Resource Constrained Project Scheduling Problem Research Articles

Exact solution methods for the Resource Constrained Project Scheduling Problem with a flexible Project Structure

Exact solution methods for the Resource Constrained Project Scheduling Problem with a flexible Project Structure

Investigating constraint programming and hybrid methods for real world industrial test laboratory scheduling

AbstractIn this paper we deal with a complex real world scheduling problem closely related to the well-known Resource-Constrained Project Scheduling Problem (RCPSP). The problem concerns industrial test laboratories in which a large number of tests are performed by qualified personnel using specialised equipment, while respecting deadlines and other constraints. We present different constraint programming models and search strategies for this problem. Furthermore, we propose a Very Large Neighborhood Search approach based on our CP methods. Our models are evaluated using CP solvers and a MIP solver both on real-world test laboratory data and on a set of generated instances of different sizes based on the real-world data. Further, we compare the exact approaches with VLNS and a Simulated Annealing heuristic. We could find feasible solutions for all instances and several optimal solutions and we show that using VLNS we can improve upon the results of the other approaches.

Optimising resource-constrained fleet selective maintenance with asynchronous maintenance breaks

This paper offers a novel and significant extension of the Fleet Selective Maintenance Problem (FSMP) by considering asynchronous maintenance breaks and resource-constrained maintenance planning. This constitutes a significant shift from the conventional focus on synchronous breaks for the FSMP formulated to plan maintenance for fleets of mission-critical systems. This paper establishes a theoretical link between the Selective Maintenance Problem (SMP) and the Resource Constrained Project Scheduling Problem (RCPSP). The proposed FSMP formulation for asynchronous breaks is more general and versatile in adapting to a broad spectrum of operational constraints and resource scarcities. Numerical experiments are conducted that highlights the trade-offs between the timing and quality levels of maintenance activities and the consumption of resources that maintenance planners can make to obtain the best system performance for the budget and maintenance windows available.

Evolutionary Algorithm for the Earliness - Tardiness Project Scheduling Problem

Completing too early or too late can cause damage to the project. For example, in transporting goods to the seaports, if the shipping arrives too early, it will take time and cost to stay at the dock. In the other case, shipping too late will reduce the quality of the product and break the contract. The goal of this paper is to minimize the tardiness and earliness of those projects. First, some related studies are briefly introduced, thereby showing the role and practical applications of the MS-RCPSP (Multi-Skill Resource Constrained Project Scheduling Problem) problem and the two factors of earliness and delay in scheduling problems. The roles of earliness and tardiness in scheduling problems are also described. At the same time, the new contribution of this research is also highlighted, which is the proposal for the latest problem E-RCPSP (Earliness tardiness MS-RCPSP). This problem is the first problem in the MS-RCPSP family that considers the sum of earliness and tardiness as the objective, which has never been considered in previous studies. Then, the mathematical model of the proposed E-RCPSP problem, which includes the objective function, project components and constraints is introduced. To solve the proposed problem, two approximate algorithms based on the evolutionary algorithms GA (Genetic Algorithm) and DE (Differential Evolution) are introduced. In the last section of the article, the performance of these two algorithms is verified and compared with each other through experiments conducted on the iMOPSE benchmark dataset.}\Keywords{Network Resources Management, Earliness-Tardiness cost, Resource-constrained project scheduling, Evolutionary Algorithms, Differential evolution algorithms.

Quadratic horizontally elastic not-first/not-last filtering algorithm for cumulative constraint

The not-first/not-last rule is a pendant of the edge finding rule, generally embedded in the cumulative constraint during constraint-based scheduling. It is combined with other filtering rules for more pruning of the tree search. In this paper, the Profile data structure in which tasks are scheduled in a horizontally elastic way is used to strengthen the classic not-first/not-last rule. Potential not-first task intervals are selected using criteria (specified later in the paper), and the Profile data structure is applied to selected task intervals. We prove that this new rule subsumes the classic not-first rule. A quadratic filtering algorithm is proposed for the new rule, thus improving the complexity of the horizontally elastic not-first/not-last algorithm from O(n3) to O(n2). The fixed part of external tasks that overlap with the selected task intervals is considered during the computation of the earliest completion time of task intervals. This improvement increases the filtering power of the algorithm while remaining quadratic. Experimental results, on a well-known suite of benchmark instances of Resource-Constrained Project Scheduling Problems (RCPSPs), show that the propounded algorithms are competitive with the state-of-the-art not-first algorithms in terms of tree search and running time reduction.

Efficient optimization of robust project scheduling for industry 4.0: A hybrid approach based on machine learning and meta-heuristic algorithms

This research contributes significantly to the domain of Industry 4.0 by offering a nuanced approach to the multi-objective optimization of the resource-constrained project scheduling problem (RCPSP) under uncertainty. Focused on the context of smart product platforming, this study introduces a novel methodology that not only considers traditional factors like time and cost but also incorporates quality and risk aspects, crucial for personalized product fulfillment. In this regard, a comprehensive four-objective mathematical model is proposed to minimize project completion time, total project costs, and project risks while simultaneously enhancing overall project quality. Real-world uncertainty is acknowledged through the incorporation of uncertain parameters for the time, risk, and quality associated with each project activity. To address this uncertainty, a robust optimization method is applied based on Bertsimas and Sim's approach. Moreover, to optimize the proposed model, the Hybrid Red Deer and Genetic Algorithm (HRDGA) is proposed, which is leveraging a machine learning approach for clustering solutions. The numerical results demonstrate that increasing the project budget by 30% leads to an upward trend in total project costs and a reduction in the minimum acceptable quality by 10%–30% results in a decreasing trend in the total project cost. This research emphasizes the adoption of Industry 4.0 enabling technology within the project scheduling platform, particularly highlighting its significance for personalized product fulfillment.

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

Preemptive and non-preemptive multi-skill multi-mode resource-constrained project scheduling problems considering sustainability and energy consumption: A comprehensive mathematical model

Modern project managers cope with significant challenges to schedule and control projects considering dynamic environments, frequent uncertainties, strict project deadlines, and stricter sustainable requirements above all. Sustainability taking into account resource utilization has been recently associated with project management. Hence, this paper presents a new mixed-integer linear programming (MILP) model with two objectives for a resource-constrained project scheduling problem (RCPSP) with multiple skills and multiple modes, assuming preemptive and non-preemptive activities in an uncertain environment. Given the importance of sustainable developments in projects, the considered objectives are to maximize job opportunities and minimize project duration, resource costs, and total energy consumption. To deal with the model, an AUGNMECON2VIKOR algorithm is utilized to create Pareto solutions. In this model, project activities can be crashed by allocating extra resources. Furthermore, multi-skill resources are used to perform project activities. This study also investigates the impact of these resources on project scheduling. To deal with uncertain circumstances, a fuzzy chance-constrained programming method is employed to develop a robust possibilistic programming model. With respect to the increasing significance of sustainability in project management, this study pioneers the examination of the impact of sustainable factors on project scheduling. Finally, the proposed formulation is validated using instances from the well-known PSPLIB and MMLIB test sets. Finally, a comparison is drawn between the presented solution method considering AUGMECON2VIKOR and AUGMECON2.

Solving the resource constrained project scheduling problem with quantum annealing

Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations research.

A matheuristic for the resource-constrained project scheduling problem

This paper presents a matheuristic solution algorithm to solve the well-known resource-constrained project scheduling problem (RCPSP). The problem makes use of a restricted neighbourhood method using an activity selection and a search space restriction module and implements them as two alternative search algorithms. The first algorithm makes use of the best-performing components of the branch-and-bound procedures from the literature, and embeds them into a greedy neighbourhood search. The second matheuristic implements the exact branch-and-bound procedures into a known and well-performing meta-heuristic search algorithm.Computational experiments have been carried out on seven different datasets consisting of 10,000+ project instances. Experiments reveal that the choice of exact algorithm is key in finding high-quality solutions, and illustrate that the trade-off between selecting an activity set size and search space restriction depends on the specific implementation. The computational tests demonstrate that the matheuristic discovered 24 new best known solutions that could not be found by either a meta-heuristic or an exact method individually. Moreover, a new benchmark dataset has been proposed that can be used to develop new matheuristic search procedures to solve the problem consisting of 461 instances from the literature.

Mixed-integer linear programming for project scheduling under various resource constraints

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget; and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

An Agile Adaptive Biased-Randomized Discrete-Event Heuristic for the Resource-Constrained Project Scheduling Problem

In industries such as aircraft or train manufacturing, large-scale manufacturing companies often manage several complex projects. Each of these projects includes multiple tasks that share a set of limited resources. Typically, these tasks are also subject to time dependencies among them. One frequent goal in these scenarios is to minimize the makespan, or total time required to complete all the tasks within the entire project. Decisions revolve around scheduling these tasks, determining the sequence in which they are processed, and allocating shared resources to optimize efficiency while respecting the time dependencies among tasks. This problem is known in the scientific literature as the Resource-Constrained Project Scheduling Problem (RCPSP). Being an NP-hard problem with time dependencies and resource constraints, several optimization algorithms have already been proposed to tackle the RCPSP. In this paper, a novel discrete-event heuristic is introduced and later extended into an agile biased-randomized algorithm complemented with an adaptive capability to tune the parameters of the algorithm. The results underscore the effectiveness of the algorithm in finding competitive solutions for this problem within short computing times.

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.

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

A multi-skill RCPSP variant for persons with disabilities in sheltered workshops

Sheltered workshops face the challenge of meeting their manufacturing objectives while considering the individual competencies and assistance needs of persons with disabilities. Moreover, work processes in sheltered workshops are weakly structured, allowing for frequent task interruptions and changes based on the preferences of impaired work persons. While the Industry 4.0 literature provides many real-time scheduling algorithms for incorporating multiple objectives and constraints, these algorithms fall short of the characteristics of sheltered workshops. The resource-constrained project scheduling problem (RCPSP) is an optimization problem for computing manufacturing plans considering multiple objectives and resource constraints. Among many different RCPSP variants proposed in the literature, the multi-skill RCPSP (MSRCPSP) variant considers the individual skills of work persons when generating manufacturing plans. With the ongoing digital transformation of enterprises, new assistance systems enter the market, providing individual support to impaired work persons and compensating for lacking skills and abilities.This paper proposes an MSRCPSP variant that incorporates assistance systems and learning tasks compensating for competence gaps in the skill matrix of impaired work persons. Furthermore, it decomposes tasks into individual work objects, which accounts for frequent task interruptions and task preferences of work persons. The algorithm is described and demonstrated using a manufacturing data set from an actual sheltered workshop. In a small evaluation study, the algorithm is tested by scheduling two impaired work persons in the assembly department of a medium-sized manufacturing company in the primary labor market. The evaluation study proves its real-world applicability and the suitability of scheduling algorithms for participation and inclusive work.

A Modular Heuristic-Based Solution for Large-Scale Outage Management in Nuclear Power Plants

The Resource Constrained Project Scheduling Problem (RCPSP) is a prominent combinatorial optimization problem in academia. It involves scheduling project activities while considering constraints arising from logical relationships between tasks, resource capacity limitations, and other projectspecific factors. In this paper, we propose a modular heuristic method for efficient outage planning and execution within Nuclear Power Plants (NPPs). The project contains more than 24,000 tasks with specific industrial-oriented constraints such as the notion of prioritization, the event of pausing tasks in progress, handling of resources incompatibility, and adjusting dynamic units of resources based on their availability. The execution speed of the entire solution has been extensively revised to reach an average of 10 to 15 minutes on a standard computer. This enables project managers to promptly evaluate various scenarios with minimal data adjustments, facilitating informed decision-making. The solutions effectiveness has been validated by domain experts, demonstrating its potential for real-world application.

Ant colony algorithms for minimizing costs in multi-mode resource constrained project scheduling problems with spatial constraints

Ant colony algorithms for minimizing costs in multi-mode resource constrained project scheduling problems with spatial constraints