A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

Metoda projektowania struktury systemu wykonawczego przedsięwzięcia budowlanego z zastosowaniem algorytmu ewolucyjnego

The paper discusses the problem of designing a construction project’s organisation structure at the operating level, where tasks and processes are of “complex of operations” type. Such a system includes heterogeneous operating units (crews, teams) of a general contractor and cooperating external ones – subcontractors, that create a temporary organisation. Its structure changes according to the project schedule as the project advances. The author identified the problem of designing a construction project operating system structure from the point of a general contractor, built the system’s model and formalised it mathematically. The contractor selection process (i.e. the selection of the system’s elements) is described as the problem of triple-criteria optimisation of the schedule. The assessment of possible variants of the system’s structure is made according the criteria crucial for the project’s efficiency and the general contractor’s objectives (i.e. minimisation of project duration and cost, and keeping subcontracting to minimum – as the general contractor is assumed to be interested in making full use of their own resources). To solve the problem, a method that uses metaheuristic approach has been worked out. An evolutionary algorithm (using stochastic processes) was adapted for solving the triple-criteria schedule optimisation problem in deterministic conditions. The author developed also a heuristic algorithm to allocate limited resources of variable availability. The solutions are generated by means of an achievement scalarising function, which is based on Tchebycheff utility function. The selection of final solution can be done by analysing the approximation of whole set of non-dominated solutions on the basis of total decision maker’s preferences, or by means of Steuer’s interactive method.W artykule podjęto problem projektowania struktury systemu wykonawczego przy harmonogramowaniu realizacji przedsięwzięcia budowlanego typu „kompleks operacji”. System ten złożony jest z niejednorodnych jednostek operacyjnych generalnego wykonawcy oraz kooperujących jednostek zewnętrznych – podwykonawców. Tworzą oni tymczasową organizację. Jej struktura zmienia się w czasie zgodnie z harmonogramem realizacji przedsięwzięcia. Autor dokonał identyfikacji modelu i formalizacji matematycznej problemu projektowania struktury systemu wykonawczego przedsięwzięcia budowlanego. Proces doboru wykonawców (elementów systemu) opisano jako problem optymalizacji trójkryterialnej harmonogramu. Ocena możliwych wariantów budowy struktury systemu wykonawczego dokonywana jest przy zastosowaniu kryteriów decydujących o efektywności przedsięwzięcia i działalności generalnego wykonawcy (minimalizacja czasu i kosztu realizacji oraz kosztu robót zleconych podwykonawcom). Do rozwiązania analizowanego problemu opracowano metodę wykorzystującą podejście metaheurystyczne. W tym celu zaadaptowano algorytm ewolucyjny (wykorzystujący procesy stochastyczne) do rozwiązywania zagadnień trójkryterialnej optymalizacji harmonogramów w warunkach deterministycznych oraz opracowano heurystyczny algorytm rozdziału ograniczonej i zmiennej w czasie liczby jednostek zasobów i wykonawców. Rozwiązania generowane są z wykorzystaniem funkcji skalaryzującej osiągnięcia celów optymalizacji, bazującej na metryce Czebyszewa. Wybór rozwiązania końcowego może być dokonany poprzez analizę przybliżenia całego zbioru rozwiązań niezdominowanych (na podstawie preferencji globalnych decydenta) lub z wykorzystaniem ineraktywnej metody Steuera

Multi-project scheduling with 2-stage decomposition

A non-preemptive, zero time lag multi-project scheduling problem with multiple modes and limited renewable and nonrenewable resources is considered. A 2-stage decomposition approach is adopted to formulate the problem as a hierarchy of 0-1 mathematical programming models. At stage one, each project is reduced to a macro-activity with macro-modes, which are systematically generated by utilizing artificial budgets. The resulting single project network problem is a Multi-Mode Resource Constrained Project Scheduling Problem (MRCPSP) with positive cash flows. MRCPSP with positive cash flows is solved to maximize NPV and to determine the starting times and resource allocations for the projects. Using the starting times and resource profiles obtained in stage one each project is solved at stage two for minimum makespan. Three different time horizon setting methods, namely, relaxed greedy approach, artificial budget and Lagrangian relaxation are developed for setting the time horizon for MRCPSP with positive cash flows. A genetic algorithm approach is adopted to generate good solutions, which is also employed as a starting solution for the exact solution procedure. The result of the second stage is subjected to a post-processing procedure to distribute the resource capacities that have not been utilized earlier in the procedure. Since currently there are no data instances with the required structure, four new test problem sets are generated with 81, 84, 27 and 4 problems each. Three different configurations of solution procedures are tested employing the first three problem sets. A new heuristic decision rule designated here as Resource Return factor is presented and tested employing the fourth problem set

Heuristic algorithms for solving a class of multiobjective zero-one programming problems

Master'sMASTER OF ENGINEERIN

Technology and Management Applied in Construction Engineering Projects

This book focuses on fundamental and applied research on construction project management. It presents research papers and practice-oriented papers. The execution of construction projects is specific and particularly difficult because each implementation is a unique, complex, and dynamic process that consists of several or more subprocesses that are related to each other, in which various aspects of the investment process participate. Therefore, there is still a vital need to study, research, and conclude the engineering technology and management applied in construction projects. This book present unanimous research approach is a result of many years of studies, conducted by 35 well experienced authors. The common subject of research concerns the development of methods and tools for modeling multi-criteria processes in construction engineering

Généralisations du problème d'ordonnancement de projet à ressources limitées

Un problème d'ordonnancement de projet à ressources limitées (POPRL) consiste en l'ordonnancement d'un ensemble de tâches, nécessitant un ou plusieurs types de ressources, renouvelables ou non renouvelables, en quantités limitées. La résolution d'un POPRL a pour but la détermination des dates d'exécution des tâches en tenant compte des contraintes de préséance et de disponibilité des ressources et ayant comme objectif la minimisation de la durée totale du projet. Le POPRL est un problème d'optimisation combinatoire de complexité NP-dur (Blazewicz et al. 1983). Une revue de littérature du (POPRL) est présentée au chapitre 2. Plus de 125 articles scientifiques sont analysés. Les contributions relatives à ce problème portent sur les méthodes exactes de résolution, la détermination de bornes inférieures sur la durée du projet et les méthodes heuristiques (approchées) de résolution. L'aspect pratique de ce problème dans des contextes industriels divers a conduit à de nombreuses généralisations du problème classique. On constate que malgré les efforts déployés pour définir des POPRL plus généraux, les contraintes de transfert des ressources continuent à être ignorées, nous constatons aussi que l'optimisation du problème en considérant les coûts a été très peu traitée dans la littérature. Ce qui forcent les gestionnaires dans la plus part des cas à se baser uniquement sur leur expérience pour réaliser ou ajuster manuellement les ordonnancements produits par des heuristiques conçues pour résoudre des versions simplifiées du problème. Cette thèse tente de combler partiellement ces lacunes. Le chapitre 3 traite le problème d'ordonnancement de projet à ressources limitées POPRLTT avec des temps de transfert des ressources. Un temps de transfert est le temps nécessaire pour transférer une ressource du lieu d'execution d'une activité vers un autre. Ainsi, le temps de transfert d'une ressource dépend des lieux des activités à exécuter, ainsi que des caractéristiques des ressources à transférer. L'objectif dans un POPRLTT est la détermination des dates d'exécution des tâches en tenant compte des contraintes de préséance et de disponibilité des ressources et les temps de transfert des ressources. L'objectif est de minimiser la durée totale du projet. Nous proposons un nouvel algorithme génétique basé sur un opérateur de croisement de deux positions. L'étude expérimentale menée sur un grand nombre de problèmes test prouve que l'algorithme proposé est meilleur que les deux méthodes déjà existantes dans la littérature. Une généralisation du problème d'ordonnancement de projet à ressources limitées et des temps de transfert des ressources au contexte multi mode (POPRL=PMETT) est présentée au chapitre 4. Dans ce problème, nous supposons que la préemption est non autorisée, et les ressources utilisées sont renouvelables et non renouvelables, chaque activité a plusieurs modes d'exécution, et les relations de préséance sont de type dit début-fin sans décalage. L'objectif est de choisir un temps de début (ou de fin) et un mode d'exécution pour chaque tâche du projet, pour que la durée du projet soit minimisée tout en respectant les contraintes de préséance, de disponibilité de ressources et les temps de transfert. Au meilleur de notre connaissance, cette version du problème n'a jamais été abordée auparavant. Nous proposons une formulation mathématique de ce problème, ensuite nous présentons un algorithme génétique, que nous avons conçu pour résoudre les instances de grandes tailles. Pour tester les méthodes proposées nous développons des nouveaux ensembles de problèmes-tests pour le POPRL=PMETT, qui pourront être utilisés dans l'avenir pour mener des recherches dans ce domaine. Dans le chapitre 5, nous définissons une nouvelle généralisation du problème d'ordonnancement de projet à ressources limitées en considérant l'objectif de minimiser le coût total d'exécution du projet. Celui-ci est composé de deux éléments principaux: le coût direct des ressources à utiliser et les frais généraux qui ne dépendent pas de la quantité de ressources allouées, mais qui sont proportionnels à la durée du projet. Ce problème, que nous appelons Problème général d'allocation et de nivellement des ressources d'un projet (PGANRP) est très commun en pratique, mais très peu de recherche est consacrée à ce problème. Dans un PGANRP, nous devons simultanément déterminer les quantités des ressources à allouer au projet au cours de son exécution et réduire la variabilité de l'utilisation des ressources au minimum tout en essayant de terminer le projet à une date de fin acceptable. Les quantités des ressources à allouer au projet devraient permettre l'accomplissement du projet à cette date et devient une limite sur la disponibilité de ces ressources durant toute l'exécution du projet. Nous proposons, une formulation mathématique du problème et deux approches de recherche dans le voisinage pour les instances de grandes tailles.The resource-constrained project scheduling problem (RCPSP) consists of scheduling a set of activities or tasks using one or more resource types available in limited quantity. In the standard version of this problem, pre-emption is not allowed, precedence relations are of the no-lag, finish-to-start type, and the used resources are renewable meaning that the same resources quantity are available each time period. Solving this NP-hard optimization problem requires the determination of tasks execution date such that the project duration is minimized without using more than the available resource quantities. In the first chapter of this thesis, the research problem and research objectives are presented while chapter 2 reviews the literature and contributions to the RCPSP and some of its extended versions. More than 125 published papers are reviewed. These contributions are divided into 4 groups of contributions. Those proposing optimal solution methods, those developing lower bounds on the project duration, those proposing heuristic and approximate solution methods, and those extending the standard version of the problem in order to make it closer to the real-life problem. This literature review revealed that very few contributions explicitly take into consideration the time required to transfer resources between execution sites of the project. Only three such contributions are published and none of these three publication deal with the case where tasks have more than one execution mode. This review also revealed that the large majority of the published research deals with the problem where the objective is to minimize the duration of the project. However, in almost all real-life situations, the objective is to minimise the total cost of the project. That is why this thesis is dedicated to solve these neglected extensions of the RCPSP. Chapter 3 deals with the resource-constrained project scheduling problem with transfer times (RCPSPTT). Thus the goal in this case is to determine execution dates that allows for resources to be transferred between execution sites while respecting the precedence relations between these tasks as well as resources availability. A new genetic algorithm (GA) is developed to solve the RCPSPTT. This algorithm uses a new and efficient crossover operator. The chapter also study the performance of the proposed genetic algorithm and shows that it produces better results than the two previously published solution heuristics. It is to notice that the proposed GA considers renewable resource types and assume that tasks have only one execution mode. Chapter 4 deals with the multi-mode resource-constrained project scheduling problem with transfer times (MRCPSPTT). Thus, it extends the problem studied in the previous chapter to the multi-mode case under the assumptions of no pre-emption while using renewable and non-renewable resources. This problem has never been the subject of any published research before. An integer linear mathematical formulation of the problem is given as well as new genetic algorithm is developed to solve it. An extensive empirical analysis is then presented and shows that the proposed GA is able to produce the optimal solution for 529 test instances with 10, 20 and 30 activities. Chapter 5 introduces the generalized resource allocation and leveling problem (GRALP). This problem can be stated as follows. Given a set of project tasks to execute, their possible execution modes and precedence relations, an upper bound on the amount of resources that can be made available to the project, a project due date, the cost of resource utilization and the overhead cost; determine the execution date and mode for each task and the amount of resources to allocate to the project. The objective is to minimize the total project execution cost while respecting precedence constraints, project due date and not using more than the amount of resources that we decided to allocate to the project. Again we notice that this problem has never been the subject of any published research work. Chapter 5 presents an integer linear formulation of the problem, a neighborhood search solution heuristic, a genetic algorithm to solve it and an empirical experiment to evaluate the proposed heuristics showing the superiority of the proposed GA. Finally, the conclusions of the thesis and some propositions for future research are given

Use of genetic algorithms in multi-objective multi-project resource constrained project scheduling

Resource Constrained Project Scheduling Problem (RCPSP) has been studied extensively by researchers by considering limited renewable and non-renewable resources. Several exact and heuristic methods have been proposed. Some important extensions of RCPSP such as multi-mode RCPSP, multi-objective RCPSP and multi-project RCPSP have also been focused. In this study, we consider multi-project and multi-objective resource constrained project scheduling problem. As a solution method, non-dominated sorting genetic algorithm is adopted. By experimenting with different crossover and parent selection mechanisms, a detailed fine-tuning process is conducted, in which response surface optimization method is employed. In order to improve the solution quality, backward-forward pass procedure is proposed as both post-processing as well as for new population generation. Additionally, different divergence applications are proposed and one of them, which is based on entropy measure is studied in depth. The performance of the algorithm and CPU times are reported. In addition, a new method for generating multi-project test instances is proposed and the performance of the algorithm is evaluated through test instances generated through this method of data generation. The results show that backward-forward pass procedure is successful to improve the solution quality

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