Resource-constrained Multi-project Scheduling Problem Research Articles

Multi-skilled resource-constrained multi-project scheduling problem with dexterity improvement of workforce

In this study, a mixed-integer mathematical model has been presented for the Multi-Skilled Resource-Constrained Multi-Project Scheduling Problem (MSRCMPSP), where the dexterity of workers can be improved via two ways: (1) Cooperating with more proficient co-workers, and (2) Practicing the possessed skills. The model aims to determine the start and finish times of activities considering the dexterity improvement of workforces. This research presents a Modified discrete variant of the Biogeography-Based Optimization (MBBO) algorithm to solve the model and to minimize the total required duration to complete all projects. The MBBO embraces two novel migration procedures, a new mutation process, and a new habitat selection operator. On several test instances and on a case study, the efficacy of the MBBO has been put to examination in comparison to four other meta-heuristics. The MBBO has overpowered other methodologies in terms of most of the assessment criteria. The obtained results have revealed that the dexterity improvement of workers significantly improves the total required duration to complete all projects. This research and its outputs can be helpful for the researchers who work on project scheduling models. Moreover, this study can inspire future project scheduling formulations, where the dexterity of human resources is affected by the learning phenomenon.

Energy-efficient resource-constrained multi-project scheduling problem with generalized precedence relations and multi-skilled resources

Energy-efficient resource-constrained multi-project scheduling problem with generalized precedence relations and multi-skilled resources

A three-stage solution approach with a repeated-negotiation mechanism for the decentralized resource-constrained multi-project scheduling problem

PurposeThis study develops a model and algorithm to solve the decentralized resource-constrained multi-project scheduling problem (DRCMPSP) and provides a suitable priority rule (PR) for coordinating global resource conflicts among multiple projects.Design/methodology/approachThis study addresses the DRCMPSP, which respects the information privacy requirements of project agents; that is, there is no single manager centrally in charge of generating multi-project scheduling. Accordingly, a three-stage model was proposed for the decentralized management of multiple projects. To solve this model, a three-stage solution approach with a repeated negotiation mechanism was proposed.FindingsThe experimental results obtained using the Multi-Project Scheduling Problem LIBrary confirm that our approach outperforms existing methods, regardless of the average utilization factor (AUF). Comparative analysis revealed that delaying activities in the lower project makespan produces a lower average project delay. Furthermore, the new PR LMS performed better in problem subsets with AUF < 1 and large-scale subsets with AUF > 1.Originality/valueA solution approach with a repeated-negotiation mechanism suitable for the DRCMPSP and a new PR for coordinating global resource allocation are proposed.

Dynamic scheduling of decentralized high-end equipment R&D projects via deep reinforcement learning

Distributed research and development (R&D) plays a pivotal role in high-end equipment manufacturing enterprises, significantly impacting interdisciplinary innovation and expediting development cycles. In the uncertain environment characterized by random arrivals of new projects, achieving dynamic scheduling and real-time coordination for decentralized R&D projects is a challenging problem. This paper studies a dynamic decentralized resource-constrained multi-project scheduling problem with product transfers (DDRCMPSP-PT). The objective is to minimize the development cycle after initial local schedules are generated to minimize the individual project makespan. To tackle the problem, we develop a decentralized multi-agent system using the dynamic coordination mechanism for resource assignment (DMAS/DCMRA). An up-to-date deep reinforcement learning (DRL) algorithm, dueling double deep Q-learning (D3QN) with prioritized replay, is employed to select the optimal strategy to resolve the global resource conflicts adaptively. Two priority rules are presented based on the structural properties and make up the action space of the DRL agent together with ten high-quality priority rules. Extensive simulation experiment results based on real enterprise cases reveal that the DMAS/DCMRA outperforms all traditional priority rule-based methods. The proposed priority rules also show competitive performance compared to other priority rules, which validates the applicability and superiority of the proposed method. This research offers a new agile project management technique for organizations running multiple R&D projects and managing crucial bottleneck resources.

The performance of priority rules for the dynamic stochastic resource-constrained multi-project scheduling problem: an experimental investigation

We consider the problem of a project manager of a matrix organization responsible for the timely completion of projects arriving over time and requiring the usage of a set of resources under his/her purview. A project is defined by a set of activities, precedence relations between activities, resource requirements, a customer due date, and a priority (a weight). Arriving projects are released to a flow control system that monitors the progress of activities and schedules the set of available activities, i.e., activities that are ready to be processed, as appropriate. A critical feature of such control systems is the decision process for choosing the next activity to seize a given resource. This is the focus of this paper. In the past several decades, various heuristic priority rules have been proposed in the literature to support this type of decision in differing settings such as the job shop problem and the deterministic resource-constrained project scheduling problem. A gap exists with respect to testing the various rules all together in the more realistic dynamic-stochastic multi-project environment when the objective is to minimize weighted project tardiness. The purpose of this paper is to fill this gap. Results show that the priority rule “Weighted Critical Ratio and Shortest Processing Time” (W(CR+SPT))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\hbox {W}(\\hbox {CR}+\\hbox {SPT}))$$\\end{document} is the best performing rule with respect to minimizing weighted project tardiness. W(CR+SPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {SPT})$$\\end{document} is shown to be a variant of the family of “Modified Due Date” rules first introduced by Baker and Bertrand (J Oper Manage 1(3):37–42, 1982). Repeated application of Duncan’s Multiple Range test demonstrates the robustness of our findings. For the environmental parameters (due date tightness, variation of expected activity durations, and utilization of resource), the W(CR+SPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {SPT})$$\\end{document} rule is dominant with respect to weighted project tardiness among the eleven priority rules tested. Only when the number of resources is very modest (either 1 or 3 resources) or under a purely parallel resource network is W(CR+SPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {SPT})$$\\end{document} not the dominant rule. In those cases, its variant W(CR+GSPT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {W}(\\hbox {CR}+\\hbox {GSPT})$$\\end{document} is the best performing rule with respect to weighted project tardiness.

Solving a real-life multi-skill resource-constrained multi-project scheduling problem

This paper addresses a multi-skill resource-constrained multi-project scheduling problem (MSRCMPSP) with different types of resources and complex industrial constraints, which originates from SNCF heavy maintenance factories. Two objective functions, that have been rarely addressed in the literature, are independently considered: (i) Minimization of the sum of the weighted tardiness of the projects and (ii) Minimization of the sum of the weighted duration of the projects. A time-indexed mixed-integer linear programming model is presented with both resource assignment and capacity constraints. To solve large instances with several thousand activities, a new memetic algorithm combining a novel hybrid simulated genetic algorithm with a simulated annealing is implemented. The memetic algorithm is compared with popular solution approaches. Computational experiments conducted on real instances and benchmark instances validate the efficiency of the proposed algorithm.

Framework for multi-project scheduling in product development based on available data

The amount of development projects in companies rises, increasing the difficulty to plan and schedule new projects since the complexity increases when the same human resources are used in a larger amount of projects. This can lead to more interdependencies between the projects and sometimes overload of the existing resources. With more interdependencies, changes in one project also affect other projects leading to more development projects missing their project objectives such as cost and/or time. Multi project management and scheduling addresses this circumstances by scheduling the resources with regard to the overall multi project environment. Although most scheduling approaches in the industry only consider resource availability on a multi-project view, while cost and time are optimized within the projects. The Resourceconstrained multi-project scheduling problem (RCMPSP) is in the scientific literature is widely researched and is concerned with the overall optimization of resource scheduling. These existing solutions for a mathematical optimization approach in resource scheduling, are rarely utilized in the industry. This paper focuses on building a framework to reduce the gap between industry and research. On the one hand, the paper analyses the requirements for project scheduling in corporate practice. On the other hand, a structured overview of the RCMPSP literature is provided from which requirements for the needed data is derived. The framework then matches the scheduling needs and existing data within a company to the research landscape of existing optimization solutions in order to support the use of resource scheduling in multiple projects.

Bi-objective multi-mode resource-constrained multi-project scheduling using combined NSGA II and Q-learning algorithm

Multi-mode resource-constrained multi-project scheduling problem (MRCMPSP) plays a pivotal role in project management, serving as a critical component in production management for Engineering-to-Order manufacturing companies to enhance productivity, reduce costs, and minimize project completion time. This paper investigates the challenging problem of a bi-objective MRCMPSP, considering resource and finish time constraints, and develops a mathematical model to reduce project cycles and achieve better resource load balancing. By leveraging on the independent nature of start time selection for each activity, which aligns with the characteristics of a Markov decision process, we propose a two-layer iterative algorithm that combines the Nondominated Sorting Genetic Algorithm II (i.e., NSGA II) and Q-learning algorithm to solve the model effectively. Hence, the NSGA II algorithm generates mode combinations, while its fitness function employs the Q-learning algorithm to search for optimal activity time selections within each mode. We verify the performance superiority of the proposed algorithm by conducting a comparative analysis against classical approaches, encompassing classical NSGA II, Particle Swarm Optimization, and Ant Colony Optimization algorithms. Furthermore, this study’s experimental results therefore unequivocally demonstrate the effectiveness of our algorithm in achieving optimized project scheduling outcomes.

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 simulation-based approximate dynamic programming approach to dynamic and stochastic resource-constrained multi-project scheduling problem

We consider the dynamic and stochastic resource-constrained multi-project scheduling problem which allows for the random arrival of projects and stochastic task durations. Completing projects generates rewards, which are reduced by a tardiness cost in the case of late completion. Multiple types of resource are available, and projects consume different amounts of these resources when under processing. The problem is modelled as an infinite-horizon discrete-time Markov decision process and seeks to maximise the expected discounted long-run profit. We use an approximate dynamic programming algorithm (ADP) with a linear approximation model which can be used for online decision making. Our approximation model uses project elements that are easily accessible by a decision-maker, with the model coefficients obtained offline via a combination of Monte Carlo simulation and least squares estimation. Our numerical study shows that ADP often statistically significantly outperforms the optimal reactive baseline algorithm (ORBA). In experiments on smaller problems however, both typically perform suboptimally compared to the optimal scheduler obtained by stochastic dynamic programming. ADP has an advantage over ORBA and dynamic programming in that ADP can be applied to larger problems. We also show that ADP generally produces statistically significantly higher profits than common algorithms used in practice, such as a rule-based algorithm and a reactive genetic algorithm.

A genetic algorithm with resource buffers for the resource-constrained multi-project scheduling problem

In this study, we compose a new metaheuristic algorithm for solving the resource-constrained multi-project scheduling problem. Our approach is based on a general metaheuristic strategy which incorporates two resource-buffered scheduling tactics. We build on the most effective evolutionary operators and other well-known scheduling methods to create a novel genetic algorithm with resource buffers. We test our algorithm on a large benchmark dataset and compare its performance to ten existing metaheuristic algorithms. Our results show that our algorithm can generate new best-known solutions for about 20% of the test instances, depending on the optimisation criterion and due date. In some cases, our algorithm outperforms all other available methods combined. Finally, we introduce a new schedule metric that can quantitatively measure the dominant structure of a solution, and use it to analyse the differences between the best solutions for different objectives, due dates, and instance parameters.

An Integrated Model for Multi-Mode Resource-Constrained Multi-Project Scheduling Problems Considering Supply Management with Sustainable Approach in the Construction Industry under Uncertainty Using Evidence Theory and Optimization Algorithms

In this study, the multi-mode resource-constrained multi-project scheduling problems (MMRCMPSPs) considering supply management and sustainable approach in the construction industry under uncertain conditions have been investigated using evidence theory to mathematical modeling and solving by multi-objective optimization algorithms. In this regard, a multi-objective mathematical model has been proposed, in which the first objective function aims to maximize a weighted selection of projects based on economic, environmental, technical, social, organizational, and competitive factors; the second objective function is focused on maximizing profit, and the third objective function is aimed at minimizing the risk of supply management. Moreover, various components, such as interest rates, carbon penalties, and other implementation limitations and additional constraints, have also been considered in the modeling and mathematical relationships to improve the model’s performance and make it more relevant to real-world conditions and related issues, leading to better practical applications. In the mathematical modeling adopted, the processing time of project activities has been considered uncertain, and the evidence theory has been utilized. This method can provide a flexible and rational approach based on evidence and knowledge in the face of uncertainty. In addition, to solve the proposed multi-objective mathematical model, metaheuristic optimization algorithms, such as the differential evolution (DE) algorithm based on the Pareto archive, have been used, and for evaluating the results, the non-dominated sorting genetic algorithm II (NSGA-II) has also been employed. Furthermore, the results have been compared based on multi-objective evaluation criteria, such as quality metric (QM), spacing metric (SM), and diversity metric (DM). It is worth noting that to investigate the performance and application of the proposed model, multiple evaluations have been conducted on sample problems with different dimensions, as well as a case study on residential apartment construction projects by a contracting company. In this respect, the answers obtained from solving the model using the multi-objective DE algorithm were better and superior to the NSGA-II algorithm and had a more favorable performance. Generally, the results indicate that using the integrated multi-objective mathematical model in the present research for managing and scheduling multi-mode resource-constrained multi-project problems, especially in the construction industry, can lead to an optimal state consistent with the desired objectives and can significantly improve the progress and completion of projects.

A Benders decomposition algorithm for the multi-mode resource-constrained multi-project scheduling problem with uncertainty

A Benders decomposition algorithm for the multi-mode resource-constrained multi-project scheduling problem with uncertainty

Tabu search for dedicated resource-constrained multiproject scheduling to minimise the maximal cash flow gap under uncertainty

Maintaining a positive balance between cash outflow and inflow is very important for contractors to smoothly implement projects. Based on this fact, with the objective of minimising the maximal cash flow gap, this paper investigates a dedicated resource-constrained multiproject scheduling problem with stochastic activity duration where renewable resources are dedicated to individual projects in advance, and the schedule of each project is then arranged independently. First, we construct an optimisation model for the problem and propose properties for it. Second, for the NP-hardness of the problem, we design a tabu search algorithm consisting of two modules and develop the measures according to the proposed properties to improve the searching efficiency of the algorithm. Finally, we conduct a computational experiment on a randomly generated dataset to evaluate the performance of the developed algorithm and analyse the effects of key parameters on the objective function value. The conclusions are as follows. The developed tabu search algorithm with the improvement measures is the most promising algorithm for solving the studied problem, and the contribution of the improvement measures may vary as the project parameters change. The maximal cash flow gap increases along with the resource factor, required robustness of project schedule, and discount rate per period of cash flows, and decreases with the increase in the project deadline, resource strength, number of milestone activities, advance payment proportion, or progress payment proportion. The interactions among the resource strength, resource factor, and project deadline may also generate an effect on the maximal cash flow gap.

A Two-Stage Algorithm Based on 12 Priority Rules for the Stochastic Distributed Resource-Constrained Multi-Project Scheduling Problem With Multi-Skilled Staff

In practical multi-skilled resource-constrained multi-project management, the activity duration is often affected by some factors (e.g., rework, increased workload), leading to uncertainty. Moreover, multiple projects are often managed under a distributed decision-making environment. To deal with uncertain activity durations in distributed multi-project management with multi-skilled staff, this paper studies a stochastic distributed resource-constrained multi-project scheduling problem with multi-skilled staff (MS-SDRCMPSP). In a distributed decision-making environment, a two-stage model with local scheduling and global coordination stages is established to describe MS-SDRCMPSP. A two-stage algorithm with 12 priority rules (TSA-12PRs) is proposed, these 12 priority rules are composed of 4 activity priority rules and 3 resource priority rules. In the local schedule stage, 4 activity priority rules (PRs) are applied to obtain the local schedule plan. In the global coordination phase, we develop 3 resource PRs based on variable neighborhood search (VNS), of which VNS is used to solve the execution order of conflicting projects, and 3 resource PRs are developed to formulate multi-skilled resource assignment strategies. Based on the multi-skilled instances adapted from benchmark instances, we evaluate the performance of the 12 PRs on different instances. The experiment results show that two PRs among 12 PRs perform better than other PRs in all-size instances. Comparing the two-stage algorithm with better two PRs with other approaches in literatures, we find that our method performs better than other approaches, especially in large-size instances. In addition, further experiments show that our method is more conducive to shortening the CPU runtime on distributed problems than centralized methods.

Multi-project scheduling: A benchmark analysis of metaheuristic algorithms on various optimisation criteria and due dates

This paper reviews a set of ten existing metaheuristic solution procedures for the resource-constrained multi-project scheduling problem. Algorithmic implementations are constructed based on the description of the original procedures in literature. Equivalence is verified on the original test instances for the original objective and parameters through a comparison with the reported results. An extensive benchmark analysis is performed on a novel, publicly available dataset for a variety of optimisation criteria and due date settings for which the original algorithms have not been tested earlier. The impact of the different objectives, due dates and test instance parameters is analysed and an overall ranking of the metaheuristic solution methods for different situations is discussed. Key insights into the structure of competitive solutions for disparate objectives and due date settings are presented and effective algorithmic components are revealed.

Dynamic multi-mode resource-constrained multi-project scheduling problem with weighted earliness and tardiness: a real-life boutique furniture implementation

Real-life project scheduling environments are often dynamic and subject to disruption. Early or late completion of interrupted projects can create costs for the business. At the same time, there is an alternative to producing multiple projects at multiple different costs. In this study, a new mixed integer linear programming model that minimizes the sum of weighted earliness and tardiness penalties and mode selection costs is proposed to solve the real-life problem faced by a boutique furniture company. A proposed dynamic model also considers the cost of deviation from the baseline schedule in case disruption scenarios corrupt the resulting baseline schedule. The problems are solved with the CPLEX solver using the GAMS program. The results show that the interruption scenarios partially change the baseline schedule and increase the total cost. In case of more than one interruption in the same schedule, the number of late completed activities and their delay times increased.

Portfolio Planning: a Comprehensive Approach to Limited Resources and Project Prioritization

The main issue for portfolio managers is to set a realistic schedule that ensures that the resources needed for operations are readily available on deadline dates, which is the classic goal of the Resource-Constrained Multi-Project scheduling problem (RCMPSP). This article presents an algorithm that provides solution to RCMPSP, where each project has a different priority for the organization. The key feature of this algorithm is that it includes project prioritization during the planning process. Before planning, the portfolio manager determines which projects are relevant for the company. With this in mind, the algorithm uses market mechanisms to determine which activities should be prioritized in the planning process. Based on this, the algorithm creates an artificial market and enables to plan those projects that are of higher priority. Thus, out of a number of possible schedules corresponding to resource constraints (i.e., the solution provided by classic approaches to RCMPSP), the approach considered in the article allows obtaining an optimal portfolio schedule. This schedule, in addition to having the shortest possible duration of the portfolio, allows planning activities in accordance with priorities of the portfolio manager and, consequently, priorities of the company.

Multi-project scheduling with multi-skilled workforce assignment considering uncertainty and learning effect for large-scale equipment manufacturer

This study addresses a resource-constrained multi-project scheduling and multi-skilled workforce assignment problem for the large-scale equipment manufacturing industry. The goal is to help the production manager perform effective planning and decrease the production cost under delivery constraints. The deterministic duration is used in most past investigations in resource-constrained multi-project scheduling problems. Uncertainty in project execution is neglected. Additional related factors are included in the current study to be close to practical circumstances. The required processing duration and material arrival time are modeled as stochastic variables. The heterogeneous skill efficiency of the internal workforce is considered with the learning effect. Skill efficiency grows with the accumulation of experience. Actual processing time is calculated on the basis of skill efficiency and stochastic process duration. The external workforce is hired when the internal workforce fails to satisfy processing demand. The objective is to minimize the expected integrated cost, which is the sum of tardiness penalty and external workforce cost. A genetic algorithm with a heuristic workforce assignment method is also developed, and a case study is illustrated to explain the scheduling result. The proposed approach with uniform crossover and local search mechanism outperforms other comparative methods by approximately 10.34% considering total costs. Furthermore, the Taguchi method of design of the experiment is conducted to find the optimal parameter setting efficiently. Afterward, the sensitivity analysis of production-related parameters is discussed.

Hybrid differential evolution particle swarm optimization (DEA-DCWPSO) for resource-constrained multi-project scheduling problem

In this paper, we studied the resource constrained project scheduling problem, and the research object is extended to the multi-project environment. On the basis of multi-project priority evaluation, with the goal of minimizing the weighted duration of multi-project, a multi-project schedule planning model is constructed. Through reasonable scheduling of multiple parallel projects sharing resources under resource constraints, it provides a decision-making basis for project managers to allocate resources reasonably under resource constraints to meet the duration requirements of each project and to shorten the weighted total duration of multiple projects as much as possible. A two-stage hybrid differential evolution particle swarm optimization algorithm is used to solve the model. In the first stage, differential evolution algorithm is used to produce new individuals, and in the second stage, particle swarm optimization algorithm uses a new speed update formula. In the first stage, in order to ensure that the optimal individual will not be destroyed by crossover and mutation, and to maintain the convergence of differential evolution algorithm, we try to introduce Elitist Retention (ER) strategy into differential evolution algorithm. In the second stage, we use a kind of particle swarm optimization algorithm with dynamically changing inertia weight. Through the dynamic changing inertia weight, the global search and local search ability of the algorithm can be adjusted flexibly. The case verification shows that the hybrid differential evolution particle swarm optimization algorithm can be used to solve the RCMPSP model more effectively.