Resource-constrained Project Research Articles

A prediction model for ranking branch-and-bound procedures for the resource-constrained project scheduling problem

The branch-and-bound (B&B) procedure is one of the most widely used techniques to get optimal solutions for the resource-constrained project scheduling problem (RCPSP). Recently, various components from the literature have been assembled by Coelho and Vanhoucke (2018) into a unified search algorithm using the best performing lower bounds, branching schemes, search strategies, and dominance rules. However, due to the high computational time, this procedure is only suitable to solve small to medium-sized problems. Moreover, despite its relatively good performance, not much is known about which components perform best, and how these components should be combined into a procedure to maximize chances to solve the problem. This paper introduces a structured prediction approach to rank various combinations of components (configurations) of the integrated B&B procedure. More specifically, two regression methods are used to map project indicators to a full ranking of configurations. The objective is to provide preference information about the quality of different configurations to obtain the best possible solution. Using such models, the ranking of all configurations can be predicted, and these predictions are then used to get the best possible solution for a new project with known network and resource values. A computational experiment is conducted to verify the performance of this novel approach. Furthermore, the models are tested for 48 different configurations, and their robustness is investigated on datasets with different numbers of activities. The results show that the two models are very competitive, and both can generate significantly better results than any single-best configuration.

A faster exact method for solving the robust multi-mode resource-constrained project scheduling problem

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions that minimise the worst-case project makespan, whilst assuming that activity durations lie in a budgeted uncertainty set. Computational experiments show that this easy-to-implement formulation is many times faster than the current state-of-the-art solution approach for this problem, whilst solving over 40% more instances to optimality over the same benchmarking set.

Dynamic Optimization of the Multi-Skilled Resource-Constrained Project Scheduling Problem with Uncertainty in Resource Availability

Multi-skilled resources have brought more flexibility to resource scheduling and have been a key factor in the research of resource-constrained project scheduling problems. However, existing studies are mainly limited to deterministic problems and neglect some uncertainties such as resource breakdowns, while resource availability may change over time due to unexpected risks such as the COVID-19 pandemic. Therefore, this paper focuses on the multi-skilled project scheduling problem with uncertainty in resource availability. Different from previous assumptions, multi-skilled resources are allowed a switch in their skills, which we call dynamic skill assignment. For this complex problem, a nested dynamic scheduling algorithm called GA-PR is proposed, which includes three new priority rules to improve the solving efficiency. Moreover, the algorithm’s effectiveness is verified by an example, and the modified Project Scheduling Problem Library (PSPLIB) is used for numerical experimental analysis. Numerical experiments show that when the uncertainty in resource availability is considered, the more skills the resource has and the more resources are supplied, the better the dynamic scheduling method performs; on the other hand, the higher the probability of resource unavailability and the more skills are required, the worse the dynamic scheduling method performs.The results are helpful for improved decision making.

Optimization Strategies for Resource-Constrained Project Scheduling Problems in Underground Mining

Effective computational methods are important for practitioners and researchers working in strategic underground mine planning. We consider a class of problems that can be modeled as a resource-constrained project scheduling problem with optional activities; the objective maximizes net present value. We provide a computational review of math programming and constraint programming techniques for this problem, describe and implement novel problem-size reductions, and introduce an aggregated linear program that guides a list scheduling algorithm running over unaggregated instances. Practical, large-scale planning problems cannot be processed using standard optimization approaches. However, our strategies allow us to solve them to within about 5% of optimality in several hours, even for the most difficult instances. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Funding: This work was supported by Alford Mining Systems, the Centro de Modelamiento Matemático [Grants ACE210010 and FB21005], ANID-Chile [BASAL funds for center of excellence and FONDEF Grant ID19-10164], and the supercomputing infrastructure of the NLHPC [Grant ECM-02].

Improved genetic algorithm based on time windows decomposition for solving resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) is one of the project scheduling problems which are widely used in construction and many industrial disciplines. The challenge of the problem is to design some appropriate search mechanism for finding solutions in feasible space. An improved genetic algorithm based on time window decomposition is proposed in this paper. Three derivation methods are applied to increase population diversity. The sampling count allocation strategy and the use of destructive lower bounds improve the search efficiency. The computational experiments on PSPLIB show that the proposed approach is more effective than that only using the decomposition mechanism and is competitive in solving two real-life cases. This research illustrates that continuously changing the search subspaces has potential advantages, which may be useful for studying RCPSP using other evolutionary algorithms in future. Some other better results may be obtained by using machine learning methods to flexibly determine the sampling times for each individual.

Investigation of benchmark dataset for many-objective Multi-Skill Resource Constrained Project Scheduling Problem

The paper presents a redefinition of Multi-Skill Resource-Constrained Project Scheduling Problem (MS-RCPSP) as a many-objective optimization problem. In effect, it brings the problem closer to real-world applications. Five objectives have been defined: cost, duration, average cash flow, average usage of resources and skill overuse. To summarize MS-RCPSP usage, the paper presents a short survey (years 2015–2021) of multi- and many-objective MS–RCPSP solving methods. Moreover, results of investigation of many-objective MS–RCPSP for classic (greedy algorithm, Unified Non-dominated Sorting Genetic Algorithm III (U-NSGA-III)), single objective (decomposition-based) Differential Evolution And Greedy (DEGR) and state-of-the-art Non-dominated Tournament Genetic Algorithm (NTGA2) have been presented. Additionally, results are analysed using multi-objective quality measures (such as Pareto Front Size (PFS), Purity or Inverted Generational Distance (IGD)) to verify the efficiency of the used methods. The paper answers 4 research questions that investigate 5-objective MS-RCPSP domains, approximations of Pareto Fronts, relations between objectives and efficiency of NTGA2 compared to other methods. Finally, the paper is concluded with a summary and propositions for future work.

Credibility-based chance-constrained multimode resource-constrained project scheduling problem under fuzzy uncertainty

This paper investigates a multimode resource-constrained project scheduling problem under hybrid uncertain environment. With the activity durations are fuzzy variables, the resource requests change with the durations. The goal is to minimize the project duration and the cost associated with the required resources. Considering the stochastic duration and resource demand, a chance constrained programming model based on credibility is established. In order to solve the model, the chance constraints and fuzziness are treated by introducing the credibility distribution function and its inverse function. And, a hybrid algorithm combining particle swarm optimization (PSO) and genetic algorithm (GA) is proposed. It has shown fine performance in solving problems with 30, 60, and 120 activities. We also analyze the sensitivity of confidence, fuzziness, number of activities, number of modes, and resource unit cost. Meanwhile, fuzzy value-at-risk is used as a risk measure, and a model based on it is constructed. These numerical results show that the developed algorithm can obtain the near optimal solution of large-scale projects in a reasonable calculation time.

Reinforcement Learning of Dispatching Strategies for Large-Scale Industrial Scheduling

Scheduling is an important problem for many applications, including manufacturing, transportation, or cloud computing. Unfortunately, most of the scheduling problems occurring in practice are intractable and, therefore, solving large industrial instances is very time-consuming. Heuristic-based dispatching methods can compute schedules in an acceptable time, but construction of a heuristic allowing for a satisfactory solution quality is a tedious process. This work introduces a method to automatically learn dispatching strategies from only a few training instances using reinforcement learning. Evaluation results obtained on real-world, large-scale instances of a resource-constrained project scheduling problem taken from the literature show that the learned dispatching heuristic generalizes to unseen instances and produces high-quality schedules within seconds. As a result, our approach significantly outperforms state-of-the-art combinatorial optimization techniques in terms of solution quality and computation time.

A constructive branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

This paper deals with the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints with the objective to minimize the project duration. The consideration of partially renewable resources allows to integrate the decision about the availability of a resource for a specific time period into the scheduling process. Together with general temporal constraints, which permit to establish minimum and maximum time lags between activities, even more aspects of real-life projects can be taken into account. We present a branch-and-bound algorithm for the stated problem that is based on a serial schedule-generation scheme. For the first time it is shown how a dominance criterion can be applied on the associated generation scheme to reduce the start times in each scheduling step. To improve the performance of the solution procedure, we integrate consistency tests and lower bounds from the literature and devise new pruning techniques. In a comprehensive experimental performance analysis we compare our exact solution procedure with all available branch-and-bound algorithms for partially renewable resources. Additionally, we investigate a directly derived priority rule-based approximation method from our new enumeration scheme. The results of the computational study demonstrate the efficiency of our branch-and-bound algorithm and reveal that the derived approximation method is only suited to solve small- and medium-sized instances.

Optimization of Apron Support Vehicle Operation Scheduling Based on Multi-Layer Coding Genetic Algorithm

Operation scheduling of apron support vehicles is an important factor affecting aircraft support capability. However, at present, the traditional support methods have the problems of low utilization rate of support vehicles and low support efficiency in multi-aircraft support. In this paper, a vehicle scheduling model is constructed, and a multi-layer coding genetic algorithm is designed to solve the vehicle scheduling problem. In this paper, the apron support vehicle operation scheduling problem is regarded as a Resource-Constrained Project Scheduling Problem (RCPSP), and the support vehicles and their support procedures are adjusted via the sequential sorting method to achieve the optimization goals of shortening the support time and improving the vehicle utilization rate. Based on a specific example, the job scheduling before and after the optimization of the number of support vehicles is simulated using a multi-layer coding genetic algorithm. The results show that compared with the traditional support scheme, the vehicle scheduling time optimized via the multi-layer coding genetic algorithm is obviously shortened; after the number of vehicles is optimized, the support time is further shortened and the average utilization rate of vehicles is improved. Finally, the optimized apron support vehicle number configuration and the best scheduling scheme are given.

Using priority rules for resource-constrained project scheduling problem in static environment

The resource-constrained project scheduling problem (RCPSP) is one of the scheduling problems that belong to the class of NP-hard problems. Therefore, heuristic approaches are usually used to solve it. One of the most commonly used heuristic approaches are priority rules (PRs). PRs are easy to use, fast and able to respond to system changes, which makes them applicable in a dynamic environment. The disadvantage of PRs is that when applied in a static environment, they do not achieve results of the same quality as heuristic approaches designed for a static environment. Moreover, a new PR must be evolved separately for each optimization criterion, which is a challenging process. Therefore, recently significant effort has been put into the automatic development of PRs. Although PRs are mainly used in a dynamic environment, they are also used in a static environment in situations where speed and simplicity are more important than the quality of the obtained solution. Since PRs evolved for a dynamic environment do not use all the information available in a static environment, this paper analyzes two adaptations for evolving PRs in a static environment for the RCPSP - iterative priority rules and rollout approach. This paper shows that these approaches achieve better results than the PRs evolved and used without these adaptations. The results of the approaches presented in the paper were also compared with the results obtained with the genetic algorithm as a representative of the heuristic approaches used mainly in the static environment.

A comparative study of modeling and solution approaches for the multi-mode resource-constrained discrete time–cost trade-off problem: Case study of an ERP implementation project

Most knowledge-intensive industries, especially companies developing software engineering projects such as Enterprise Resource Planning (ERP) implementation projects, generally necessitate finding the optimal trade-off between the project duration and total usage cost of the renewable resource costs (e.g., human resource expertise costs). Therefore, the MRC-DTCTP, which integrates classical multi-mode resource-constrained project scheduling (MRCPSP) and discrete time–cost trade-off problems (DTCTP), can be seen as a more applicable problem since it better reflects the objectives and requirements of today’s real-life software project applications. The MRC-DTCTP is a much more complex variant of the MRCPSP since it aims to minimize total direct/indirect costs of the resources simultaneously under a pre-specified project deadline. Based on this motivation, a new explicit integer-linear programming (ILP) model of the MRC-DTCTP was first developed based on the implicit non-linear programming model of Wuliang and Chengen (2009). Due to its NP-hard nature, we also proposed a constraint programming (CP) model that includes several search strategies to solve large-sized problem instances within reasonable computation time. In addition, a genetic algorithm (GA) approach in combination with a Modified Serial Schedule Generation scheme (SSGS) is implemented to make further comparisons on several benchmark instances, which are generated based on the existing MRCPSP data sets taken from the project scheduling problem library (PSPLIB) by considering additional problem characteristics. A comprehensive experimental study has shown that the proposed CP model and GA approach can provide superior results in shorter run times for large-sized benchmark instances. Finally, an international Enterprise Resource Planning (ERP) Software Company’s real-life application is presented. The ERP projects generally necessitate finding the optimal trade-off between project makespan and human resource costs, making the MRC-DTCTP much more difficult than classical MRCPSPs & DTCTPs. For further analysis, time–cost trade-off curves under different human resource availabilities and project deadlines are drawn to provide managerial insights to ERP project managers.

A hybrid projection method for resource-constrained project scheduling problem under uncertainty

A hybrid projection method for resource-constrained project scheduling problem under uncertainty

Multi-objective stochastic project scheduling with alternative execution methods: An improved quantum-behaved particle swarm optimization approach

This paper addresses the multi-objective resource-constrained project scheduling problems with stochastic activity durations and alternative execution methods. Three objectives are considered: minimizing expected makespan, expected cost and robustness. Chance constrained programming is applied for formulating this stochastic problem. A hybrid approach that integrates sample average approximation (SAA) and an improved multi-objective chaotic quantum-behaved particle swarm optimization (MOCQPSO) algorithm is proposed. To improve the diversity of solutions and enhance the global search ability, a two-stage learning strategy that balances the exploration and the exploitation is proposed for MOCQPSO. In addition, chaotic operators including chaotic initialization, crossover and mutation are also introduced. Six benchmark functions and an instance generator based on the RCPSP dataset of PSPLIB are designed to validate the performance of the proposed algorithm. The experimental results demonstrate that our proposed method outperforms the original algorithms in solution diversity and quality.

MULTI-MODE RESOURCE CONSTRAINED MULTI PROJECT SCHEDULING PROBLEM OPTIMIZATION WITH SYMBIOTIC ORGANISMS SEARCH

Multi-mode resource-constrained multi project scheduling problem (MRCMPSP) is the extension of standard resource constrained project scheduling problem which considers multiple activity execution modes and multiple projects, subject to precedence and resource constraints. Multiple execution modes allow the activities to have different duration and resource requirement. Furthermore, companies and project managers normally also handle many projects. This study proposed metaheuristic method Symbiotic Organisms Search (SOS) along with random-key (RK) representations, parallel schedule generation scheme (P-SGS), and forward backward scheduling, to find the feasible schedule and minimal project duration of the project portfolio. The evaluation results from standard benchmark instances shows that SOS can get the best solution in most of the tested instances and also achieve better solution in some of them. The validation results from real project case MRCMPSP show that SOS has better performance than other tested metaheuristic methods, namely GA and PSO. Thus, validate the performance of SOS.

A Binary Integer Linear Programming Approach for Risk Minimization of a Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off

The multi-mode resource-constrained project scheduling problem (MRCPSP) allows project managers to assign schedules and limited resources to project activities while minimizing total duration. This time objective has been extended to include the trade-offs of cost and quality called the discrete time-cost-quality trade-off problem (DTCQTP) to provide project managers an overview of indicators affecting project performance. However, the impacts of the COVID-19 pandemic have led project managers and consultants to assess their projects’ risks regarding scheduling and resource assignment decisions. Hence, this paper aims to extend the MRCPSP and the DTCQTP to include risk at the resource level to highlight the importance of hiring the proper resources in project scheduling. A binary integer linear programming model named the multi-mode resource-constrained project scheduling with discrete time-cost-quality-risk trade-off (MRCPSP-DTCQRT) was developed with risk minimization as the objective function. A case study from prior literature was used to illustrate the model using the open-sourced Python-MIP package, which uses the branch-and-cut methodology for generating optimal solutions. A set of schedules that either prioritize time, cost, quality, risk, or a balance among the four was generated for the use of the project manager to make decisions based on the current situation. Future research may extend the model further to include resource skills, test large-scale case studies, and use other methodologies such as metaheuristics and machine learning to arrive at optimal solutions within reasonable computing time.

Mathematical formulations for project scheduling problems with categorical and hierarchical skills

In this paper, we present six extensions to the multi-skilled resource-constrained project scheduling problem (MSRCPSP) by introducing hierarchical levels of skills. These hierarchical skills can impact the MSRCPSP in multiple different ways. This paper studies efficiency differences, cost differences, quality differences and more. For each of these problems we propose and analyse seven continuous and time-indexed (mixed-)integer linear programming formulations. A modular artificial dataset is generated that assembles instances of the presented problems as well as combinations of these problems. In the computational experiments, we solve these instances using the proposed mathematical formulations with the CPLEX solver. Finally, we compare the results of the different formulations for the resource-constrained project scheduling problems with hierarchical levels of skills in order to explain their inherent similarities and differences.

Bi-objective resource-constrained project scheduling problem with time-dependent resource costs

This work provides new insights on bi-criteria resource-constrained project scheduling problems. We define a realistic problem where the objectives to combine are the makespan and the total cost for resource usage. Time-dependent costs are assumed for the resources, i.e., they depend on when a resource is used. An optimization model is presented and it is followed by the development of an algorithm aiming at finding the set of Pareto solutions. The intractability of the optimization models underlying the problem also justifies the development of a metaheuristic for approximating the same front. We design a bi-objective evolutionary algorithm that includes problem-specific knowledge and is based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). The results of extensive computational experiments performed using instances built from those available in the literature are reported. The results demonstrate the efficiency of the metaheuristic proposed.

A Robust Bi-objective Optimization Model for Resource Levelling Project Scheduling Problem with Discounted Cash Flows

Due to limited financial resources and high costs of infrastructure projects, project stakeholders seek to gain maximum profits with optimal resource utilization as well as cost and time minimization. Therefore, this study presents a multi-mode resource-constrained project scheduling model considering the uncertain parameters of cost and time together with the goals of maximizing the net present value and minimizing resource usage fluctuation. Also, the assumptions related to the real-world projects regarding multi-mode activities, limitation of renewable resources, and the deadline of project are incorporated into the proposed model. Moreover, a robust scheduling method is presented to better deal with the inherent uncertainties of projects regarding cost and time. The model is solved with the exact method named lexicographic goal programming (LGP). Due to the NP-hardness of the problem, two metaheuristic algorithms named Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are applied to solve various medium and large size problems. The obtained results indicate the high efficiency of the two metaheuristic algorithms in solving the problem and the better performance of the MOPSO algorithm compared with NSGA-II in terms of five indices. Furthermore, the model is implemented in an offshore equipment installation phase of a wellhead platform project. Finally, the sensitivity analysis of the proposed robust model is performed considering different conservation levels, and the results are evaluated by Monte Carlo simulation with three normal, uniform and triangular distributions. The findings demonstrate that the robustness of the model against the variations of uncertain parameters.

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

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