Resource Constrained Project Scheduling Research Articles

Multi-objective planning for time-cost trade-offs in multi-project parallel environment

PurposeProject managers bear the responsibility of selecting and developing resource scheduling methods that align with project requirements and organizational circumstances. This study focuses on resource-constrained project scheduling in multi-project environments. The research simplifies the problem by adopting a single-project perspective using gain coefficients.Design/methodology/approachIt employs uncertainty theory and multi-objective programming to construct a model. The optimal solution is identified using Matlab, while LINGO determines satisfactory alternatives. By combining these methods and considering actual construction project situations, a compromise solution closely approximating the optimal one is derived.FindingsThe study provides fresh insights into modeling and resolving resource-constrained project scheduling issues, supported by real-world examples that effectively illustrate its practical significance.Originality/valueThe research highlights three main contributions: effective resource utilization, project prioritization and conflict management, and addressing uncertainty. It offers decision support for project managers to balance resource allocation, resolve conflicts, and adapt to changing project demands.

A chance-constrained optimization approach integrating project scheduling and material ordering to manage the uncertain material supply

To deal with the impact of uncertain material supply on the implementation of projects, we investigate a problem of concurrently finding a robust baseline schedule and a material ordering plan under different levels of uncertainty. Assuming the material warehouses are restricted, a chance-constrained model of the integrated resource-constrained project scheduling and material ordering problem with a confidence level (1−θ) is thus formulated. To tackle the difficult joint chance constraints, we firstly transform the chance-constrained model into a scenario-based integer programming model by the sample average approximation approach. Based on dominance relationship among scenarios, we then derive an exact branch-and-bound algorithm and a sampling-based genetic algorithm (SGA) to solve the model. For the branch-and-bound algorithm, a tailor-made branching scheme and four pruning rules are developed to accelerate the search process. For the SGA, two sampling methods and a local search procedure are presented to boost solution quality. Furthermore, extensive numerical experiments are carried out to test the performance of the proposed algorithms. Specifically, 4608 instances with four different confidence levels and six different sample sizes are generated. Then the Taguchi method is employed to calibrate the parameters of the SGA. Besides, the numerical results demonstrate that the proposed branch-and-bound algorithm can solve more instances with shorter CPU times than the CPLEX solver, and the solution quality of the proposed SGA is far better than that of two existing meta-heuristics and two variants of SGA. Finally, a sensitivity analysis for the key parameters of the model is conducted. By considering the uncertain material supply, limited warehouse capacity and various confidence levels, our research contributes to the effective decision on project scheduling and material ordering in real-world contexts.

Balancing Pareto Front exploration of Non-dominated Tournament Genetic Algorithm (B-NTGA) in solving multi-objective NP-hard problems with constraints

The paper presents a new balanced selection operator applied to the proposed Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA) that actively uses archive to solve multi- and many-objective NP-hard combinatorial optimization problems with constraints. The primary motivation is to make B-NTGA more efficient in exploring Pareto Front Approximation (PFa), focusing on “gaps” and reducing some PFa regions' sampling too frequently. Such a balancing mechanism allows B-NTGA to be more adaptive and focus on less explored PFa regions. The proposed B-NTGA is investigated on two benchmark multi- and many-objective optimization real-world problems, like Thief Traveling Problem and Multi-Skill Resource-Constrained Project Scheduling Problem. The results of experiments show that B-NTGA has a higher efficiency and better performance than state-of-the-art methods.

A genetic algorithm for the Resource-Constrained Project Scheduling Problem with Alternative Subgraphs using a boolean satisfiability solver

This study evaluates a new solution approach for the Resource-Constrained Project Scheduling with Alternative Subgraphs (RCPSP-AS) in case that complex relations (i.e. nested and linked alternatives) are considered. In the RCPSP-AS, the project activity structure is extended with alternative activity sequences. This implies that only a subset of all activities should be scheduled, which corresponds with a set of activities in the project network that model an alternative execution mode for a work package. Since only the selected activities should be scheduled, the RCPSP-AS comes down to a traditional RCPSP problem when the selection subproblem is solved. It is known that the RCPSP and, hence, its extension to the RCPSP-AS is NP-hard. Since similar scheduling and selection subproblems have already been successfully solved by satisfiability (SAT) solvers in the existing literature, we aim to test the performance of a GA-SAT approach that is derived from the literature and adjusted to be able to deal with the problem-specific constraints of the RCPSP-AS. Computational results on small- and large-scale instances (both artificial and empirical) show that the algorithm can compete with existing metaheuristic algorithms from the literature. Also, the performance is compared with an exact mathematical solver and learning behaviour is observed and analysed. This research again validates the broad applicability of SAT solvers as well as the need to search for better and more suited algorithms for the RCPSP-AS and its extensions.

The Multi-Skilled Resource-Constrained Project Scheduling Problem: A Systematic Review and an Exploration of Future Landscapes

Abstract The Multi-skilled Resource Constrained Project Scheduling Problem (MS-RCPSP) is a complex and multi-faceted problem that involves scheduling activities whilst considering various resource constraints. These constraints include limited availability of workers, equipment, and materials, with each activity requiring a minimal set of skills to be executed. Furthermore, for a better resemblance to reality, workers/machines are assumed to be multi-skilled/multi-purpose posing another dimension of complexity to the problem. The objective is to minimize project duration, cost, or other relevant criteria while accounting for the inherent resources flexibility. This paper provides a systematic review of the literature pertaining to MS-RCPSP, and an in-depth analysis of 171 papers published between 2000 and 2021 inclusive. The conducted bibliometric analysis identifies the top contributing authors, most influential papers, existing research tendencies, and thematic research topics within the field. In addition, this review highlights different aspects of the MS-RCPSP, spanning the significance of performance measures, solution approaches, application areas, and the incorporation of time constraints. While project completion time, cost, and tardiness are common performance indicators, other measures such as multi-skilled staff assignment and schedule robustness are also deemed important. Although various methods have been employed to solve the MS-RCPSP including exact and approximate approaches, the selection of the most-suited approach depends on the problem’s scale, complexity, and constraints, necessitating careful consideration of each method’s strengths and weaknesses. Interestingly, several studies have jointly addressed resource and time constraints in the context of MS-RCPSP, often considering tardiness, and have proposed different algorithms, models, and metaheuristics to tackle these challenges. This paper clearly highlights research gaps and promising avenues for future research. This work provides valuable insights for project managers to effectively schedule tasks in the presence of multiple flexible resources.

Multi-Objective Multi-Skill Resource-Constrained Project Scheduling Considering Flexible Resource Profiles

This paper addresses a novel multi-skill resource-constrained project scheduling problem with flexible resource profiles (F-MSRCPSP), in which the resource allocation of each activity consists of a certain number of discrete resources and is allowed to be adjusted over its duration. The F-MSRCPSP aims, therefore, to determine the flexible resource profile of each activity to minimize the make-span and total cost simultaneously. Then, a hybrid multi-objective fruit fly optimization algorithm is proposed to handle the concerned problem. In the proposed algorithm, two flexible parallel and serial schedule generation schemes are introduced, aiming to schedule activities and adjust allocated resource combinations. Additionally, two heuristic strategies are proposed to effectively select suitable resource combinations for activities. Moreover, a series of operators has been developed, including the rejoining operator, empirical re-arrangement operator, and empirical re-selection operator. These operators aim to accelerate the convergence speed and enhance the exploration of the proposed algorithm. Finally, the orthogonal test is used to select the optimal parameter combination, and comparative experiments based on tests with different scales are conducted, along with a t-test. The experimental results demonstrate that MOFOA-HS is effective in solving the F-MSRCPSP.

AdaL-PSO A New Adaptive Algorithm for the Multi-Skilled Resource-Constrained Project Scheduling Problem

MS-RCPSP is a combinatorial optimization problem that has many practical applications, this problem has been proven to belong to the NP-hard class, the approach to solving this problem is to use algorithms to find approximate solution. This paper proposed a New Adaptive Local Particle Swarm Optimization algorithm for the MS-RCPSP problem. The solution for the class of NP-Hard problems is to find approximate solutions using metaheuristic algorithms. However, most metaheuristic-based algorithms have a weakness that can be fallen into local extreme after a number of evolution generations. In this paper, we adopted a new adaptive nonlinear weight update strategy based on fitness value and new neighborhood topology for Particle Swarm Optimization algorithm, thereby helping to prevent PSO from falling into local extremes. The new algorithm is called AdaL-PSO. A numerical analysis is carried out using iMOPSE benchmark dataset and is compared with some other early algorithms. Results presented suggest the prospect of our proposed algorithm.

Deep reinforcement learning for solving resource constrained project scheduling problems with resource disruptions

Deep reinforcement learning for solving resource constrained project scheduling problems with resource disruptions

Weighted Multi-Skill Resource Constrained Project Scheduling: A Greedy and Parallel Scheduling Approach

Weighted Multi-Skill Resource Constrained Project Scheduling: A Greedy and Parallel Scheduling Approach

Solving the Resource-Constrained Project Scheduling Problem (RCPSP) with Quantum Annealing

Solving the Resource-Constrained Project Scheduling Problem (RCPSP) with Quantum Annealing

A Practical Approach for Resource-Constrained Project Scheduling

A Practical Approach for Resource-Constrained Project Scheduling

Proposing new clustering-based algorithms for the multi-skilled resource-constrained multi-project scheduling problem with resource leveling adjustments

PurposeThe target of this research is to develop a mathematical model which combines the Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) and the Multi-Skilled Resource-Constrained Project Scheduling Problem (MSRCPSP). Due to the importance of resource management, the proposed formulation comprises resource leveling considerations as well. The model aims to simultaneously optimize: (1) the total time to accomplish all projects and (2) the total deviation of resource consumptions from the uniform utilization levels.Design/methodology/approachThe K-Means (KM) and Fuzzy C-Means (FCM) clustering methods have been separately applied to discover the clusters of activities which have the most similar resource demands. The discovered clusters are given to the scheduling process as priori knowledge. Consequently, the execution times of the activities with the most common resource requests will not overlap. The intricacy of the problem led us to incorporate the KM and FCM techniques into a meta-heuristic called the Bi-objective Symbiosis Organisms Search (BSOS) algorithm so that the real-life samples of this problem could be solved. Therefore, two clustering-based algorithms, namely, the BSOS-KM and BSOS-FCM have been developed.FindingsComparisons between the BSOS-KM, BSOS-FCM and the BSOS method without any clustering approach show that the clustering techniques could enhance the optimization process. Another hybrid clustering-based methodology called the NSGA-II-SPE has been added to the comparisons to evaluate the developed resource leveling framework.Practical implicationsThe practical importance of the model and the clustering-based algorithms have been demonstrated in planning several construction projects, where multiple water supply systems are concurrently constructed.Originality/valueReviewing the literature revealed that there was a need for a hybrid formulation that embraces the characteristics of the RCMPSP and MSRCPSP with resource leveling considerations. Moreover, the application of clustering algorithms as resource leveling techniques was not studied sufficiently in the literature.

A Risk Minimization Model for a Multi-Skilled, Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off

A novel model called Multi-Skilled, Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off (MS-MRCPSP-DTCQRTP) was formulated, focusing primarily on minimizing project risks. This integer programming-based model generates various schedules that aim to optimize time, cost, quality, and risk, either individually or by achieving a balanced combination of these factors. By allocating accessible resources to the tasks of the project and adhering to precedence and resource constraints dictated by availability and skills, a collection of viable schedules was generated. Using a uniform distribution for time, cost, quality, and risk, three project case studies were derived from existing literature and expanded upon. These case studies were then employed to showcase the model. To generate optimal solutions, an open-source Python-MIP package employing the branch-and-cut methodology was employed. It was found that time is not a factor in minimizing the risk of a project, except for large-scale projects. Meanwhile, cost is a factor in all sizes of the project. Quality has no significant impact on risk. Project managers must strike a balance between resources that contain skills set with short to medium duration, moderate to high cost, and moderate to high-quality level to minimize project risk.

Robustifying the resource-constrained project scheduling against uncertain durations

This paper studies the resource-constrained project scheduling problem where uncertain durations are caused by various disruptions with unknown probabilistic functions. To achieve a balance between risk control and computational efficiency, we employ distributionally robust optimization minimizing the worst-case Conditional Value-at-Risk when the upper bounds of durations are not explicitly stipulated. We build a path-based two-stage model over a moment-based ambiguity set. The first stage explicitly generates paths satisfying precedence and resource constraints without any information of uncertainties, while the second stage determines the critical paths over the ambiguity set. Thus, we employ an enhanced Benders decomposition to solve this model where a weighted Benders cut may discriminatingly remove arcs on the critical paths. To ease the computation burden, we develop priority constraints for resource flow and a path elimination method to handle the paths generated by the first stage. A numerical experiment shows that this Benders cut together with the path elimination method can solve more complicated instances efficiently. The result further indicates that this model performs better than the classical model of robust optimization when providing upper bounds for durations. We extract some managerial insights that suggest important guidelines for controlling risk in project scheduling.

Project scheduling to minimize the makespan under flexible resource profiles and marginal diminishing returns of the resource

A standard approach to project scheduling that tackles the problem of minimizing the makespan under variable resource profiles is the Flexible Resource-Constrained Project Scheduling Problem (FRCPSP). This approach traditionally considers constant marginal returns from increasing the allocation of a particular resource, whereas in practice, project and operational managers are often faced with diminishing marginal returns. This work is the first to integrate these two interrelated aspects of resource allocation (flexible profiles and diminishing marginal returns) in order to determine the optimal resource allocation and project scheduling that will minimize the project makespan. This paper develops a mixed-integer linear programming model to obtain an optimal solution of the FRCPSP assuming diminishing marginal returns as the resource allocations are increased. In addition, to solve medium-sized instances of the problem, a heuristic algorithm based on relaxation of this mixed-integer programming model is presented. Through a series of computational tests, we further show that the average deviation in the makespan between the two strategies (optimal vs. heuristic solution) does not exceed 5%.

Integrated resource-constrained project scheduling and material ordering problem considering storage space allocation

Limited storage space has become a tricky bottleneck for projects that are executed in downtown areas. To relieve this practical dilemma, this paper addresses the concurrent decisions on storage space allocation, activity scheduling and material ordering under limited storage space. Aiming to minimize the total cost of project execution, an integrated model for the resource-constrained project scheduling and material ordering problem with limited storage space (RCPSMOP-LSS) is constructed, and a space-saving material ordering strategy, namely OSTP (Ordering Strategy with Time Period) is utilized. Due to the NP-hardness of the RCPSMOP-LSS, a double-layer heuristic algorithm (DLHA) is designed to solve the model. In the outer layer, an improved genetic algorithm is proposed to obtain a space allocation plan and a schedule of all activities. Based on the outcome from the outer layer, an exact algorithm is developed in the inner layer to determine the material ordering scheme. Furthermore, numerical experiments are carried out to verify the efficiency of the proposed DLHA. Specifically, the Taguchi method is utilized to calibrate the parameters of DLHA. Besides, the experimental results demonstrate that the DLHA can greatly save the total cost compared to a traditional decentralized method (TDM). The efficiency of DLHA is also superior to CPLEX solver and TDM, especially for medium- and large-sized instances. Finally, a sensitivity analysis of key components shows that increasing the storage space exerts an increasing effect on cost reduction.

Modified Resource-Constrained Project Scheduling to Minimize Idle Time for Banbury Mixing Process: A Case Study in the Tire Manufacturing Industry

Abstract The Banbury mixing process (BMP) is to supplies the specific characteristic compounds for the tire manufacturing process. Idle time in the BMP was a problem caused by the aging process between mixing steps and the limited space for processing, measured in pallets. In this study, the resource-constrained project scheduling model (RCPS) is modified in case of the objective function and the input value of resource constraint to minimize idle time (SST). The complete minimization (Cmax) is changed from minimizing the starting time of the last job to the starting time of all jobs. In addition, the non-limited resource is defined as the input for the space capacity to reduce the idle time. As the results, the SST can provide the schedule that make less 5 time periods of idle time. Moreover, when considering the relationship between mixing and aging, aging process that is scheduled from SST starts immediately comparison to Cmax that some of aging process are not. Furthermore, the effect of the quantity of pallets was also examined. Although the non-limited resource does not make any delay to the schedule but the limited quantity is not. When pallets are limited, aging jobs were significantly impacted, with the last aging pallet being delayed. To reduce delays, it prepares an adequate supply of pallets that is close to or equal to its requirement that is defined by the non-limited resource. Further research combining the scheduling of the BMP with the tire manufacturing process and more techniques to modify RCPS are applied.

A GA-Based Scheduling Method for Civil Aircraft Distributed Production with Material Inventory Replenishment Consideration

The production of civil aircrafts is confronted with a significant demand for the interconnectivity of production resources among distributed factories, while the complex coupling relationships among various production resources might restrict the improvement of production efficiency. Therefore, researching scheduling methods for civil aircraft distributed production is necessary, but previous studies have not taken material inventory into account sufficiently. This article proposes a scheduling method for civil aircraft distributed production that aims to minimize the production time to complete all the jobs in a large production station under the condition of material inventory replenishment. Firstly, we analyze the factors constraining civil aircraft production efficiency, and formulize the production scheduling problem into the Resource-Constrained Project Scheduling Problem model with Inventory Replenishment (RCPSP-IR). Precedence constraints and resource constraints, especially the inventory constraints, are mainly considered in RCPSP-IR. To solve the corresponding scheduling problem, the Genetic Algorithm (GA) is applied and multiple approaches are introduced to handle the complex constraints and avoid local optimum. Finally, we applied the proposed scheduling method to a case study of a jet twin-engine civil aircraft production of COMAC. The results of the case study show that the proposed method can give a nearly optimal scheduling strategy to be applied to actual civil aircraft production.

A priority rule for scheduling shared due dates in the resource-constrained project scheduling problem

In resource-constrained project scheduling, project milestones, rental equipment, contracted labor, and product development checkpoints all conceptually impose shared due dates, which expand the concept of conventional due dates by permitting their assignment to sets of activities and by allowing multiple shared due date assignments, or none at all, to a single activity. Existing heuristic algorithms in the literature that solve the resource-constrained project scheduling problem are agnostic to shared due dates and cannot utilize information about their assignments in making scheduling decisions. To this end, we propose a novel priority rule compatible with both serial and parallel schedule generation schemes that integrates shared due date information into the heuristic scheduling decisions. We evaluate the effectiveness of our priority rule by demonstrating its dominance over existing priority rules in the literature and by comparing its performance with an exact algorithm. In comparing with the latter, we demonstrate both the computational efficiency of the heuristic as well as the quality of the solutions it produces.

Fast and Robust Resource-Constrained Scheduling with Graph Neural Networks

Resource-Constrained Project Scheduling Problems (RCPSPs) are NP-complete, which makes it challenging to efficiently solve large instances and robustify solutions in the presence of uncertainty. To remedy this, we learn to efficiently mimic the solutions produced by Constraint Programming (CP) solver, using a Graph Neural Network (GNN) architecture designed to capture the structure of RCPSPs. Since the GNN solution may violate constraints, we ensure schedule feasibility at inference time by extracting the task ordering from the GNN schedule and post-processing it with the well-known Schedule Generation Scheme (SGS). We find that SIREN, the resulting algorithm, produces schedules that are of higher quality than those produced by the CP solver within the same computation time budget. The speed and solution quality of SIREN make it suitable as a component of an on-line scenario-based optimisation procedure for RCPSPs with stochastic durations. This leads to the SERENE system, which robustly selects, in real-time, the best next tasks to start in order to minimise the average makespan over the scenarios. Empirically, SERENE achieves better average makespan over different realisations of uncertainty than deterministic algorithms that continuously reschedule on the basis of either the worst, best or average task durations.