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Review

Multi-Project Scheduling with Uncertainty and Resource Flexibility: A Narrative Review and Exploration of Future Landscapes

by
Marzieh Aghileh
1,
Anabela Tereso
1,*,
Filipe Alvelos
1 and
Maria Odete Monteiro Lopes
2
1
ALGORITMI Research Centre/LASI, University of Minho, 4800-058 Guimarães, Portugal
2
Mechanical Engineering and Industrial Management Department, Instituto Politécnico de Viseu, 5100-074 Viseu, Portugal
*
Author to whom correspondence should be addressed.
Algorithms 2025, 18(6), 314; https://doi.org/10.3390/a18060314
Submission received: 24 April 2025 / Revised: 18 May 2025 / Accepted: 20 May 2025 / Published: 26 May 2025
(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)
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Abstract

This paper presents a narrative review on the Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) under uncertainty and resource flexibility. Traditional project scheduling assumes complete information and a deterministic environment where a pre-computed baseline schedule is executed. However, real-world projects frequently face uncertainty, such as variable task durations and fluctuating resource availability. Analyzing studies from 2013 to 2024, this review examines optimization models addressing multiple objectives, including minimizing project duration, cost, and resource leveling. It categorizes solution approaches, from exact algorithms to heuristic and metaheuristic methods, while reviewing the primary instance sets and benchmarks used in the field. Additionally, it highlights the value of flexible resource management approaches that enable adaptive responses to real-time project demands, thereby enhancing scheduling robustness. By systematically addressing RCMPSP under uncertainty, this paper provides a valuable framework for researchers and practitioners seeking to develop resilient, adaptive scheduling solutions for complex, dynamic project environments.

Graphical Abstract

1. Introduction

In realistic scheduling situations, companies typically manage multiple projects concurrently rather than a single one [1]. This transition from single-project to multi-project management introduces a significant layer of complexity to the scheduling process. The scheduling process becomes more challenging in this multi-project case, as some resources might need to be shared across multiple projects (e.g., facilities, machines, human resources). This resource dispute gives rise to intricate scheduling challenges, as decisions made for one project can have cascading effects on the timelines and budgets of others. The study of these complexities and the development of effective methodologies to navigate them is known as the Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) [2].
The RCMPSP aims to optimize allocation of resources across multiple projects while adhering to project-specific constraints, such as activity precedence relationships and deadlines. However, the inherent assumption of deterministic conditions—where activity durations, resource availability, and project parameters are known with certainty—underlies many traditional RCMPSP models. This assumption is a significant oversimplification of real-world project environments, which are characterized by a high degree of uncertainty.
During project execution, random events such as activities taking different durations than expected, introducing new projects, and resources being unavailable cause production instability and significant delays. Therefore, these uncertainties must be considered in project scheduling.
To increase flexibility, workloads corresponding to each activity can be defined, and resource requirements can be adjusted flexibly. This approach, rooted in the concept of the Flexible Resource Constrained Project Scheduling Problem (FRCPSP) [3], has led to the development of several models/methods aimed at optimizing resource allocation under uncertainty [4], with further exploration into resource flexibility [5,6,7,8]. This paper looks closely at both uncertainty and flexibility with RCMPSP. Therefore, the two main contributions of this paper are (i) a comprehensive review of the literature analyzing and discussing the characteristics and objective functions proposed so far for the RCMPSP, as well as solution methods and existing benchmark datasets; and (ii) an examination of the main trends over the last 12 years, along with insights into how the RCMPSP is applied in real-world environments, helping to point out future research directions. The structure of this paper is organized as described below.
The findings of this research will offer valuable guidance for both researchers and practitioners in multi-project scheduling. By synthesizing the existing body of knowledge and highlighting key research gaps, it seeks to advance the development of more effective, resilient, and practical scheduling methodologies for multi-project environments.
Section 2 provides the background. In Section 3, the methodology used to carry out this research is described. In Section 4, a review of resource characteristics and the variants used to address the RCMPSP is explored. Discussion and findings are presented in Section 5, and finally, the conclusion appears in Section 6.

2. Background

2.1. Resource-Constrained Multi-Project Scheduling Problem (RCMPSP)

In practical scheduling scenarios, companies typically manage multiple projects simultaneously. This multi-project case increases the complexity of the scheduling process due to the possible existence of resources that need to be shared across multiple projects. This challenge is studied under the term Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) [9].
RCMPSP is an expanded version of the Resource-Constrained Project Scheduling Problem (RCPSP), which involves scheduling multiple projects concurrently while sharing common resources. This extension also incorporates consideration of each project’s arrival time; that is, the time at which the activities can start. It is a practical problem that aims at minimizing project duration under resource constraints by determining start dates for each activity within a portfolio of projects. Since the RCMPSP, which is based on the RCPSP, is NP-hard [2,10], it becomes computationally challenging for large-scale instances. Consequently, researchers have developed heuristics and meta-heuristics to solve the related problems [11,12,13,14].

2.2. Uncertainty

Project execution in a real environment involves considerable uncertainty. Several factors contribute to uncertainty in multi-project scheduling. These uncertainties can be broadly divided into two main categories. The first kind is the uncertainty caused by the external environment; for example, adding more activities due to temporary increased orders, information uncertainty, and weather conditions. The second type of uncertainty relates to production factors, known as resource uncertainty. The most common uncertainties in project scheduling are a temporary shortage of resources and equipment failure [15].
During project execution, uncertainty is a significant factor that frequently affects the baseline scheduling plan, leading to delayed start times and resource supply interruptions. For instance, project duration may fluctuate because of a temporary change in activity duration, a new activity introduced during project execution, or cancellation of the original activity. Consequently, the entire project scheduling process becomes difficult to control [15]. According to Fox and Ringer’s survey, about 5% of scheduling time is spent developing new schedules, while 95% is dedicated to revising and maintaining schedules in response to daily progress and changes in assumptions [16].
Uncertainty factors may impact multi-project scheduling schemes in more complex ways at any point during project execution. A multi-project scheduling plan cannot accurately predict the completion times of each activity, thereby weakening its performance. Furthermore, the impact of these uncertain factors on multi-project scheduling leads to frequent modifications of scheduling plans, which significantly diminishes scheduling robustness and greatly increase the risk of delays [15].

2.3. Resource Flexibility

By introducing flexibility in resource allocation, the problem extends the RCPSP, leading to an optimal makespan that is at least as efficient as the makespan of the RCPSP. In this new scenario, the usage of resources and the duration of each activity are not predetermined. Instead, they are determined when scheduling the activities based on their starting times. This problem is known as the RCPSP with Flexible Resource Profiles (FRCPSP) [7].
This problem is initially introduced by Kolisch et al. [17] in the context of pharmaceutical research. Despite its significant potential, the problem has not been as extensively explored as the RCPSP. However, in recent years, the FRCPSP has attracted wider attention from researchers, resulting in the development of various model formulations and heuristic methods.
While the RCPSP assumes that the resources are allocated in constant amounts over the entire duration of each activity, Kolisch et al. [17] proposed a model in which resource allocation must be determined. In Ranjbar and Kianfar’s [18] proposal, RCPSP-FWP (RCPSP with Flexible Work Profiles) is used with the same meaning as FRCPCP. The RCPS-FWP is a different version of the well-known RCPSP, which consists of interrelated activities with a zero-time lag that are interconnected via finish-start-type precedence relations, where a single renewable resource is available, and activity duration and resource usage to a single renewable resource are known constants. The total work content of each activity is given, instead of the duration and resources required for each activity, which essentially indicates how much work needs to be done. In other words, activities’ durations and resource usage at any time are unknown. FRCPSP assumes that activity duration is not set, being part of the problem to be solved [18].
Naber and Kolisch [7] presented the FRCPSP. They used a Mixed Integer Programming (MIP) approach to address this problem. In addition to the MIP formulation, a priority rule (PR) heuristic is proposed, along with a scheme for creating both serial and parallel schedules. In their schedule generation scheme (SGS), activities are scheduled as early as possible, and the greatest number of resources is allocated per iteration.
This means that, in each iteration of the scheduling process, resources are assigned to activities based on their availability and the requirements of the activities being scheduled at that point [8].
This new approach to RCPSP, renamed Resource Constraint Project Scheduling Problem with Flexible Resource Management (RCPSP-FRM), takes into account the flexibility of limited resources [5].

3. Research Methodology

The following section outlines the methodology applied to collect and analyze relevant works to address key research questions within the research field of this study and derive new insights from publications. Specifically, the research seeks to answer the following questions:
RQ1. 
What are the objectives in multi-project scheduling problems?
RQ2. 
What are the different types of solving methods in multi-project scheduling problems?
RQ3. 
What types of instance sets are used in multi-project scheduling problems?
RQ4. 
What are the potential future research directions in multi-project scheduling problems?
To find the answers to the above questions, Aghileh et al. [19] was used as a reference paper. An extensive Systematic Literature Review (SLR) was conducted, sourcing relevant publications from academic databases such as Scopus, Web of Science, and Google Scholar. The SLR spanned studies published between 2013 and 2023 and applied specific keywords—such as “multi-project scheduling problem”, “uncertainty”, and “flexibility”—to capture a comprehensive view of developments in this field. After the initial identification of 826 records, a screening process yielded a refined selection of 108 studies that fit the established criteria. These included both qualitative studies lacking formalized models and calculations and quantitative studies that presented specific models and statistical analyses.
The primary distinction between qualitative and quantitative research lies in data collection and analysis. Quantitative research focuses on numerical data and employs statistical analysis, whereas qualitative research provides descriptive insights, exploring concepts and experiences in depth.
Given this study’s emphasis on evaluating optimization models, the final selection prioritized quantitative studies. A total of 53 quantitative papers were chosen, since this research is based on a previous study and aims to evaluate optimization models, supplemented by 23 additional papers containing relevant insights published in 2024 for further review. This process resulted in a comprehensive pool of 76 studies (as shown in Figure 1).
The design of this study is oriented toward analysis of the RCMPSP and related variants through the detailed study of each included paper in terms of problem characteristics, solution approaches, proposed benchmarks, and analysis through various statistics.
This methodology thus enabled a robust foundation for responding to each research question. While RQ2 was only partially addressed in Aghileh et al. [19], this study significantly expanded upon it, providing a thorough and detailed investigation into the diverse solution methods used within multi-project scheduling.

4. A Review of Variants in Project Scheduling Problem

This section presents a brief overview of the project scheduling problem variants studied in the literature and enables precise responses to each question within the study’s broader inquiry. Given the nature of the problem and collected papers, variants are analyzed in terms of objectives in multi-project scheduling problems to address the RQ1, different types of solving methods to provide insights for the RQ2, types of instance sets to address the RQ3, and potential directions for future research to address the RQ4.

4.1. Based on Objectives

4.1.1. Time-Based Objectives

The following classification groups those objective functions that evaluate completion time or the delays that may occur during projects.
  • Delays: Project delays occur when completion exceeds the due date. A project delay is formally defined as the difference between the finishing date of a project and its desired due date if, and only if, the first exceeds the latter; otherwise, the delay is zero. There are several objective functions associated with the delays. Commonly used delay-based metrics include minimizing the average project delay (APD). Other metrics, including those related to delays and the efficiency of the schedules generated, were analyzed in terms of the average percentage of project delay, efficiency, and robustness. In this review, measures related to efficiency, either average or total values, are classified as minimization of the average percent project delay (APPD) if the activity duration is deterministic; and maximization of robustness in the cases of the research presented by Zhu et al. [20], Chen et al. [21], and Wang et al. [22]. On the other hand, delays are also influenced by project weights, leading to the weighted project delay minimization (WPD) objective.
  • Completion: The completion time of a project, or makespan, is defined as the time when all activities related to the project are fully completed. Meanwhile, weights are used to minimize the weighted makespan (WM), where the makespan value is multiplied by the corresponding weight, so the higher the weight, the greater the impact it has on the objective function. Table 1 shows the existing research in the reviewed literature that addresses time-based objective functions.

4.1.2. Cost-Based Objectives

The goal of minimizing project costs in an RCMPSP is to optimize allocation of resources across multiple projects, thereby reducing the total expenses associated with project execution. Maximizing total profit while minimizing project costs can involve various factors, such as minimizing the expenses associated with the allocation and utilization of resources, including labor, equipment, and materials. This ensures that resources are not idle and are used effectively across multiple projects. In addition, projects must be completed on or before deadlines to avoid penalties. This also allows for quicker project finishes, increasing the capacity for taking on new projects. This dual focus on cost minimization and profit maximization ensures that projects are both cost-effective and financially rewarding. Table 2 shows the existing research addressing cost-based objective functions.

4.1.3. Cost- and Time-Based Objective Functions

Project completion time and resource use are two of the most extensively studied factors in the literature. In the previous sections, the related objective functions were defined individually. Table 3 now shows the existing research that addresses both resource and time objectives together.

4.1.4. Resource Leveling Objectives

Resources should be managed in such a way that all activities get completed without encountering shortages. Resource management enables a project to be accomplished on time, at or below cost, and without compromising quality. Nevertheless, resource scarcity and common activity requirements will lead to conflicts in schedules. These conflicts worsen when dealing with a limited number of resources assigned to multiple simultaneous projects. Hence, there should be an efficient approach to consuming available resources [82]. Resource leveling addresses this issue by trying to make resource consumption as efficient as possible without extending the project completion time [87].
In Maenhout and Vanhoucke’s [63] approach, an attempt was made to level staffing requirements over the planning horizon, which reduced the need for costly temporal resources and overtime significantly.
Table 4 shows the existing research that addresses the resource leveling objective.

4.1.5. Research on Objective Functions: Summary and Analysis

Figure 2 classifies the works’ percentages according to the different classifications proposed. The most frequently considered objective functions are makespan minimization (38.75%), total project cost minimization (18.75%), and cost-time (12.50%). Weighted project delay (7.50%) and resource leveling (6.25%) are the next most pursued objectives corresponding to completion and delay sub-classifications.
For a more in-depth review, Figure 3 and Figure 4 show the percentage of works that consider time-based and cost-based objective functions, respectively. As can be observed in Figure 3 and Figure 4, makespan (66%) and total project cost (83%) are the most studied.

4.2. Based on Solution Methods

In real life, project constraints present only one of the challenges in project planning. Over the past two decades, various techniques of planning project scheduling under resource constraints were proposed, implemented, and controlled, which can broadly be categorized into exact and approximate methods. In fact, it is known that the Resource-Constrained Project-Scheduling Problem has a history longer than 40 years. There are two approaches, exact and approximate, for solving the problem. Each of these approaches has disadvantages and advantages. Exact approaches for solving the RCPSP were first proposed by Talbot [88], followed by Sprecher and Drexl [89]. Exact methods provide optimal results. Exact methods include Dynamic Programming, Constraint Programming, and Mixed Integer Programming, including Lagrangian Relaxation, Zero-One Programming, and Branch and Bound (B&B). These algorithms only solve small problems and cannot find optimal solutions in reasonable computation times. Thus, these algorithms cannot work for large and complex projects. Many research papers have employed exact methods to deal with RCPSP [90,91].
To overcome the computational burden of exact methods, at the expense of optimality, approximate methods are an alternative. These methods, instead of searching the entire problem space, search only a part of it, so the results may not be optimal. They aim, instead, to achieve an approximate solution, but they can solve huge problems quickly.
The approaches are categorized into two different groups: (1) approaches based on heuristic methods such as PR-based approaches, Forward and Backward Improvement (FBI), and Network analysis; and (2) approaches based on meta-heuristic methods such as genetic algorithm (GA), Tabu Search (TS), Simulated Annealing (SA), and Ant Colony Optimization (ACO) [14,16,30,47,67,92,93]. Recent years have witnessed a rise in hybrid optimization approaches for solving complex variants, like the Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP). For instance, Toffolo et al. [40] proposed an integer programming-based approach for multi-mode scheduling, while Zarei et al. [77] explored a bi-objective hybrid model combining MILP with GAs. Other hybrid algorithms merge TS with decomposition methods [94] or integrate local searching within evolutionary algorithms to improve convergence speed and solution diversity.
In addition, Artificial Intelligence (AI) and machine learning techniques are increasingly applied in project scheduling. Chen et al. [54] proposed a genetic programming framework for stochastic RCMPSP under project insertions. Neural networks have also been explored for predictive modeling of activity durations and decision support in dynamic environments (e.g., Hematian et al. [80] and Yuan et al. [95]). These AI-based approaches enhance adaptability and robustness in uncertain and multi-mode settings. An overview of the project scheduling problem can be seen in Figure 5.
Table 5 and Table 6 show the works that used each exact or approximate algorithm, respectively, to solve the problem.
Initially, RCMPSP variants were solved mainly using mathematical models and PR-based heuristics. With increasing complexity and the emergence of new solution techniques, a broader array of proposed solution methodologies was expanded. Figure 6 shows the percentages of use of approximate and exact algorithms. It is clear that meta-heuristics are the most widely used (65%).
To identify the primary solution methods employed for addressing the problem in recent years, Figure 7 illustrates the research conducted since 2013, focusing on methods that have been examined in a minimum of 12 studies.
To the best of our knowledge, PR-based heuristic and genetic algorithms are the most used algorithms for solving the problem since the beginning, presenting a stable growth since 2013, with 37% and 14% of studies, respectively. Algorithms based on Tabu search (8%), Particle Swarm Optimization (PSO), and simulated annealing appear in up to 6% of the works. Furthermore, algorithms based on multi-agent systems and integer programming are used in 4% of the works. Finally, algorithms based on linear programming showed important growth in the last three years.

4.3. Based on Benchmarks

When research on the RCMPSP first began, there were no established instance sets available to assess the performance of the proposed algorithms, so most studies relied on problem examples for validation. This approach is still common in recent studies, primarily because of the numerous features introduced and the absence of instance sets for each specific problem variant. Furthermore, many studies evaluate their models and algorithms using instances they generate themselves for the particular RCMPSP variant they are examining. Kolisch and Sprecher [97] proposed a project scheduling problem library (PSPLIB) for study of the RCPSP. Subsequently, numerous studies on the RCMPSP utilized that benchmark in their numerical experiments by merging two or more single-project instances, incorporating the necessary elements to address the relevant features, and creating specific multi-project instances. Additionally, various studies were conducted using real-world instances, highlighting the significance of this problem in the industrial sector. The initial and most well-known set of instances is the multi-project scheduling problem library (MPSPLIB), presented by Homberger [98], which focuses on RCMPSP with local resources. MPSPLIB contains 80 generated instances from the combination of 2, 5, 10, or 20 projects from the PSPLIB, each consisting of 30, 90, or 120 activities. Each project is assigned an arrival time, and resources can be utilized both globally and locally. Later, this library was expanded by Homberger [99], adding 60 more instances that vary in terms of access to local resources. MPSPLIB supports the online evaluation of solutions and offers a range of objective functions. Another notable variant with a specific set of instances is the multi-mode RCMPSP. This set was developed for the MISTA-2013 challenge and is composed of project groups taken from the PSPLIB by adding multiple execution modes. Table 7 shows the research in the reviewed literature that uses each instance set.
Figure 8 shows the percentages of works using the different instance sets described above. The generated sets represent the highest percentage of the most used benchmark (27%). Then, the second highest percentage is represented by the PSPLIB in the different works, at 23%. It is important to note that 20% of the research was conducted using real-world-based instances.

5. Discussion and Findings

The main goal of this section is to provide an insightful analysis of advancements in multi-project scheduling under conditions of uncertainty and resource flexibility. A brief description of them was presented in Section 2, and in the following section achievements will be reported for each of them.
Key findings are organized around the major objectives in this domain, such as minimization of project makespan, minimization of project cost, or resource leveling. Overall, while minimization of project delay or project makespan is not always considered an objective in papers about RCMPSP, some papers take it into account and propose novel algorithms or models to optimize it, along with other objectives such as minimization of project cost. This is because delay, which refers to the amount of time by which a project is postponed or extended beyond its original due date, is often seen as a result.
This section provides a detailed analysis of the studies reviewed in earlier sections, focusing exclusively on those addressing real-world-based case studies, to survey the gap between theoretical approaches and practical applications concerning the RCMPSP and related variants. Table 8 presents research developed in real environments, highlighting the significance of this problem within the industrial sector. Column 2 shows the application domain. Columns 3–5 show the dimensions of the scenarios handled by each case in terms of the maximum number of projects, the maximum number of activities, and the maximum number of different resources considered. Following the categorization provided in Section 4, columns 6–10 report the objective functions.
Additionally, to analyze the different objective functions applied in real environments, this table shows the applications in the manufacturing field that are the most representative ones, while 15 real-world-based cases are examined. The most used objectives are related to time-based objective functions. Based on the reported works, it can be observed that makespan minimization is the most used one, followed by minimization of total project cost.
To provide a broader perspective, a separate table (Table 9) was compiled in which the key contributions, strengths, weaknesses, and future suggestions of some related studies were randomly reviewed. Through this comparative analysis, existing research gaps are identified, and the novelty and relevance of the proposed approach are clarified. In this way, a more comprehensive understanding of the current state of the field is facilitated, and the positioning of the present work within the broader academic discourse is strengthened.

6. Conclusions

This paper shows a comprehensive review of multi-project scheduling approaches, with a focus on uncertainty and resource flexibility methodologies. This is a topic of growing interest for academics and users. From the SLR [19], the authors initially selected a limited number of studies (52 papers) from a pool of 108 papers. Additional relevant works and newly published papers from 2024 were subsequently incorporated, resulting in a final set of 76 papers being curated for review.
The paper presented a review of RCMPSP evolution by analyzing related variants in terms of the objective functions, proposed solution methods, benchmarks, and connection to practice. The following text will report the achievements in light of the research questions.
RQ1. 
What are the objectives in multi-project scheduling problems?
The objective functions in multi-project scheduling typically include time-based, cost-based, cost-and-time-based, and resource leveling objectives. Among these, time-based and cost-based objectives are the most extensively studied. Specifically, minimization of the makespan, weighted project delay, and total project cost are the predominant goals within these categories.
RQ2. 
What are the different types of solving methods in multi-project scheduling problems?
There are two primary approaches for solving multi-project scheduling problems: exact and approximate methods. Among these, approximate algorithms are the most frequently used for addressing RCMPSP. Notably, genetic algorithms and PR-based algorithms are particularly prominent in the resolution of these issues.
RQ3. 
What types of instance sets are used in multi-project scheduling problems?
Regarding benchmarks, various instance sets are utilized, including generated instances, problem examples, real-world instances, MPSPLIB, PSPLIB, PostgreSQL, MMLIB, MPLIB1, MPLIB2, MISTA 2013, and iMOPSE. Among these, generated sets and the PSPLIB are the most frequently used, representing the two highest percentages of instance sets employed in research and practical applications.
RQ4. 
What are the potential future research directions in multi-project scheduling problems?
It is hoped that this work will encourage future research to explore this area further, fostering the development of more effective strategies and methodologies. A summary of the identified problems, objectives, and proposed future research directions is presented in Table 10.
This research brings the user a researcher database for existing methodologies to improve investigation in the future to solve the problem using the available information on these topics and approaches. For example, consider the following:
  • Integrating concepts such as activity flexibility and activity priority into project scheduling.
  • Different types of uncertain factors should be considered, for example, dynamic project arrival, stochastic resource availability, etc., and their impact on the resource usage deviation levels of the projects should be measured.
  • Deviation in customer demand.
  • Different scenarios for project duration (pessimistic, most probable, and optimistic).
  • Design different PRs for the stochastic environment and compare them to the performance of the previous PRs.
  • Use the exact method along with a heuristic or meta-heuristic method to compare the results.
  • Analyze whether the company accepts delays and late penalty fees or outsourcing.

Funding

This work was supported by Fundação para a Ciência e Tecnologia, IP (FCT) under grant [UI/BD/151165/2021] and within the R&D Units Project Scope: UID/00319/Centro ALGORITMI (ALGORITMI/UM). Furthermore, we would like to thank the Research Centre in Digital Services (CISeD) and the Instituto Politécnico de Viseu for their support. I.P. was funded by National Funds through the Foundation for Science and Technology (FCT) within the scope of project UIDB/05583/2020 and DOI identifier https://doi.org/10.54499/UIDB/05583/2020.

Data Availability Statement

No new data were created or analyzed in this study.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

AbbreviationDescription
ACOAnt Colony Optimization Algorithm
AIArtificial Intelligence
APDAverage Project Delay
APPDAverage Percent Project Delay
B&BBranch and Bound
CPMCritical Path Method
FBIForward and Backward Improvement
FRCPSPFlexible Resource-Constrained Project Scheduling Problem
GAGenetic Algorithm
IPInteger Programming
MIPMixed Integer Programming
MILPMixed Integer Linear Programming
MPSPLIBMulti-Project Scheduling Problem Library
MRCPSPMulti-Mode Resource-Constrained Project Scheduling Problem
NP-hardNondeterministic Polynomial-Time Hard
PERTProgram Evaluation and Review Technique
PSOParticle Swarm Optimization
PRPriority Rule
PSPLIBProject Scheduling Problem Library
RCPSPResource-Constrained Project Scheduling Problem
RCMPSPResource-Constrained Multi-Project Scheduling Problem
RCPSP-FRMRCPSP with Flexible Resource Management
RCPSP-FWPRCPSP with Flexible Work Profiles
RQResearch Question
SASimulated Annealing
SGSSchedule Generation Scheme
SLRSystematic Literature Review
TSTabu Search
WPDWeighted Project Delay
WMWeighted Makespan

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Algorithms 18 00314 g001
Figure 1. Methodology, Aghileh et al. [19].
Figure 1. Methodology, Aghileh et al. [19].
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Figure 2. Percentage of research by classification of the different objective functions studied.
Figure 2. Percentage of research by classification of the different objective functions studied.
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Figure 3. Percentage of research by classification of time-based objective function studied.
Figure 3. Percentage of research by classification of time-based objective function studied.
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Figure 4. Percentage of research by classification of cost-based objective function studied.
Figure 4. Percentage of research by classification of cost-based objective function studied.
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Figure 5. An overview of project-scheduling problems and solving methods.
Figure 5. An overview of project-scheduling problems and solving methods.
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Figure 6. Percentages of different solution methods applied to the RCMPSP.
Figure 6. Percentages of different solution methods applied to the RCMPSP.
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Figure 7. Contribution of different algorithms applied to scheduling problems since 2013.
Figure 7. Contribution of different algorithms applied to scheduling problems since 2013.
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Figure 8. Percentage of research on a different set of instances.
Figure 8. Percentage of research on a different set of instances.
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Table 1. Research works that address time-based objective functions.
Table 1. Research works that address time-based objective functions.
Objective FunctionResearch Works
APPD [23]
APD [24,25,26]
WPD [27,28,29,30,31,32]
Delay [33,34,35]
Makespan [2,3,7,16,24,25,26,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]
Sum of WM [14,20,60]
Table 2. Research works that address cost.
Table 2. Research works that address cost.
Objective FunctionResearch Works
Total project cost [15,47,61,62,63,64,65,66,67,68,69,70,71,72,73]
Total project profit [74,75,76]
Table 3. Research works that address cost-and-time-based objectives.
Table 3. Research works that address cost-and-time-based objectives.
ObjectiveAuthor
Time-BasedCost-Based
Min the makespanMin the cost [77,78,79,80,81]
Min the difference between resource demands and resource uniform levels [82]
Min the total cost of the shared resources [83]
Min the delayMin the cost [84,85,86]
Table 4. Research works that address the resource leveling objective.
Table 4. Research works that address the resource leveling objective.
Objective FunctionResearch Works
Balanced resource utilization [32,36,49,63,82]
Table 5. Reports of exact solution methods for RCMPSP variants.
Table 5. Reports of exact solution methods for RCMPSP variants.
Solution MethodsResearch Works
ExactB&B [63]
IP [40,53,72]
MILP [33,38,49,58,59,62,71,77,96]
Table 6. Reports of approximate solution methods for RCMPSP variants.
Table 6. Reports of approximate solution methods for RCMPSP variants.
Solution MethodsResearch Works
HeuristicPR [2,7,23,25,31,41,46,51,55,56,78]
Multi agent [74,86,93]
Meta-heuristicGA [14,15,16,23,24,26,32,34,35,36,37,39,44,45,48,50,52,54,56,69,70,75,76,79,81,82,83,84,85]
SA [15,34,37,42,60]
TS [43,44,47,68,73,94]
PSO [44,47,61,65,73]
ACO [3,35]
Fuzzy [30,64,80,95]
Table 7. Research works that address benchmarks.
Table 7. Research works that address benchmarks.
InstancesResearch Works
Generated instances [26,28,29,31,32,39,48,49,50,52,56,60,61,63,64,67,68,71,72,80,94,95]
Problem examples [42,58,65,74,78,85]
Real-world instances [14,15,33,37,38,43,44,45,53,57,62,69,75,76,81]
MPSPLIB [2,24,41,46,51,66,70,93]
PSPLIB [3,7,16,21,28,36,45,52,54,57,58,84,85,86,88,97]
PostgreSQL [73]
MMLIB [30,77]
MPLIB1 [25]
MPLIB2 [23]
MISTA 2013 [34,40]
iMOPSE [79]
Table 8. Research works applied to real environments.
Table 8. Research works applied to real environments.
Research WorksInstanceObjective Functions
Domain# Proj.# Activities# Rsrc.Rsrc.Time
Total Project CostTotal ProfitDelayMakespanSum of Weighted Makespan
[14]Heath Care389 √
[15]Undefined-287√
[33]Manufacturing1111475 √
[37]Construction1206 √
[38]Undefined242 √
5
[43]Undefined230- √
[44]Undefined230175 √
[45]Manufacturing353 √
9
13
[53] Manufacturing475 √
[57]Manufacturing1383 √
[62]Manufacturing2011-√
15
25
14
[69]Manufacturing12106√ √
[75]Financial3-20 √
[76]Construction10106 √
[81]IT product development108-√ √
Table 9. Comparison of the papers.
Table 9. Comparison of the papers.
Feature [31] [32] [58] [100] [101]
TopicPriority rules for the dynamic stochastic
RCMPSP.		A robust multi-project scheduling problem under a resource dedication-transfer policy.Algorithm for the multi-mode
resource-constrained multi-project scheduling problem (MRCMPSP).		Heuristic optimization for scheduling.Literature survey on solving the RCPSP
and RCMPSPs from an activity assumptions perspective.
Key
Contribution		Control systems is the decision process for choosing the next activity to seize a given resource.Introduces a hierarchical multi-objective optimization model under the resource dedication-transfer policy.MRCMPSP with Multi-Mode Execution and Budget Constraints.Comparison of different approaches to project scheduling under uncertainty.Categorization of project activities.
StrengthsRealistic modeling with contractor influence and budget constraints.Adaptive and efficient in handling high-dimensional data.Competitive performance against other algorithms.Provides a good overview of the major approaches to handling uncertainty in project scheduling.
Offers a critical perspective on the strengths and weaknesses of each approach.		Well-organized survey.
WeaknessesComputationally complex.

Model may be harder to scale in larger industrial settings.		Focused on random datasets.Limited to benchmark problems.

No real-world case study.		Needs comparison with modern techniques.Limited discussion of real-world applications.
Future Work SuggestedExtend to more project types and larger projects.Test on broader datasets.

Hybridize with other algorithms.		Extend to dynamic/multi-modal problems.

Integrate with other metaheuristics.		Generation of robust multi-resource baseline schedules.
Implementation and validation of reactive scheduling mechanisms in a project-scheduling environment.		Addressing dynamic scheduling challenges.
Table 10. Problem, objective, and future work.
Table 10. Problem, objective, and future work.
ProblemObjectiveFuture Work
Inefficient resource utilization in real environments.Minimize idle resources to enable efficient resource use.Study and promote the use of objectives such as minimizing idle resources in real-world scenarios.
Inability to consider the size and complexity of different projects with current solution methods.Develop advanced methods tailored to current project requirements.Investigate and expand the application of multi-agent systems as a promising approach for solving multi-project scheduling problems.
Limited evaluation of proposed algorithms in the RCMPSP domain.Enhance the reliability and effectiveness of algorithms for multi-project scheduling.Conduct thorough assessment and comparison of algorithmic execution to advance the field of RCMPSP research.
Limited exploration of AI and hybrid methods in dynamic multi-project settings.Improve adaptability and efficiency in complex, uncertain environments.Investigate hybrid metaheuristic and AI models for stochastic multi-project scheduling.
Inability to adapt schedules in real time when project dynamics change.Increase responsiveness and robustness of project plans.Dynamic project environments: investigate rescheduling strategies in environments with dynamically arriving and departing projects.
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Aghileh, M.; Tereso, A.; Alvelos, F.; Lopes, M.O.M. Multi-Project Scheduling with Uncertainty and Resource Flexibility: A Narrative Review and Exploration of Future Landscapes. Algorithms 2025, 18, 314. https://doi.org/10.3390/a18060314

AMA Style

Aghileh M, Tereso A, Alvelos F, Lopes MOM. Multi-Project Scheduling with Uncertainty and Resource Flexibility: A Narrative Review and Exploration of Future Landscapes. Algorithms. 2025; 18(6):314. https://doi.org/10.3390/a18060314

Chicago/Turabian Style

Aghileh, Marzieh, Anabela Tereso, Filipe Alvelos, and Maria Odete Monteiro Lopes. 2025. "Multi-Project Scheduling with Uncertainty and Resource Flexibility: A Narrative Review and Exploration of Future Landscapes" Algorithms 18, no. 6: 314. https://doi.org/10.3390/a18060314

APA Style

Aghileh, M., Tereso, A., Alvelos, F., & Lopes, M. O. M. (2025). Multi-Project Scheduling with Uncertainty and Resource Flexibility: A Narrative Review and Exploration of Future Landscapes. Algorithms, 18(6), 314. https://doi.org/10.3390/a18060314

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