master's) -- Bilkent University, 2005.Includes bibliographical references leaves 48-54.In this thesis, we study the problem of scheduling the activities of a single project in order for all resource and precedence relationships constraints to be satisfied with an objective of minimizing the project completion time. To solve this problem, we propose an Integer Programming based approximation algorithm, which has two phases. In the first phase of the algorithm, a subproblem generation technique and enumerative cuts used to tighten the formulation of the problem are presented. If an optimal solution is not found within a predetermined time limit, we continue with the second phase that uses the cuts and the lower bound obtained in the first phase. In order to evaluate the efficiency of our algorithm, we used the benchmark instances in the literature and compared the results with the best known solutions available for these instances. Finally, the computational results are reported and discussed.Büyüktahtakın, İsmet EsraM.S

Decomposition method for project scheduling with spatial resources

Project scheduling problems are in practice often restricted by a limited availability of spatial resources. In this paper we develop a decomposition method for the Time-Constrained Project Scheduling Problem (TCPSP) with Spatial Resources. Spatial resources are resources that are not required by single activities, but by activity groups. As soon as an activity of such a group starts, the spatial resource units are occupied, and they are not released before all activities of that group are completed. On top of that, the spatial resource units that are assigned to a group have to be adjacent. The developed decomposition method separates the spatial resource assignment from the rest of the scheduling problem. Test results demonstrate the applicability of the decomposition method. The presented decomposition forms a first promising approach for the TCPSP with spatial resources and may form a good basis to develop more elaborate methods

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

A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

Highlights • Project staffing with discrete time/resource trade-offs and calendar constraints. • An iterated local search procedure is proposed. • Different problem decomposition techniques are applied. Abstract When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability and activities are planned each with its own duration and resource requirements. In resource scheduling, important assumptions are made with respect to the staffing requirements. Both problems are typically solved in a sequential manner leading to a suboptimal outcome. We integrate these two interrelated scheduling problems to determine the optimal personnel budget that minimises the overall cost. Integrating these problems increases the scheduling flexibility, which improves the overall performance. In addition, we consider some resource demand flexibility in this research as an activity can be performed in multiple modes. In this paper, we present an iterated local search procedure for the integrated multi-mode project scheduling and personnel staffing problem. Detailed computational experiments are presented to evaluate different decomposition heuristics and comparison is made with alternative optimisation techniques

On the integration of diverging material flows into resource‐constrained project scheduling

This study deals with an extension of the resource-constrained project scheduling problem (RCPSP) by constraints on material flows released during the execution of project activities. These constraints arise from limited processing capacities for materials and maximum inventories of intermediate storage facilities. Production scheduling problems with converging material flows have been studied extensively. However, this is the first project scheduling problem integrating diverging material flows typically observed in dismantling projects, e.g., building deconstruction, power plant decommissioning, or battery/car decommissioning. Diverging material flows do not directly impact the project planning but only impose delays in the case of congestion. We model material flows by using operations that represent the processing of materials, and cumulative resources that represent storage facilities. As a method for efficiently generating starting solutions, we propose a schedule generation scheme tailored to the particular precedence structure of such problems. Furthermore, we extensively study the schedule generation scheme’s performance on generated test instances and compare it to the constraint programming solver IBM ILOG CP Optimizer. It turns out that the solution quality strongly depends on the employed model and that neither of the two solution methods is generally superior