A genetic algorithm for the project scheduling with the resource constraints

The resource-constrained project scheduling problem (RCPSP) has received the attention of many researchers because it can be applied in a wide variety of real production and construction projects. This paper presents a genetic algorithm (GA) solving the RCPSP with the objective function of minimizing makespan. Standard genetic algorithm has to be adapted for project scheduling with precedence constraints. Therefore, an initial population was generated by a random procedure which produces feasible solutions (permutation of jobs fulfilling precedence constraints). Besides, all implemented genetic operators have taken sequential relationships in a project into consideration. Finally, we have demonstrated the performance and accuracy of the proposed algorithm. Computational experiments were performed using a set of 960 standard problem instances from Project Scheduling Problem LIBrary (PSPLIB) presented by Kolisch and Sprecher [1]. We used 480 problems consisting of 30 jobs and 480 90-activity instances. We have tested effectiveness of various combinations of parameters, genetic operators to find the best configuration of GA. The computational results validate the good effectiveness of our genetic algorithm

Mode-Based versus Activity-Based Search for a Nonredundant Resolution of the Multimode Resource-Constrained Project Scheduling Problem

[EN] This paper addresses an energy-based extension of the Multimode Resource-Constrained Project Scheduling Problem (MRCPSP) called MRCPSP-ENERGY. This extension considers the energy consumption as an additional resource that leads to different execution modes (and durations) of the activities. Consequently, different schedules can be obtained. The objective is to maximize the efficiency of the project, which takes into account the minimization of both makespan and energy consumption. This is a well-known NP-hard problem, such that the application of metaheuristic techniques is necessary to address real-size problems in a reasonable time. This paper shows that the Activity List representation, commonly used in metaheuristics, can lead to obtaining many redundant solutions, that is, solutions that have different representations but are in fact the same. This is a serious disadvantage for a search procedure. We propose a genetic algorithm(GA) for solving the MRCPSP-ENERGY, trying to avoid redundant solutions by focusing the search on the execution modes, by using the Mode List representation. The proposed GA is evaluated on different instances of the PSPLIB-ENERGY library and compared to the results obtained by both exact methods and approximate methods reported in the literature. This library is an extension of the well-known PSPLIB library, which contains MRCPSP-ENERGY test cases.This paper has been partially supported by the Spanish Research Projects TIN2013-46511-C2-1-P and TIN2016-80856-R.Morillo-Torres, D.; Barber, F.; Salido, MA. (2017). Mode-Based versus Activity-Based Search for a Nonredundant Resolution of the Multimode Resource-Constrained Project Scheduling Problem. Mathematical Problems in Engineering. 2017:1-15. https://doi.org/10.1155/2017/4627856S1152017Mouzon, G., Yildirim, M. B., & Twomey, J. (2007). Operational methods for minimization of energy consumption of manufacturing equipment. International Journal of Production Research, 45(18-19), 4247-4271. doi:10.1080/00207540701450013Hartmann, S., & Sprecher, A. (1996). A note on «hierarchical models for multi-project planning and scheduling». European Journal of Operational Research, 94(2), 377-383. doi:10.1016/0377-2217(95)00158-1Christofides, N., Alvarez-Valdes, R., & Tamarit, J. M. (1987). Project scheduling with resource constraints: A branch and bound approach. European Journal of Operational Research, 29(3), 262-273. doi:10.1016/0377-2217(87)90240-2Zhu, G., Bard, J. F., & Yu, G. (2006). A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem. INFORMS Journal on Computing, 18(3), 377-390. doi:10.1287/ijoc.1040.0121Kolisch, R., & Hartmann, S. (1999). Heuristic Algorithms for the Resource-Constrained Project Scheduling Problem: Classification and Computational Analysis. International Series in Operations Research & Management Science, 147-178. doi:10.1007/978-1-4615-5533-9_7Józefowska, J., Mika, M., Różycki, R., Waligóra, G., & Węglarz, J. (2001). Annals of Operations Research, 102(1/4), 137-155. doi:10.1023/a:1010954031930Bouleimen, K., & Lecocq, H. (2003). A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version. European Journal of Operational Research, 149(2), 268-281. doi:10.1016/s0377-2217(02)00761-0Alcaraz, J., Maroto, C., & Ruiz, R. (2003). Solving the Multi-Mode Resource-Constrained Project Scheduling Problem with genetic algorithms. Journal of the Operational Research Society, 54(6), 614-626. doi:10.1057/palgrave.jors.2601563Zhang, H., Tam, C. M., & Li, H. (2006). Multimode Project Scheduling Based on Particle Swarm Optimization. Computer-Aided Civil and Infrastructure Engineering, 21(2), 93-103. doi:10.1111/j.1467-8667.2005.00420.xJarboui, B., Damak, N., Siarry, P., & Rebai, A. (2008). A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Applied Mathematics and Computation, 195(1), 299-308. doi:10.1016/j.amc.2007.04.096Li, H., & Zhang, H. (2013). Ant colony optimization-based multi-mode scheduling under renewable and nonrenewable resource constraints. Automation in Construction, 35, 431-438. doi:10.1016/j.autcon.2013.05.030Lova, A., Tormos, P., Cervantes, M., & Barber, F. (2009). An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes. International Journal of Production Economics, 117(2), 302-316. doi:10.1016/j.ijpe.2008.11.002Peteghem, V. V., & Vanhoucke, M. (2010). A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem. European Journal of Operational Research, 201(2), 409-418. doi:10.1016/j.ejor.2009.03.034Węglarz, J., Józefowska, J., Mika, M., & Waligóra, G. (2011). Project scheduling with finite or infinite number of activity processing modes – A survey. European Journal of Operational Research, 208(3), 177-205. doi:10.1016/j.ejor.2010.03.037Kolisch, R., & Hartmann, S. (2006). Experimental investigation of heuristics for resource-constrained project scheduling: An update. European Journal of Operational Research, 174(1), 23-37. doi:10.1016/j.ejor.2005.01.065Debels, D., De Reyck, B., Leus, R., & Vanhoucke, M. (2006). A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. European Journal of Operational Research, 169(2), 638-653. doi:10.1016/j.ejor.2004.08.020Paraskevopoulos, D. C., Tarantilis, C. D., & Ioannou, G. (2012). Solving project scheduling problems with resource constraints via an event list-based evolutionary algorithm. Expert Systems with Applications, 39(4), 3983-3994. doi:10.1016/j.eswa.2011.09.062Drexl, A. (1991). Scheduling of Project Networks by Job Assignment. Management Science, 37(12), 1590-1602. doi:10.1287/mnsc.37.12.1590BOCTOR, F. F. (1996). Resource-constrained project scheduling by simulated annealing. International Journal of Production Research, 34(8), 2335-2351. doi:10.1080/0020754960890502

A genetic algorithm-based method for solving multi-mode resource-constrained project scheduling problem in uncertain environment

Project scheduling models with resource constraints and multi-mode activities aims to create a schedule for carrying out activities considering precedence constraints and available resources in order to minimize the project duration. In the real world, we face uncertainty related to projects, where there are no historical data, hence, we should rely on the experts' judgements to estimate activity durations. For this purpose, in this paper, the 99-simulation method is used to deal with uncertainty. The exact mathematical programming model is presented in this paper and the hybrid algorithm based on Genetic Algorithm is used to solve this type of project scheduling problem which finds the near-optimal solution in a short computational time. Finally, the effectiveness of the proposed model is examined with a numerical example.Peer reviewedFinal article published.MRCPSPSimulationUncertaintyGenetic algorith

The Resource Leveling Problem with multiple resources using an adaptive genetic algorithm

Resource management ensures that a project is completed on time and at cost, and that its quality is as previously defined; nevertheless, resources are scarce and their use in the activities of the project leads to conflicts in the schedule. Resource Leveling Problems consider how to make the resource consumption as efficient as possible. This paper presents a new Adaptive Genetic Algorithm for the Resource Leveling Problem with multiple resources, and its novelty lies in using the Weibull distribution to establish an estimation of the global optimum as a termination condition. The extension of the project deadline with a penalty is allowed, avoiding the increase in the project criticality punishing the shift of activities. The algorithmis tested with the standard Project Scheduling Problem Library PSPLIB, and a complete analysis and benchmarking test instances are presented. The proposed algorithm is implemented using VBA for Excel 2010 in order to provide a flexible and powerful decision support system that enables practitioners to choose between different feasible solutions to a problem, and in addition it is easily adjustable to the constraints and particular needs of each project in realistic environments.This study was partially funded by the Spanish Ministry of Science and Innovation (research project BIA2011-23602).Ponz Tienda, JL.; Yepes Piqueras, V.; Pellicer Armiñana, E.; Moreno Flores, J. (2013). The Resource Leveling Problem with multiple resources using an adaptive genetic algorithm. Automation in Construction. 29(1):161-172. doi:10.1016/j.autcon.2012.10.003S16117229

The trade off between diversity and quality for multi-objective workforce scheduling

In this paper we investigate and compare multi-objective and weighted single objective approaches to a real world workforce scheduling problem. For this difficult problem we consider the trade off in solution quality versus population diversity, for different sets of fixed objective weights. Our real-world workforce scheduling problem consists of assigning resources with the appropriate skills to geographically dispersed task locations while satisfying time window constraints. The problem is NP-Hard and contains the Resource Constrained Project Scheduling Problem (RCPSP) as a sub problem. We investigate a genetic algorithm and serial schedule generation scheme together with various multi-objective approaches. We show that multi-objective genetic algorithms can create solutions whose fitness is within 2% of genetic algorithms using weighted sum objectives even though the multi-objective approaches know nothing of the weights. The result is highly significant for complex real-world problems where objective weights are seldom known in advance since it suggests that a multi-objective approach can generate a solution close to the user preferred one without having knowledge of user preferences

Uma metaheurística para a programação de projectos com multi-modos e recursos limitados

Este artigo apresenta uma nova abordagem (MM-GAV-FBI), aplicável ao problema da programação de projectos com restrições de recursos e vários modos de execução por actividade, problema conhecido na literatura anglo-saxónica por MRCPSP. Cada projecto tem um conjunto de actividades com precedências tecnológicas definidas e um conjunto de recursos limitados, sendo que cada actividade pode ter mais do que um modo de realização. A programação dos projectos é realizada com recurso a um esquema de geração de planos (do inglês Schedule Generation Scheme - SGS) integrado com uma metaheurística. A metaheurística é baseada no paradigma dos algoritmos genéticos. As prioridades das actividades são obtidas a partir de um algoritmo genético. A representação cromossómica utilizada baseia-se em chaves aleatórias. O SGS gera planos não-atrasados. Após a obtenção de uma solução é aplicada uma melhoria local. O objectivo da abordagem é encontrar o melhor plano (planning), ou seja, o plano que tenha a menor duração temporal possível, satisfazendo as precedências das actividades e as restrições de recursos. A abordagem proposta é testada num conjunto de problemas retirados da literatura da especialidade e os resultados computacionais são comparados com outras abordagens. Os resultados computacionais validam o bom desempenho da abordagem, não apenas em termos de qualidade da solução, mas também em termos de tempo útil.As the complexity of projects increases, the requirement of an organized planning and scheduling process is enhanced. The need for organized planning and scheduling of a construction project is influenced by a variety of factors (e.g., project size and number of project activities). To plan and schedule a construction project, activities must be defined sufficiently. The level of detail determines the number of activities contained within the project plan and schedule. So, finding feasible schedules which efficiently use scarce resources is a challenging task within project management. In this context, the well-known Resource Constrained Project Scheduling Problem (RCPSP) has been studied during the last decades. In the RCPSP the activities of a project have to be scheduled such that the makespan of the project is minimized. So, the technological precedence constraints have to be observed as well as limitations of the renewable resources required to accomplish the activities. Once started, an activity may not be interrupted. This problem has been extended to a more realistic model, the multi-mode resource constrained project scheduling problem (MRCPSP), where each activity can be performed in one out of several modes. Each mode of an activity represents an alternative way of combining different levels of resource requirements with a related duration. Each renewable resource has a limited availability such as manpower and machines for the entire project. The objective of the MRCPSP problem is minimizing the makespan. While the exact methods are available for providing optimal solution for small problems, its computation time is not feasible for large-scale problems. This paper presents a genetic algorithm-based approach (MM-GAV-FBI) for the multi-mode resource constrained project scheduling problem. The idea of this new approach is integrating a genetic algorithm with a schedule generation scheme. This study also proposes applying a local search procedure trying to improve the initial solution. The chromosome representation of the problem is based on random keys. The schedule is constructed using a schedule generation scheme (SGS) in which the priorities of the activities are defined by the genetic algorithm. The experimental results of MM-GAV-FBI on project instances show that this approach is an effective method for solving the MRCPSP

Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance

Pre-emptive resource-constrained multimode project scheduling using genetic algorithm: a dynamic forward approach

Purpose: The issue resource over-allocating is a big concern for project engineers in the process of scheduling project activities. Resource over-allocating drawback is frequently seen after scheduling of a project in practice which causes a schedule to be useless. Modifying an over-allocated schedule is very complicated and needs a lot of efforts and time. In this paper, a new and fast tracking method is proposed to schedule large scale projects which can help project engineers to schedule the project rapidly and with more confidence. Design/methodology/approach: In this article, a forward approach for maximizing net present value (NPV) in multi-mode resource constrained project scheduling problem while assuming discounted positive cash flows (MRCPSP-DCF) is proposed. The progress payment method is used and all resources are considered as pre-emptible. The proposed approach maximizes NPV using unscheduled resources through resource calendar in forward mode. For this purpose, a Genetic Algorithm is applied to solve. Findings: The findings show that the proposed method is an effective way to maximize NPV in MRCPSP-DCF problems while activity splitting is allowed. The proposed algorithm is very fast and can schedule experimental cases with 1000 variables and 100 resources in few seconds. The results are then compared with branch and bound method and simulated annealing algorithm and it is found the proposed genetic algorithm can provide results with better quality. Then algorithm is then applied for scheduling a hospital in practice. Originality/value: The method can be used alone or as a macro in Microsoft Office Project® Software to schedule MRCPSP-DCF problems or to modify resource over-allocated activities after scheduling a project. This can help project engineers to schedule project activities rapidly with more accuracy in practice.Peer Reviewe

The Project Scheduling Problem with Non-Deterministic Activities Duration: A Literature Review

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration.Peer Reviewe

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