Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications
Abstract
This title presents a large variety of models and algorithms dedicated to the resource-constrained project scheduling problem (RCPSP), which aims at scheduling at minimal duration a set of activities subject to precedence constraints and limited resource availabilities. In the first part, the standard variant of RCPSP is presented and analyzed as a combinatorial optimization problem. Constraint programming and integer linear programming formulations are given. Relaxations based on these formulations and also on related scheduling problems are presented. Exact methods and heuristics are surveyed. Computational experiments, aiming at providing an empirical insight on the difficulty of the problem, are provided. The second part of the book focuses on several other variants of the RCPSP and on their solution methods. Each variant takes account of real-life characteristics which are not considered in the standard version, such as possible interruptions of activities, production and consumption of resources, cost-based approaches and uncertainty considerations. The last part presents industrial case studies where the RCPSP plays a central part. Applications are presented in various domains such as assembly shop and rolling ingots production scheduling, project management in information technology companies and instruction scheduling for VLIW processor architectures.
... Bài toán lập lịch thực hiện dự án với tài nguyên giới hạn RCPSP (Resource Con-strained Project Scheduling Problem) [1,2], là bài toán đặt ra mục tiêu tìm phương án lịch biểu để bố trí các tài nguyên cho trước thực hiện và hoàn thành mọi công việc (tác vụ) trong một dự án với thời gian ngắn nhất hoặc chi phí thấp nhất hoặc cân bằng cả hai yếu tố thời gian và chi phí. Thông thường, số lượng tác vụ cần thực hiện của dự án lớn hơn nhiều so với số lượng tài nguyên có thể sử dụng. ...
... Thông thường, số lượng tác vụ cần thực hiện của dự án lớn hơn nhiều so với số lượng tài nguyên có thể sử dụng. Bài toán MS-RCPSP (Multi Skill -RCPSP) [1][2][3][4] mở rộng từ RCPSP bằng việc bổ sung thêm ràng buộc mới, gần với các dự án trong thực tế hơn, đó là: mỗi tài nguyên có thể có nhiều kỹ năng khác nhau và mỗi kỹ năng có mức/bậc kỹ năng nhất định. Mỗi tác vụ sẽ có yêu cầu về tài nguyên thực hiện cần đáp ứng loại kỹ năng cụ thể và mức kỹ năng nhất định. ...
... Là bài toán mở rộng từ bài toán RCPSP, MS-RCPSP [1][2][3]12] bổ sung thêm ràng buộc về kỹ năng của tài nguyên thực hiện: mỗi tài nguyên có nhiều kỹ năng (skill) khác nhau và mỗi kỹ năng có một mức/bậc (level) cụ thể. Để thực hiện được tác vụ, tài nguyên cần đáp ứng về kỹ năng và mức kỹ năng theo yêu cầu của tác vụ. ...
Bài báo đề xuất phương pháp tìm lời giải cho Bài toán MS-RCPSP (Multi Skill-Resource Constrained Project Scheduling Problem). MS-RCPSP đã được chứng minh là bài toán NP-Khó, do vậy cần sử dụng các phương pháp tính toán tiến hóa, cận tối ưu nhằm tìm được lời giải phù hợp trong thời gian chấp nhận được. Thuật toán đề xuất là thuật toán lai ghép giữa thuật toán Cuckoo Search (CS) và kỹ thuật Rotate giúp mở rộng không gian tìm kiếm sau mỗi thế hệ tiến hóa, nhằm tăng khả năng tìm được lời giải tốt hơn. Thuật toán mới gọi là Ro-CS có khả năng áp dụng để tìm lời giải cho bài toán MS-RCPSP. Để kiểm chứng thuật toán Ro-CS, bài báo tiến hành thực nghiệm trên bộ dữ liệu chuẩn iMOPSE, kết quả thực nghiệm được tổng hợp, đánh giá, so sánh, phân tích cho thấy tính hiệu quả của thuật toán đề xuất.
... The structure of the processes to be operated is defined by precedence relations among the activities, the associated processing times can be modeled through random variables to consider the associated uncertainty. The aim of the scheduling approach is the minimization of the makespan, supporting the optimized utilization of the resources [23]. ...
... , p 40 ] is used to describe the processing time for all the activities. Since only extreme scenarios need to be examined in the maximum regret minimization model [30], 2 (41−2) scenarios in total need to be evaluated in this case study, the scenario relaxation algorithm with accelerated convergences for robust resourceconstrained project scheduling problem proposed in [23] has been adopted to support the definition of robust schedules. ...
Refurbished products are gaining importance in many industrial sectors, specifically high-value products whose residual value is relevant and guarantee the economic viability of the re-manufacturing at an industrial level, e.g., turbine blades for power generation. In this paper, we address the robust scheduling scheme of re-manufacturing activities for turbine blades. Parts entering the process may have very different wear states or presence of defects. Thus, the repair process is affected by a significant degree of uncertainty. The paper investigates the uncertainties and discusses how they affect the scheduling performance of the re-manufacturing system. We then present a robust scheduling framework for the re-manufacturing scheduling strategies, policies, and methods. This framework is based on a wide variety of experimental and practical approaches in the re-manufacturing scheduling area, which will be a guideline for the planning and scheduling of re-manufacturing activities of turbine blades. A case study approach was adopted to examine how re-manufacturers design their scheduling strategies.
... It has been widely studied in the scheduling literature. It is NP-hard in the strong sense and computationally challenging (Artigues et al., 2008). ...
... The RCPSP is to find a minimum makespan schedule for the jobs of a project under precedence constraints and scarce resource availability. By contrast with PERT Scheduling, the RCPSP is a classical problem that is NP-hard and computationally challenging to solve in practice (see, e.g., (Artigues et al., 2008) ...
If the instance of an optimization problem changes, an initial solution may become suboptimal or infeasible. It is then necessary to compute a new solution, but it is also desirable to keep some decisions from the initial solution unchanged. In this thesis we propose the anchoring criterion to favor unchanged decisions between solutions. In a reoptimization setting, the goal is to find a new solution while keeping a maximum number of decisions from the initial solution. In a robust 2-stage optimization setting, we propose the anchor-robust approach to compute in advance a baseline solution, along with a subset of so-called anchored decisions. For any realization in the considered uncertainty set, it is possible to repair the baseline solution into a new solution without changing anchored decisions. The anchor-robust approach allows for a trade-off between the cost of a solution and guaranteed decisions. Anchoring problems are formally defined and studied on two problem classes. The first one is the class of integer programs in binary variables, including classical polynomial problems such as spanning trees. The second one is project scheduling, where jobs must be scheduled under precedence only, or precedence and resource constraints. The complexity of anchoring problems is analyzed. Combinatorial properties of anchored solutions are exhibited, and dedicated algorithmic and polyhedral approaches are devised. Mixed-integer programming techniques are investigated, that highlight the practical implementability of anchoring problems.
... Resource constraints forbid that the amount of resources used by activities running simultaneously exceed the availability of that resource. The typical objective is to minimize the duration of the project (makespan) (Artigues, Demassey, & Neron, 2013). There exist many variants of this problem: considering multiple execution modes of the activities with different durations and resource demands, as well as distinguishing between renewable and non-renewable resources (Multimode Resource-Constrained Scheduling Problem, MRCPSP); considering minimum and maximum time lags between start-times of pairs of activities (RCPSP/max), possibly with multiple execution modes (MR-CPSP/max); considering time-varying resource availabilities and demands (Resource-Constrained Project Scheduling Problem with Time-Dependent Resource Capacities and Requests, RCPSP/t), or considering • A task-indexed SMT formulation, and experiments, for the RCPSP and the MRCPSP, and a discussion on the unsuitability of taskindexed formulations for the RCPSP/t. ...
... This preprocess resembles the energy based reasoning used by some constraint propagators (see, e.g., Artigues et al., 2013). It can be easily adapted to the multi-mode case by considering the minimum possible consumptions , ⋅ , , over modes in Eq. (1), and minimum durations , in Eq. (2). ...
The Resource-Constrained Project Scheduling Problem (RCPSP) is a paradigmatic scheduling problem where the activities of a project have to be scheduled while respecting a combination of precedence and resource constraints. Precedence constraints are relations between two activities stating that one can not start until the other has ended, and resource constraints bound the amount of resources used by activities running simultaneously. Many generalizations of the RCPSP have been proposed in the literature, including multiple execution modes for the activities (MRCPSP), or time varying resource availabilities and demands (RCPSP/t).
In this work we present Satisfiability Modulo Theories (SMT) formulations to solve the RCPSP, as well as its two variants MRCPSP and RCPSP/t. Although it is really natural to formulate resource constraints of RCPSP-like problems using the linear integer arithmetic (LIA) theory, we show how, by exploiting the information provided by the precedence relations, we can obtain compact and efficient encodings of resource constraints to Boolean Satisfiability (SAT) formulas. Using these SAT encodings instead of the LIA ones, turns to be crucial regarding efficiency. The method is adapted to encode resource constraints for the other two considered variants. In this adaptation, the method exploits not only precedences, but multiple execution modes or time varying resource availabilities and demands. Our experimental results show that the proposed encodings are more efficient than existing state-of-the-art exact solving techniques for the studied problems.
... The RCPSP constitutes a fundamental problem in the field of discrete optimization because it subsumes and combines various hard problems, such as partition, packing and color-ing, into one common optimization problem. It has extensive applications in project planning, production industry, supply chain management, logistics and health care, see, for example, Artigues et al. (2013), Cardoen et al. (2010) and Weglarz (2012). Exact solution methods for the RCPSP, in its general form, exist since the late 1960s with a first work of Johnson (1967) who proposes a branch-and-bound algorithm for the RCPSP. ...
... Each instance considers four resources with individual capacities, resource demands and precedence constraints. In previous works, the instances also have been parameterized by different parameters such as: order strength, network complexity, resource factor, resource strength, disjunction ratio and process range, see Artigues et al. (2013) and Koné et al. (2011). We implemented the models DDT, OOE, SEE, RSEE and IEE using the C++ interface of the commercial MIP solver Gurobi 7.5.1 in default settings. ...
In this paper, we study event-based mixed-integer programming (MIP) formulations for the resource-constrained project scheduling problem (RCPSP) that represent an alternative to the more common time-indexed model (DDT) (Pritsker et al. in Manag Sci 16(1):93–108, 1969; Christofides et al. in Eur J Oper Res 29(3):262–273, 1987) for the case when the scheduling horizon is large. In contrast to time-indexed models, the size of event-based models does not depend on the time horizon. For two event-based models OOE and SEE introduced by Koné et al. (Comput Oper Res 38(1):3–13, 2011), we first present new valid inequalities that strengthen the original formulation. Furthermore, we state a new event-based model, the Interval Event-Based Model (IEE), and deduce natural linear transformations between all three models. Those transformations yield the strict domination order for their respective linear programming relaxations, meaning that the new IEE model has the strongest linear relaxation among all known event-based models. In addition, we show that DDT can be retrieved from IEE by subsequent expansion and projection of the underlying solution space. This yields a unified polyhedral view on a complete branch of MIP models for the RCPSP. Finally, we also compare the computational performance between all models on common test instances of the PSPLIB (Kolisch and Sprecher in Eur J Oper Res 96(1):205–216, 1997).
... The Deadline-Aware Service Function Chaining Scheduling model is a Mixed Integer Linear problem ((DA-SFCS-MILP) which is complex to solve. It is NP-Hard given that it is a combination of three NP-Hard sub-problems which are the NFs mapping sub-problem [8], [31], the traffic routing subproblem [32], [33] and the deadline-aware service scheduling sub-problem [34], [35]. Thus, in the next Sections we present several heuristics to solve it. ...
... Constraint (28) specifies that a NS is served and finishes its processing before its deadline u s . Constraint (29) Given that LAMS and RMS use the DA-MILP which is a scheduling problem, known to be NP-Hard [34], [35], we propose a tabu search-based algorithm (TS-DA-SFCS) to efficiently solve the DA-SFCS problem. Our tabu-based approach consists of building an initial solution for the provided NSs first, through traversing them in a pre-defined order and attempting to map their NFs using the random mapping (Section IV-A), route their traffic by running a shortest path algorithm (Section IV-B) and scheduling their traffic on a First Come First Served (FCFS) based scheduling. ...
... The third category is the resource constrained project scheduling. A good source of information on this category is the book of Artigues et al. [6]. ...
... The problem F easible(Q) can be viewed as a multi-mode project scheduling problem, in which an activity (operation) is assigned a mode (set of workers) and has the mode dependent duration, see Kolisch et al. [62], Tseng and Chen [86] and Artigues et al. [6] for the definitions of the latter problem. The known mathematical programming formulations of such problems include variables with indices whose number is equal to the number of modes, see Kolisch and Sprecher [61]. ...
An overview of existing problems and methods for the design of assembly and transfer lines is given. A new workforce assignment problem for a paced multi-product assembly line with a goal of minimizing the number of workers is studied. Various precedence relations between operations and functions of operation processing times dependent on the number of workers areconsidered. A new problem of multi-objective optimization for a single product transfer line is solved. Several exact and heuristic methods and their computer implementations for both problems are developed by the author. An application of developed approaches to solving a real production problem relevant to the European project amePLM is demonstrated.
... The Resource Constrained Scheduling Problem (RCSP) is a subclass of scheduling problems and is mostly related to the Project Scheduling domain. In other words, scheduling problems that deal with personnel or workforce constraints are referred to as Resource Constrained Project Scheduling Problems (RCPSP) (Pinedo, 2007;Artigues et al., 2008). Details of RCPSP are beyond the scope of this paper and the interested reader is referred to Brucker et al. (1999) and Hartmann and Briskorn (2010). ...
In this paper, we consider a problem inspired by a real-life problem, which aims to schedule high multiplicity jobs on a single machine by taking into account the organization-specific constraints in a different schedule structure. The schedule is daily with daytime and nighttime periods. The operator is considered as an additional resource that varies in terms of consumption and scheduling depending on the period. There are specific rest periods before and after night-period jobs, and night-period jobs affect both the daily working time and number of the jobs in the daytime- period. In addition, the operator's daily workload is divided into two categories: normal and heavy. If the workload is heavy on consecutive days, specific rest periods must be scheduled. The integer programming model of the problem is presented. The feasible solutions obtained in a short time with greedy constructive heuristic algorithms are used in the exact solution approach as both upper bound and warm-start point. Finally, the effectiveness of the solution approaches is compared and evaluated through numerical experiments carried out for a variety of problem instances of different sizes.
... In addition, interdependencies and the influence of imprecise or missing process parameters and the relevance of the disturbance variables are increasing. To deal with the above tasks, hyper heuristics emerged as a promising option because finding the global optimum with justifiable efforts for PPC problems remains illusory even with improved computational power due to the size and the NP-hardness of such problems (see (Artigues et al., 2013;Snauwaert and Vanhoucke, 2023;Hartmann and Briskorn, 2022) for surveys on resource-constrained project scheduling problems (PSP) and (Ɖurasević and Jakobović, 2023;Guo et al., 2022;Zhang et al., 2021;Branke et al., 2016;Burke et al., 2013;Luo et al., 2022) for surveys focussing on algorithms). Moreover, even the appropriate application of heuristics causes serious difficulties because the number and the value range of the parameters to be taken into account as well as the diversity of the existing algorithms exceed what is intuitively comprehensible and there is still a lack of systematic, theoretically sound selection criteria (Burke et al., 2013). ...
A simulation framework is presented which covers both generation and simulation of production planning and control problems which include transfer times and stochastic influences and therefore extend classical multi-mode multi-project RCPSPs. This allows for systematic and in-depth investigations of the quality and the behaviour of heuristics. In addition, the automated design of heuristics based on Boolean operators applied to relations of problem specific quantities leads on average to better results than a manual selection and adjustment of heuristic strategies.
... Due to the strongly NP-hardness of the problem (Blazewicz et al., 1983), many researchers have placed this problem at the centre of their research agenda, and in the following paragraphs a brief overview will be given of some of the recent lines of research that have led to the investigation of the current study. For a more detailed overview of the research into this challenging project scheduling problem, the reader is referred to (rather old) survey papers (Özdamar and Ulusoy, 1995;Herroelen et al., 1998;Kolisch and Padman, 2001), two classification schemes Brucker et al., 1999) and a handful of research books (Demeulemeester and Herroelen, 2002;Neumann et al., 2002;Dorndorf et al., 2002;Brucker and Knust, 2012;Vanhoucke, 2012;Artigues et al., 2013;Schwindt and Zimmermann, 2015a,b). ...
... There have been a wide range of studies on both heuristic and metaheuristic methods for solving the RCPSP, as well as different MILP models (Artigues et al., 2010(Artigues et al., , 2015Wang et al., 2010;Hartmann and Briskorn, 2010;Brucker and Knust, 2011;Nouri et al., 2013). The first MILP formulations proposed for the RCPSP were discrete time formulations (Pritsker et al., 1969). ...
This paper deals with a scheduling problem arising at the tactical decision level in aeronautical assembly line. It has the structure of a challenging multi-mode resource-constrained project scheduling problem with incompatibility constraints, a resource leveling objective and also a large number of tasks. We first present a new event-based mixed-integer linear programming formulation and a standard constraint programming formulation of the problem. A large-neighborhood search approach based on the constraint programming model and tailored to the resource leveling objective is proposed. The approaches are tested and compared using industrial instances, yielding significant improvement compared to the heuristic currently used by the company. Moreover, the large-neighborhood search method significantly improves the method proposed in the literature on a related multi-mode resource investment problem when short CPU times are required.
... The Resource-Constrained Project Scheduling Problem (RCPSP) is to find a minimum makespan schedule for the jobs of a project under precedence constraints and scarce resource availability. This problem finds a large variety of applications in the industry, see, e.g., (Artigues et al., 2008) overhead computational effort for solving the Adjustable-Robust RCPSP, in comparison with the deterministic RCPSP, is low. We then provide numerical results for the Anchor-Robust RCPSP, for both MIP reformulation and heuristics. ...
The concept of anchored solutions is proposed as a new robust optimization approach to the Resource-Constrained Project Scheduling Problem (RCPSP) under processing times uncertainty. The Anchor-Robust RCPSP is defined, to compute a baseline schedule with bounded makespan, sequencing decisions, and a max-size subset of jobs with guaranteed starting times, called anchored set. It is shown that the Adjustable-Robust RCPSP from the literature fits within the framework of anchored solutions. The Anchor-Robust RCPSP and the Adjustable-Robust RCPSP can benefit from each other to find both a worst-case makespan, and a baseline schedule with an anchored set. A dedicated graph model for anchored solutions is reviewed for budgeted uncertainty. Compact MIP reformulations are derived for both the Adjustable-Robust RCPSP and the Anchor-Robust RCPSP. Dedicated heuristics are designed based on the graph model. For both problems, the efficiency of the proposed MIP reformulations and heuristic approaches is assessed through numerical experiments on benchmark instances.
... Energy consumption of building with gains, air infiltration[24] ...
This study aims to develop a new energy certification rating system in hot and dry climates. To do this, sustainable strategies must be applied for tertiary buildings. The methodology consists to evaluate these passive strategies by covering three proportions of sustainability (energy, economic and comfort), with a dynamic simulation. In addition, to calculate energy performance and energy savings indicators, we are carrying out a survey to establish reasonable and fair criteria for case study. In this study, four stages were carried out data collection and analysis, evaluation of the energy performance indicators of the strategies. With a multi-criteria analysis, we can evaluate indices of the energy performance of a building, in order to set up a new energy certification, which can allow energy savings and maintain comfort.
... ;Yang et al. (2001);Hartmann and Briskorn (2010);Artigues et al. (2013). ...
Les travaux de cette thèse proposent des méthodes d’optimisation sur des problèmes d’ordon- nancement de travaux multiressources et à intervalles fixes sur machines parallèles identiques. Les "problèmes d’ordonnancement monocritère" et "problèmes d’ordonnancement multiagent" sont considérés. Nous développons un panel d’ordonnanceurs basés sur des méthodes exactes et ap- prochées pour déterminer des solutions réalisables où l’objectif est de maximiser la somme totale pondérée des travaux ordonnancés (ou équivalent, minimisant le coût total pondérée des travaux rejetés), durant un horizon de planification. L’application des méthodes d’optimisation exactes s’avère illusoire dans la pratique en raison du temps de calcul, plus particulièrement lorsqu’il s’agit des systèmes distribués. En revanche ces méthodes exactes serviront comme références pour évaluer les méthodes approchées.La première partie est consacrée à l’étude des problèmes d’ordonnancement monocritères. Après l’analyse de complexité, trois programmes linéaires en nombres entiers (PLNEs), un modèle basé sur la programmation par contrainte (PPC), une méthode hybride entre la PPC et un PLNE sont proposés pour résoudre à l’optimum le problème d’ordonnancement. Nous développons également une méthode exacte de type génération de colonnes basée sur la décomposition de Dantzig-Wolfe qui nous conduit à proposer un algorithme de type Branch & Price. Le Branch & Price offre de meilleures performances que les autres méthodes exactes sur des instances allant jusqu’à 150 tra- vaux. Pour résoudre des instances de très grandes tailles, des heuristiques de liste basées sur des règles de priorité sont proposées. Afin d’éviter les choix myopes de ces algorithmes gloutons, nous introduisons une heuristique constructive PILOT combinant deux ou plusieurs règles d’ordonnan- cement et d’affectation ainsi qu’un algorithme évolutionnaire (AE). Les résultats expérimentaux mettent en évidence les performances de PILOT et AE.La seconde partie de nos travaux est dédiée à l’étude de l’ordonnancement multiagent des travaux multiressources à intervalles fixes. Ce modèle considère plusieurs agents associés à des sous-ensembles de travaux disjoints, chacun d’eux cherche à maximiser la somme totale pondérée de ses travaux ordonnancés. Les trois approches suivantes sont considérées : combinaison linéaire des critères, l’approche ε-contrainte et l’énumération de l’ensemble des optima de Pareto. Après une analyse de la complexité des problèmes étudiés, des programmes dynamiques polynomiaux ont été développés pour résoudre des cas particuliers. Les fronts optimaux de Pareto sont obtenus par l’approche ε-contrainte utilisant le PLNE, la méthode hybride PPC & PLNE ou encore la méthode Branch & Price. Les résultats des expérimentations montrent que les méthodes exactes sont beaucoup moins performantes. Pour résoudre des problèmes de grande taille, des heuristiques de liste et une méthode évolutionnaire de type NSGAII sont développées. Toutes ces méthodes ont été implémentées et testées.
... There also exist variants which consider the minimization of resource consumption as an objective (instead of a constraint). The interested reader can refer to the surveys [BDM + 99] and [HB10] or to the book [ADN08] for further details on RCPSP. ...
The Infologic company develops an ERP, called Copilote, specialized for companies in the agri-food sector. It integrates several modules which allow to schedule different operations of the supply chain. These modules provide solutions to different scheduling problems with different constraints and objectives. Moreover, although the literature on scheduling problems is vast, a particular constraint encountered by Copilote users can only be modeled with difficulty using the elements known from the literature. In the problem encountered, the operations to be scheduled are divided into groups. The schedule must satisfy a constraint on these groups ensuring that at any given time there are no more than k groups such that some operations of these groups have been started while some others have not been completed. In this thesis, we study this new scheduling problem from a theoretical point of view, and we propose adaptations for the methods classically used for scheduling problems (integer linear programming, constraint programming, ant colony optimization, and local search). We also introduce a new approach hybridizing constraint programming and ant colony optimization to solve this problem. We experimentally compare these different algorithms on a test set constructed from real data, and we show that the best algorithm changes depending on the features of the instance to be solved. We then propose a method, which, depending on the features of the instance to be solved, automatically chooses the most suitable solving method. Finally, we evaluate, in a dynamic context, the cost of disrupting as little as possible the already established schedules when new data are revealed.
... First and foremost, the summary papers written by Icmeli et al. (1993), Elmaghraby (1995), Ö zdamar and Ulusoy (1995), Herroelen et al. (1998), Brucker et al. (1999) are most likely outdated, but nevertheless interesting to get an overview of the research done in the previous century. Much of the work presented in these papers is also published in research books such as Demeulemeester and Herroelen (2002), Brucker and Knust (2006) and Vanhoucke (2012) and book chapters such as Artigues et al. (2008), Schwindt and Zimmermann (2015a) and Schwindt and Zimmermann (2015b), each time providing some new insights in the progress made in the early '00s. In a recent paper, Coelho and Vanhoucke (2018) have integrated most of the work presented in these summary paper in a so-called composite lower bound strategy search which incorporates the best performing branch-andbound procedures from the academic literature. ...
In the past decades, the resource on the resource-constrained project scheduling problem (RCPSP) has grown rapidly, resulting in an overwhelming amount of solution procedures that provide (near)-optimal solutions in a reasonable time. Despite the rapid progress, little is still known what makes a project instance hard to solve. Inspired by a previous research study that has shown that even small instances with only up to 30 activities is sometimes hard to solve, the current study provides an analysis of the project data used in the academic literature. More precisely, it investigates the ability of four well-known resource indicators to predict the hardness of an RCPSP instance. The study introduces a new instance equivalence concept to show that instances might have very di_erent values for their resource indicators without changing any possible solution for this instance. The concept is based on four theorems and a search algorithm that transforms existing instances into new equivalent instances with more compact resources. This algorithm illustrates that the use of resource indicators to predict the hardness of an instance is sometimes misleading. In a set of computational experiment on more than 10,000 instances, it is shown that the newly constructed equivalent instances have values for the resource indicators that are not only di_erent than the values of the original instances, but also often are better in predicting the hardness the project instances. It is suggested that the new equivalent instances are used for further research to compare results on the new instances with results obtained from the original dataset.
... The authors argue that despite the impressive growth of computational power and new algorithms, many RCPSP instances can still not be solved to optimility, and therefore state that the research on the RCPSP should still not be abandoned. Fourtly, various interesting articles can be found in recent books by Artigues et al. (2008) and Schwindt and Zimmermann (2015a,b) and are worth exploring to get a good overview of the latest research findings for the RCPSP. Finally, Pellerin et al. (2020) give a survey of hybrid meta-heuristics for the resource-constrained project scheduling problem, and compare the results of different hybrid procedures on the well-known PSPLIB instances. ...
The resource-constrained project scheduling problem (RCPSP) is one of the most studied problems in the project scheduling literature, and aims at constructing a project schedule with a minimum makespan that satisfies both the precedence relations of the network and the limited availability of the renewable resources. The problem has attracted attention due to its NP hardness status, and different algorithms have been proposed that solve a wide variety of RCPSP instances to optimality or near-optimality. In this paper, we analyse the hardness of this problem from an experimental point-of-view by testing different algorithms on a huge set of existing instances and detect which ones are difficult to solve. To that purpose, we propose a three-phased approach that makes use of five elementary blocks, well-performing algorithms and a huge amount of computational power to transform easy RCPSP instances into very hard ones. The purpose of this study is to create insight and understanding into what makes an RCPSP instance hard, and propose a new dataset that consists of a small set of instances that are impossible to solve with the algorithms currently existing in the literature. These instances should be as small as possible in terms of number of activities and resources, and should be as diverse as possible in terms of network structure and resource strictness. Such a dataset should enable researchers to focus their attention on the development of radically new algorithms to solve the RCPSP rather than gradually improving current algorithms that can solve the existing RCPSP instances only slightly better.
... The Underground Resource Constrained Production Scheduling Problem (UG-RCPSP) model builds on the work of Brickey (2015), a particular case of the resource constrained project scheduling problem (RCPSP). The RCPSP is a known NP-hard problem (Artigues et al., 2013) that consists of scheduling activities over time, subject to precedence and resource availability constraints. The following generalized formulation illustrates the UG-RCPSP. ...
... Resource Constrained Project Scheduling Problem (RCPSP) is a well-established project scheduling methodology, more inclined to operational research field (e.g., automobile manufacturing, power generation system, steel production, assembly production scheduling, and jobshop environments [8][9][10]), in which the principal objective is to minimize project completion time or makespan [11]. To succeed in the digitalized era, integration of intelligent approaches should start from the very early stage of a product's lifecycle. ...
In the presence of increasingly dynamic environments, frequent uncertainties, high customer specifications, strict project deadlines, and stricter requirements on sustainability, modern project managers are challenged in their ability to schedule and control projects. Thus, in the context of sustainable project scheduling problem, two important elements are to be considered as decision variables: the input elements of a scheduling (e.g. resources: workforce, machine, money) that enable the realization of a schedule for a project and the output element that are consequences of the realization of the project (e.g. completion time, energy, noise, pollution, waste etc.). In this context, integration of innovative approaches and concepts under the framework of fourth generation industrial revolution is must to build up a sustainable project scheduling model (SPSM). Considering this burning issue, this paper introduces digital twin (DT) technology and cyber physical system (CPS) principles to develop effective and efficient sustainable project scheduling systems and proposes a framework to show how they are interconnected through physical and cyber layers. The proposed framework is also applied to a real-life energy system as a case study for identification of the degradation of a physical layer.
... De plus, il existe toujours une liste de priorité telle que la solution renvoyée par le SSGS appliqué sur cette liste est optimale (pour une preuve de ce résultat, voir par exemple Artigues et al. (2008), chapitre 6). Ce résultat ne s'applique pas au PSGS. ...
La structure de projet se retrouve dans de nombreux contextes de l'industrie et des services. Il s'agit de réaliser un ensemble d'activités pouvant être connectées par des liens logiques de séquence (antériorité), en faisant appel à des ressources disponibles en quantité limitée. L'objectif est la minimisation d'un critère généralement lié à la durée ou au coût du projet. La plupart des problèmes d'ordonnancement de projet dans la littérature considèrent une unité de temps commune pour la détermination des dates d'exécution des activités et pour l'évaluation instantanée du respect des capacités des ressources qu'elles utilisent. Or, s'il est souvent nécessaire en pratique d'obtenir un calendrier détaillé des plages d'exécution des activités, l'utilisation des ressources peut être évaluée sur un horizon plus agrégé, comme par exemple les quarts de travail des employés. Dans cette thèse, un nouveau modèle intégrant ces deux échelles de temps est présenté afin de définir le problème d'ordonnancement de projet avec agrégation périodique des contraintes de ressources (PARCPSP). Ce problème est étudié du point de vue de la théorie de la complexité et des propriétés structurelles sont établies, mettant notamment en évidence des différences majeures avec le problème classique d'ordonnancement de projet sous contraintes de ressources (RCPSP). De ces propriétés sont dérivées des formulations exactes basées sur la programmation linéaire en nombres entiers, comparées en termes de qualité de la relaxation linéaire. Par ailleurs, plusieurs heuristiques, telles que des algorithmes de liste, ou une méthode approchée basée sur une résolution itérative qui exploite différentes échelles de temps, sont proposées. Les résultats expérimentaux montrent l'intérêt de ces différentes méthodes et illustrent la difficulté du problème.
... For the 30-activity instances from PSPLIB, it has been observed that the computational time increases with the increase of RF from 0.25 to 1. Another important indicator is resource strength (RS), which is a hybrid indicator which mixes both resource and time parameters. It is designed so that the smallest feasible resource availability for any particular resource corresponds to RS = 0, while RS = 1 corresponds to the absence of resource constraints, since the peak resource demand for the earliest feasible precedence schedule is satisfied [34]. Considering all those aspects, the selected benchmark instances are divided into eight groups according to their problem hardness, increasing from type 1 to 8, as shown in Table 1. ...
The Resource Constrained Project Scheduling Problem (RCPSP) is a well-known complex scheduling problem. In real world situations, the parameters of projects are vulnerable to uncertainty, change or disruption, which necessitates that the initial baseline schedule must be revised. In this work, we have proposed two different mathematical models for both the Discrete Time-Based Reactive Approach (DTRA) and the Event-Based Reactive Approach (EBRA), in an attempt to reduce the number of variables required in representing RCPSPs. The EBRA and DTRA are, therefore, to simultaneously determine the recovery start time, the resource profile, and the duration of each activity in the recovery schedule, in order to minimize the makespan for a single disruption, as well as a series of disruptions, without having any advance activity interruption information. To test the proposed approach, a set of thirty-activity test instances from the Project Scheduling Library (PSPLIB) and one real-life scheduling problem are solved with randomly generated disruption events. Computational experiments were also conducted to analyse the effects of different factors that relate to the disruption recovery process. The experimental study reveals that the re-optimization process can reduce the revised makespan, as compared to simple right shifting of affected activities, and the level of improvement depends on the duration of the affected activities, their resource requirements, their relationships with forwarding activities, the disruption duration and the amount of disrupted resources.
... However, in practice, resource constrained project scheduling problem is more in demand. There exist many algorithms for solving this problem [6][7][8][9]. The most well-known are those algorithms that are oriented toward the speedy completion of all works. ...
The paper suggests one of the approaches to solving the problem of planning multi-stage service systems, the distinguishing feature of which is the availability of time constraints and a resource criterion. At the heart of the approach lie heuristics, which make it possible to obtain a suboptimal solution in an acceptable time. Based on these heuristics, the process of making decisions about assigning jobs to a given time interval, determining the optimal time interval for the return, and estimating the remaining service time are carried out.
... For this extension the variable z pqt can again be the indicator variable for the decision that activity q of project p is scheduled in time period t. A constraint ∑ q z pqt ≤ 1 has to be added, and the precedence constraints have to be expressed by a more flexible set of constraints (Artigues et al., 2008) as those given by Eq. (4). ...
This paper presents two stochastic optimization approaches for simultaneous project scheduling and personnel planning, extending a deterministic model previously developed by Heimerl and Kolisch. For the problem of assigning work packages to multi-skilled human resources with heterogeneous skills, the uncertainty on work package processing times is addressed. In the case where the required capacity exceeds the available capacity of internal resources, external human resources are used. The objective is to minimize the expected external costs. The first solution approach is a 'matheuristic' based on a decomposition of the problem into a project scheduling subproblem and a staffing subproblem. An iterated local search procedure determines the project schedules, while the staffing subproblem is solved by means of the Frank-Wolfe algorithm for convex optimization. The second solution approach is Sample Average Approximation where, based on sampled scenarios, the deterministic equivalent problem is solved through mixed integer programming. Experimental results for synthetically generated test instances inspired by a real-world situation are provided, and some managerial insights are derived.
... Popular in project scheduling, resource-constrained models seek to minimize the duration of a set of activities that are subject to precedence (or sequencing) constraints and limited resources (Artigues et al. 2008). Resource-constrained models are typically composed of activities, resources, constraints, objectives, and dynamic variations that can be described deterministically or probabilistically. ...
The goal of this paper is to facilitate a community of practice for disaster recovery modeling. This community should include hazard and disaster researchers without modeling experience and modelers with no experience in hazard and disaster research, not just the growing number of researchers that have experience with both. Disaster recovery modelers should develop mutual resources such as data sets, programming libraries, documentation, and terminology. For a community of practice to function, it needs to generate and appropriate a shared repertoire of ideas, approaches, and institutional memory. A potential shared repertoire of eight complimentary recovery modeling approaches to adopt, research, and advance is laid out. The largest need for lifeline recovery modeling—the most commonly researched recovery topic—is to research how to simulate lifeline infrastructure as sociotechnical systems in comprehensive, meaningful ways. For housing recovery modeling, a major gap is the inability to simulate rental dynamics, as well as the role of race and ethnicity. Lastly, a concerted and coordinated research effort is needed to create comprehensive platforms for simulating community recovery.
... Despite different surveys have been published, we have found only one [30] about the SPSP, yet it focuses primarily on the methods used to solve the problem. The majority of the surveys we found are mostly focused upon a related problem called Resource Constrained Project Scheduling (RCPS) [51]. RCPS, as we discuss in Section 2, is sufficiently different from SPSP to grant the need for a survey regarding the SPSP. ...
Creating a plan for a software project is a recurring activity in software development organizations that plays a critical role in the project success. When creating a plan for a project, these organizations must deal with the problem of allocating resources to tasks in the project. Because of its importance, there has been considerable research focused on finding ways to solve this problem, which is known as the Software Project Scheduling Problem (SPSP). Solving this problem usually focuses on creating a schedule for a project with minimal duration and cost. As part of our work, we have found only one survey about the SPSP, however it focuses primarily on the methods used to solve it, while the rest of the surveys focus primarily on other scheduling problems such as the Resource-Constrained Project Scheduling Problem. In this paper, we present a survey of the current research focused on solving the SPSP. For this survey, we have analyzed and classified a number of research studies considering a set of criteria that include: the model used to represent the problem, the optimization goals, the optimization techniques used to solve the problem, the methodology used to evaluate the different approaches, and the main results. From our analysis, we produce a set of general observations and provide suggestions that we believe can be useful for future research in this field.
... In a feasible schedule, if there aren't any possible local left shifts, it is a semi-active schedule and if for all activities neither local shift nor global left shift can be performed, it is an active schedule. A non-delay schedule is a feasible schedule that for all activities neither local shift nor global left shift can be performed even if the activities can be preempted at integer time points [2][8] [12] [22] [33] [50]. The optimal schedule is an active schedule but not necessary a non-delay schedule [45]. ...
In this paper, a hybrid method is proposed to generate feasible neighbors for the flexible job shop scheduling problem. Many of the optimization and artificial intelligence methods have been used to solve this important and NP-hard combinatorial problem which provide the basis for solving real-life problems. It is well-known that for such problems the hybrid methods obtain better results than the other approaches. For instance, the applied non-hybrid neural networks for the combinatorial problems, as the Hopfield neural network, usually converge early. Also, their results almost always
contain large gaps. These shortcomings prevent them to find good results. Another necessity for a quality search is to find suitable neighbors of the obtained solutions, however, it is possible to create infeasible neighbors during the optimization process. The aim of this study is to overcome these deficiencies. In the suggested approach, at first, an initial solution is generated and then using the left shift heuristics, its gaps are removed. Based on the critical path and critical block concepts, 6 neighbors are constructed for the obtained solution. After the generation of each neighbor, a neural network runs and controls the constraints of the problem. If the achieved neighbor is feasible it is saved. Else if it is infeasible, the neural network tries to transform it into a feasible solution. This is done by applying penalties to the start time of the operations on the violated constraints, which shifts them to the right or the left. During this process, if there are not
any violated constraints, the neural network reaches the stable condition so it stops and the obtained solution is saved as a feasible neighbor. Otherwise, after a certain number of the iterations, it stops without any feasible neighbors. Then these steps are repeated for the other created neighbors. This constraint-based process provides an effective and diverse search. Finally, the obtained neighbors, are improved using the left shift heuristics. Also to demonstrate the importance of the initial solutions, they are generated randomly and also using the Giffler and Thompson’s heuristic. The comparison
between the proposed approach and the methods from the literature shows that it constructs better neighbors. However, using the Giffler and Thompson heuristic to create the initial solution improves the results significantly.
... There exists a wide range of exact and heuristic approaches for the RCPSP and its extensions, for an overview, see Brucker et al. (1999), Neumann et al. (2003, and Artigues et al. (2008). Here, we specifically want to focus on exact approaches. ...
We consider a resource‐constrained project scheduling problem originating in particle therapy for cancer treatment, in which the scheduling has to be done in high resolution. Traditional mixed integer linear programming techniques such as time‐indexed formulations or discrete‐event formulations are known to have severe limitations in such cases, that is, growing too fast or having weak linear programming relaxations. We suggest a relaxation based on partitioning time into so‐called time‐buckets. This relaxation is iteratively solved and serves as basis for deriving feasible solutions using heuristics. Based on these primal and dual solutions and bounds, the time‐buckets are successively refined. Combining these parts, we obtain an algorithm that provides good approximate solutions soon and eventually converges to an optimal solution. Diverse strategies for performing the time‐bucket refinement are investigated. The approach shows excellent performance in comparison to the traditional formulations and a metaheuristic.
... These exact algorithms had success only with small and limited RCPSP problems. Large RCPSP problems require the use of heuristic algorithms (Artigues, Demassey, & Neron, 2013). Various meta-heuristic techniques were developed for these problems (Fahmy, Hassan, & Bassioni, 2014), (Shahsavar, Najafi, & Niaki, 2015), (Ponz-Tienda, Yepes, Pellicer, & Moreno-Flores, 2013). ...
This paper presents a novel method for solving the previously un-researched problem of multi-release work plan (MRWP). The research also suggests a technique for improving the run-time of metaheuristic search optimizations for this problem. The MRWP is required for many products and R&D projects that are characterized by a long-term planning horizon, spaced by intermediate releases. The intermediate releases enable the organization to keep its liquidity and survive and materialize the value for a given investment. The inclusion of features in a certain release impacts the value of the release, impacts the required workload, and impacts future development of other features. This problem is NP-hard. Thus, practical instances of this problem cannot be solved optimally in polynomial time. In this paper, we apply a clustering algorithm, based on novel similarity coefficients to reduce complexity and accelerate the convergence of a clonal selection search algorithm. Our goal is to provide a near-optimal yet simple method for quantitatively determining the feature content of all project releases. The four versions of the proposed algorithms are tested on a newly-developed set of instances and the results show the advantages of the combination of clustering mutations and random mutations over the pure cluster-based search. To examine the optimality-gap, a sample of benchmark MRWP solutions was generated. These solutions were obtained by a specially developed branch and bound algorithm developed for this study. The comparison of the optimal results to the metaheuristic results, proved that the metaheuristic yields optimal solutions in small problems, and their performance deteriorates slightly as the problem grows.
... The prime stepping stone of success in project planning is to estimate the cost involved in the software project development. Therefore, we can define software cost estimation as the mechanism that performs forecasting the original and cumulative cost required to complete the software project on a tentative time in presence of all resources and constraints [9][10]. It is assumed to be highly complexities for many industries as cost involvement differs for different project and there are numerous factors that affect it. ...
Software cost estimation is of the most challenging task in project management in order to ensuring smoother development operation and target achievement. There has been evolution of various standards tools and techniques for cost estimation practiced in the industry at present times. However, it was never investigated about the overall picturization of effectiveness of such techniques till date. This paper initiates its contribution by presenting taxonomies of conventional cost-estimation techniques and then investigates the research trends towards frequently addressed problems in it. The paper also reviews the existing techniques in well-structured manner in order to highlight the problems addressed, techniques used, advantages associated and limitation explored from literatures. Finally, we also brief the explored open research issues as an added contribution to this manuscript.
... Given a set of resources (i.e., the robotic arm and the workstations of the islands) of limited availability, and a set of activities (i.e., the mechatronic tasks) of known duration and resources requests, and linked by precedence and non overlapping relations the RCPSP consists of finding a schedule of minimal duration (i.e., minimum makespan) with the assignment of a start time to each activity such that the precedence relations and the resource availabilities are respected [5]. ...
The Production Scheduling is an important phase in a manufacturing system, where the aim is to improve the productivity of one or more factories. Finding an optimal solution to scheduling problems means to approach complex combinatorial optimization problems, and not all of them are solvable in a mathematical way, in fact a lot of them are part of the class of NP-hard combinatorial problems. In this paper a joint mixed approach based on a joint use of Evolutionary Algorithms and their quantum version is proposed. The context is ideally located inside two factories, partners and use cases of the white’R FP7 FOF MNP Project, with high manual activity for the production of optoelectronics products, switching with the use of the new robotic (re)configurable island, the white’R, to highly automated production. This is the first paper approaching the problem of the dynamic production scheduling for these types of production systems proposing a cooperative solving method. Results show this mixed method provide better answers and is faster in convergence than others.
This paper proposed a new algorithm to solve the Real-RCPSP problem (Real-RCPSP: Real-Resource Constrained Project Scheduling Problem). The algorithm is developed from the Differential Evolution (DE) algorithm hybrid with the adaptive method, which dynamically changes the crossover probability parameter during the evolution process. That parameter value is calculated from the neighborhood particles. The individuals used to make dynamic crossover probability are found by the star-topology. The new algorithm is called A-DEM. The effectiveness of the new algorithm is verified based on experiments with the iMOPSE dataset, which is the standard data set for this problem. Experimental results show that the proposed algorithm is more effective for this problem.KeywordsProject schedulingEvolutionary algorithmsDifferential algorithmsOptimization computation
Discrete-event simulation (DES) is not really used in construction industries that require more flexibility. However, use cases can be found where DES can support the construction industries. One use case is schedule optimization. This paper presents an agent-based DES method for optimizing schedules in the construction industry taking resource-dependent process-lengths into account. The approach is based on a theoretical level. Furthermore, there is a high potential when it is updated with actual equipment data. Therefore, we combine the project schedule optimization with a detailed model to update the equipment activities using a cyclic approach. This hybrid simulation approach is evaluated by taking a real use case of pile manufacture as an example. The results show the possibilities for the combination of different types of DES models in the context of the optimization of construction site performance.
In scheduling problems, the goal is to assign time slots to a set of activities. In these problems, there are typically precedence constraints between activities that dictate the order in which they can be carried out and resource constraints that limit the number that can simultaneously be executed. In this thesis, we develop mixed integer programming methodologies, based on decomposition methods, for two very different classes of scheduling problems. These are the Strategic Open Pit Mine Planning Problem (SOPMP) and the Bin Packing Problem with Time Lags.Given a discretized representation of an orebody known as a block model, the SOPMP that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. These problems are known to be very difficult due to the large size of real mine planning problems (eg, millions of blocks, dozens of years). They are also very important in the mining industry. Every major mining operation in the world must solve this problem, at the very least, on a yearly basis.In this thesis, we tackle the SOPMP in Chapters 2 and 3.In Chapter 2 we begin by studying a lagrangean algorithm developed by Dan Bienstock and Mark Zuckerberg (henceforth, the BZ algorithm) in 2009 for solving the LP relaxation of large instances of SOPMP. In this study we generalize the classes of problems that can be solved with the BZ algorithm, and show that it can be cast as a special type of column generation algorithm. We prove, for general classes of mixed integer programming problems, that the BZ relaxation provides a bound that lies between the LP relaxation and Dantzig-Wolfe bounds. We further develop computational speed-ups that improve the performance of the BZ algorithm in practice, and test these on a large collection of data-sets. In Chapter 3 we deal with the problem of computing integer-feasible solution to SOPMP. Using the BZ algorithm developed in Chapter 2, we develop heuristics for this. In addition, we develop pre-procesing algorithms that reduce problem size, and embed the BZ algorithm in a branch-and-cut framework that makes use of two new classes of cutting planes. When comparing the value of the heuristics to the LP relaxation bound, the average gap computed is close to 10\%. However, when applying the pre-processing techniques and cutting planes, this is reduced to 1.5\% at the root node. Four hours of branching further reduces this to 0.6\%.In Chapter 4, the BPPTL is presented. This is a generalization of the Bin Packing Problem in which bins must be assigned to time slots, while satisfying precedence constraints with lags. Two integer programming formulations are proposed: a compact formulation that models the problem exactly, and an extended formulation that models a relaxation. For two special cases of the problem, the case with unlimited bins per period and the case with one bin per period and non-negative time lags, we strengthen the extended formulation with a special family of constraints. We propose a branch-cut-and-price (BCP) algorithm to solve this formulation, with separation of integer and fractional solutions, and a strong diving heuristic. Computational experiments confirm that the BCP algorithm outperforms solving the compact formulation with a commercial solver. Using this approach we were able to optimally solve 70\% of a class of previously open instances of this problem.
Disasters impact the delivery of infrastructure services and disrupt the normal functioning of communities. A primary goal of recovery is to restore patterns of activity to pre-disaster levels in the shortest time possible with minimum performance loss. Resourcing strategies (amounts and allocations) in the post-disaster period should be efficient to maximize benefits with minimum resources and effectively ensure the desired results. Limited resources force recovery planners to choose among multiple competing priorities across infrastructures and populations (e.g., tourism, transportation, workforce, businesses, public health, residents). Optimal resource sequencing, amounts, and timing to improve recovery depend on the capacities of these interdependent community sectors, which interact through multiple delayed feedback loops. Understanding how the structure of community infrastructure systems impacts recovery can improve recovery resource planning by identifying dominant causal structures and high leverage points in the community recovery process. This research combines system dynamics and design structure matrix (DSM) modeling to build, test, and apply a feedback theory of community disaster recovery. The model is used to investigate optimal resource loading and sequencing strategies using a simplified sector model. Initial results, implications, and opportunities for future research are discussed.
This paper deals with a real manufacturing scheduling problem that is particularly encountered in the tannery industries. This problem often integrates employee timetabling and production scheduling. The employee timetabling problem is addressed in the context of skill requirements and under availability and legislative constraints. The production scheduling is considered as a re-entrant hybrid job-shop problem with time lags and sequence dependent setup times, under machine availability constraints. The objective is to minimize the labor cost, while respecting a maximum makespan and a maximum tardiness constraints. Two different models and exact resolution methods are proposed, using Mixed Integer Linear Programming (MILP) and Constraint Programming (CP). Numerical experimentations are conducted to compare and evaluate their performances, based on randomly generated instances. The results show that the CP model is slower than the MILP model in terms of finding optimal solutions for large instances, but is more efficient in generating feasible solutions. Thus, providing a feasible initial solution to the MILP model using the CP model is a promising hybrid approach to reduce the computational time.
Scheduling tasks with variable durations across multiple agents is an NP-hard problem for even two agents. Typically, the run-time of any exact algorithm is dominated by the number of tasks because of an exponential dependence. We shift this exponential dependency from the number of tasks to a new parameter, which we call window length. This novel parameterization enables to reduce the problem of finding an optimal schedule to one of searching for winning strategies in a two-player reachability game on graphs of size polynomial in the number of tasks. As such, the complexity of finding an optimal schedule is polynomial in the number of tasks but exponential in the window length. We demonstrate that, in practice our algorithm runs faster than the worst-case complexity. The approach we present is applicable for most common optimization criteria, such as minimization of makespan and total load. We demonstrate the practical value of this technique by finding optimal schedules for astronauts aboard the International Space Station. Finally, experiments on randomly generated instances show that, on average, this technique is at least two orders of magnitude faster than an integer program formulation.
The Resource Constrained Project Scheduling Problem (RCPSP) is a combinatorial optimization problem whichis non-deterministic polynomial-time (NP)-hard in nature. Due to the diversified applications of RCPSPs, theyhave been commonly used as scheduling procedures in real-world problems. Since, in practice, project data areprone to changes or disruptions, this paper introduces a mathematical model for a reactive scheduling approach,called the Event Based Reactive Approach (EBRA). This proposed EBRA approach is employed to examine itsrecovery performance under both a single disruption and a series of independent resource disruptions. Severalsimulated disruption data are hypothesized to represent real-world disruption scenarios and, without loss ofgenerality, the proposed reactive approach is proved to be efficient in reducing the number of variables andcomputational complexity and also to be resilient in realistic changes, such as duration inflation and dynamicresource usages. Along with employing an exact method by LINGO software, this paper also proposes anenhanced iterated greedy (EnIG) approach to meta-heuristically solve larger and computationally expensivebenchmark instances taken from the Project Scheduling Library (PSPLIB).
The concept of anchored solutions is proposed as a new robust optimization approach to the Resource-Constrained Project Scheduling Problem (RCPSP) under processing times uncertainty. The Anchor-Robust RCPSP is defined, to compute a baseline schedule with bounded makespan, sequencing decisions, and a max-size subset of jobs with guaranteed starting times, called anchored set. It is shown that the Adjustable-Robust RCPSP from the literature fits within the framework of anchored solutions. The Anchor-Robust RCPSP and the Adjustable-Robust RCPSP can benefit from each other to find both a worst-case makespan and a baseline schedule with an anchored set. A dedicated graph model for anchored solutions is proposed for budgeted uncertainty. Compact MIP reformulations are derived for both the Adjustable-Robust RCPSP and the Anchor-Robust RCPSP. Dedicated heuristics are designed based on the graph model. For both problems, the efficiency of the proposed MIP reformulations and heuristic approaches is assessed through numerical experiments on benchmark instances.
This research develops a method for optimizing the construction phases for an automated demand responsive feeder transit (ADRFT) service projects in suburban and rural areas with the objective of minimizing implementation makespan costs. In this research, the small-sized automated demand responsive door-to-door feeder bus system, which fits well in the suburban and rural areas, is applied to perform activities of the project. A metaheuristic method of the simulated annealing (SA) optimization method has been implemented to solve the proposed Resource constrained project scheduling problem (RCPSP) that considers the precedence and relations among project tasks for the automated demand responsive feeder transit. As a result of this study, the proposed algorithm could find the near-optimal solution to the problem. A sensitivity analysis has been conducted on resources to assess the possible influence of each resource on the optimal solution and obtain more accurate tasks effects on the optimized phases. The results of this study could be utilized by transportation authorities, transport investment agencies, and collaborators in innovating and emerging transportation systems.
The scheduling problem is a widespread one, and it is still not automatized mostly because of the so-called combinatorial explosion. The paper describes two different approaches to solving a hierarchical scheduling problem based on solution representation. The first one proposes to find an optimal order of projects and then to solve the resource-constrained project scheduling problem for each of them. The second one assumes that we can find a priority of all activities for all projects and use it in the schedule building process if there is a conflict in the choosing of the next activity. The paper considers some nature-inspired algorithms such as the intelligent water drops algorithm, a genetic algorithm and ant colony optimization as well as a self-configuring version of the last two. The algorithm performance and different solution representation approaches are compared using the results of solving the test problems.
This paper aims at providing a fast near‐optimum solution to the multi‐mode resource‐constrained project scheduling problems (MRCPSPs), for projects with activities that have known deterministic renewable and nonrenewable resource requirements. The MRCPSP is known to be nondeterministic polynomial‐time hard and has been solved using various exact, heuristic, and meta‐heuristic procedures. In this paper, a modified variable neighborhood search heuristic algorithm is used as an advanced optimization technique that suits scheduling problems. For the experimental study, we have considered a standard set of 3929 multi‐mode benchmark instances from the project scheduling library with a range of projects comprising 10–30 activities. Moreover, for a better comparison, this research also considers a standard set of 4320 newly developed multi‐mode instances from MMLIB50, MMLIB100, and MMLIB+ datasets. With the limit of 50,000 schedules on these datasets, our proposed algorithm provides better makespan for 106, 34, and 1601 instances, respectively, which justifies the efficiency of the proposed algorithm, particularly for projects with a larger number of activities. The results reported in this paper can be used as a benchmark for other researchers to compare and improve.
Mit Hilfe von modernen Feinplanungssystemen kann die Produktions-, Flotten- oder Personaleinsatzplanung nahezu vollständig automatisiert werden. Für den Disponenten wird dadurch der Planungsaufwand erheblich reduziert. Gleichzeitig bieten diese Systeme dem Disponenten jedoch häufig nur unzureichende Interaktionsmöglichkeiten, um sein eigenes Expertenwissen in die Planerstellung einfließen zu lassen. Das Finden und Umsetzen von passenden Planungsentscheidungen ist häufig ein aufwändiger und fehleranfälliger Prozess, der vom Computer nicht unterstützt wird. Dieser Mangel kann die Brauchbarkeit der Pläne und damit den Nutzen des Planungssystems erheblich beeinträchtigen. In dieser Arbeit wird ein Konzept für die Gestaltung der Mensch-Computer-Interaktion in Feinplanungssystemen entwickelt, mit dem eine effektive Einbeziehung des Disponenten abgesichert werden kann. Im Gegensatz zu herkömmlichen Interaktionskonzepten baut es auf wissenschaftlichen Erkenntnissen über menschliche Entscheidungs- und Entwurfsprozesse auf. Dadurch ist es möglich, eine Computerunterstützung sowohl für die Ermittlung als auch für die Umsetzung von Planungsentscheidungen durch den Disponenten zu definieren. Zudem ist das Konzept auf beliebige Feinplanungsprobleme anwendbar. Es setzt sich aus 9 Interaktionsrichtlinien zusammen, deren Effektivität in einem Anwendertest nachgewiesen wird.
This paper focuses on the robust resource-constrained project scheduling problem (RCPSP) with discrete time/resource trade-offs, in which activity duration and resource are uncertain variables. Combining flexible RCPSP (FRCPSP) with robustness, a discrete mathematical model is developed and resource leveling problem objective is considered to describe the flexible resource allocation comprehensively. In addition, surrogate measures are also introduced, providing an accurate estimate of the schedule robustness. Priority-based heuristic methods and resource assignment heuristic are employed to generate and modify the priorities of selected activities, meanwhile obtain the different executing modes. Furthermore, each surrogate measure is compared according to the scheduling performance through the computational experiments. The practicability of proposed multi-objective mathematical model and the efficiency of algorithm are verified by a numerical example. Finally, the performance analysis is also presented by the robustness assessment, and the results prove that the proposed approach is more effective than the traditional one.
In this paper, we study the problem of coordinating supplier selection and project scheduling, motivated by a real-life operational challenge encountered in the construction industry. In particular, we consider a project network consisting of multiple concurrent projects, with the objective of minimising the total tardiness of all projects. These projects are independent in operation but are subject to shared suppliers and the final quality inspection by the same committee, which then leads to the need for project review sequencing. The earliest starting time of each activity in a project depends on the availability of required resources (both renewable and non-renewable), as well as the activity precedence constraints. We formulate this problem as a mixed integer linear programming model, and propose a mathematical programming-based heuristic to solve the model. The heuristic decomposes the model into subproblems, and solves the subproblems through an iterative process. Each subproblem has a much smaller size and can be solved quickly and independently. The information obtained in solving subproblems is used to guide the search process. Numerical examples show the computational effectiveness of the proposed heuristic, and the benefits of coordination.
In this work, we introduce a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC). In the FRRC, besides the constraints of the classical Flexible Job-shop Scheduling Problem (FJSP), operations may require resources to be processed. The resources are available in batches and a recovery time is required between each batch. This problem is inspired by a real situation faced by a brewing company where different yeasts are available in a limited quantity and are recovered only once they have been completely used. The objective is to schedule the operations such that the makespan is minimised. A mathematical model and a metaheuristic based on a General Variable Neighborhood Search is proposed for the solution of the FRRC. Computational results over a large set of instances, adapted from the FJSP literature, are presented.
Remote Piloted Aircraft Systems (RPAS) are operating in highly critical contexts and carry out a wide collection of complex mission tasks through the use of sensors. In this paper, we present a new agent-based architecture that handles sensors of these platforms. Today, the requirements of the platform in terms of autonomy, modularity, robustness and reactivity as well as the industrial constraints call for the design of a new multifunction system architecture. Such a design may rely on multi-agent paradigm since it is modular by design and the agents naturally bring autonomy and pro-activity to the system. This paper presents new and original contributions: (1) an original agentification of the system in the form of a multi-agent architecture that helps to capture the dynamic of the environment; (2) firsts results of the architecture’s simulation for autonomy and scheduling evaluation.
Project scheduling problems (PSP) could be defined as allocating scarce resources over time to perform a given set of activities.
ResearchGate has not been able to resolve any references for this publication.