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Keywords = RCPSP

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23 pages, 769 KB  
Article
Enhancing Urban Air Mobility Scheduling Through Declarative Reasoning and Stakeholder Modeling
by Jeongseok Kim and Kangjin Kim
Aerospace 2025, 12(7), 605; https://doi.org/10.3390/aerospace12070605 - 3 Jul 2025
Viewed by 566
Abstract
The goal of this paper is to optimize mission schedules for vertical airports (vertiports in short) to satisfy the different needs of stakeholders. We model the problem as a resource-constrained project scheduling problem (RCPSP) to obtain the best resource allocation and schedule. As [...] Read more.
The goal of this paper is to optimize mission schedules for vertical airports (vertiports in short) to satisfy the different needs of stakeholders. We model the problem as a resource-constrained project scheduling problem (RCPSP) to obtain the best resource allocation and schedule. As a new approach to solving the RCPSP, we propose answer set programming (ASP). This is in contrast to the existing research using MILP as a solution to the RCPSP. Our approach can take complex scheduling restrictions and stakeholder-specific requirements. In addition, we formalize and include stakeholder needs using a knowledge representation and reasoning framework. Our experiments show that the proposed method can generate practical schedules that reflect what stakeholders actually need. In particular, we show that our approach can compute optimal schedules more efficiently and flexibly than previous approaches. We believe that this approach is suitable for the dynamic and complex environments of vertiports. Full article
(This article belongs to the Special Issue Next-Generation Airport Operations and Management)
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25 pages, 933 KB  
Article
Efficient Rollout Algorithms for Resource-Constrained Project Scheduling with a Flexible Project Structure and Uncertain Activity Durations
by Chunlai Yu, Xiaoming Wang and Qingxin Chen
Mathematics 2025, 13(9), 1395; https://doi.org/10.3390/math13091395 - 24 Apr 2025
Viewed by 625
Abstract
This study addresses the resource-constrained project scheduling problem with flexible structures and uncertain activity durations. The problem is formulated as a Markov decision process, with the optimal policy determined through stochastic dynamic programming. To mitigate the curse of dimensionality in large-scale problems, several [...] Read more.
This study addresses the resource-constrained project scheduling problem with flexible structures and uncertain activity durations. The problem is formulated as a Markov decision process, with the optimal policy determined through stochastic dynamic programming. To mitigate the curse of dimensionality in large-scale problems, several approximate methods are proposed to derive suboptimal policies. In addition to traditional methods based on priority rules and metaheuristic algorithms, we focus on the application of rollout algorithms. To improve the computational efficiency of the rollout algorithms, only the best-performing priority rules are employed for action evaluation, and the common random numbers technique is also incorporated. Experimental results demonstrate that rollout algorithms significantly outperform priority rules and metaheuristics. The common random numbers technique not only enhances computational efficiency but also improves the accuracy of action selection. The post-rollout algorithm reduces computation time by 44.37% compared to the one-step rollout, with only a 0.02% performance gap. In addition, rollout algorithms perform more stably than other methods under different problem characteristics. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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23 pages, 2981 KB  
Article
IoT-Driven Intelligent Scheduling Solution for Industrial Sewing Based on Real-RCPSP Model
by Huu Dang Quoc, Loc Nguyen The, Truong Bui Quang and Phuong Han Minh
Future Internet 2025, 17(2), 56; https://doi.org/10.3390/fi17020056 - 26 Jan 2025
Cited by 1 | Viewed by 1585
Abstract
Applying IoT systems in industrial production allows data collection directly from production lines and factories. These data are aggregated, analyzed, and converted into reports to support manufacturers. Business managers can quickly and easily grasp the situation, making timely and effective management decisions. In [...] Read more.
Applying IoT systems in industrial production allows data collection directly from production lines and factories. These data are aggregated, analyzed, and converted into reports to support manufacturers. Business managers can quickly and easily grasp the situation, making timely and effective management decisions. In industrial sewing, IoT applications collect production data from sewing lines, especially from industrial sewing machines, and transmit that data to cloud-based systems. This allows businesses to analyze production situations, thereby improving management capacity. This article explores the implementation of IoT applications at industrial sewing enterprises, focusing on data collection during the production process and proposing a data structure to integrate this information into the company’s MIS system enterprise. In addition, the research also considers applying the Real-RCPSP problem to support businesses in planning automatic production operations. Full article
(This article belongs to the Special Issue Joint Design and Integration in Smart IoT Systems)
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21 pages, 2146 KB  
Article
Optimization Model for Mine Backfill Scheduling Under Multi-Resource Constraints
by Yuhang Liu, Guoqing Li, Jie Hou, Chunchao Fan, Chuan Tong and Panzhi Wang
Minerals 2024, 14(12), 1183; https://doi.org/10.3390/min14121183 - 21 Nov 2024
Cited by 1 | Viewed by 1070
Abstract
Addressing the resource constraints, such as manpower and equipment, faced by mine backfilling operations, this study proposed an optimization model for backfill scheduling based on the Resource-Constrained Project Scheduling Problem (RCPSP). The model considered backfilling’s multi-process, multi-task, and multi-resource characteristics, aiming to minimize [...] Read more.
Addressing the resource constraints, such as manpower and equipment, faced by mine backfilling operations, this study proposed an optimization model for backfill scheduling based on the Resource-Constrained Project Scheduling Problem (RCPSP). The model considered backfilling’s multi-process, multi-task, and multi-resource characteristics, aiming to minimize total delay time. Constraints included operational limits, resource requirements, and availability. The goal was to determine optimal resource configurations for each stope’s backfilling steps. A heuristic genetic algorithm (GA) was employed for solution. To handle equipment unavailability, a new encoding/decoding algorithm ensured resource availability and continuous operations. Case verification using real mine data highlights the advantages of the model, showing a 20.6% decrease in completion time, an 8 percentage point improvement in resource utilization, and a 47.4% reduction in overall backfilling delay time compared to traditional methods. This work provides a reference for backfilling scheduling in similar mines and promotes intelligent mining practices. Full article
(This article belongs to the Special Issue Advances in Mine Backfilling Technology and Materials)
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21 pages, 1929 KB  
Article
An Agile Adaptive Biased-Randomized Discrete-Event Heuristic for the Resource-Constrained Project Scheduling Problem
by Xabier A. Martin, Rosa Herrero, Angel A. Juan and Javier Panadero
Mathematics 2024, 12(12), 1873; https://doi.org/10.3390/math12121873 - 16 Jun 2024
Cited by 2 | Viewed by 1329
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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25 pages, 3878 KB  
Article
A GA-Based Scheduling Method for Civil Aircraft Distributed Production with Material Inventory Replenishment Consideration
by Xumai Qi, Dongdong Zhang, Hu Lu and Rupeng Li
Mathematics 2023, 11(14), 3135; https://doi.org/10.3390/math11143135 - 16 Jul 2023
Cited by 1 | Viewed by 1978
Abstract
The production of civil aircrafts is confronted with a significant demand for the interconnectivity of production resources among distributed factories, while the complex coupling relationships among various production resources might restrict the improvement of production efficiency. Therefore, researching scheduling methods for civil aircraft [...] Read more.
The production of civil aircrafts is confronted with a significant demand for the interconnectivity of production resources among distributed factories, while the complex coupling relationships among various production resources might restrict the improvement of production efficiency. Therefore, researching scheduling methods for civil aircraft distributed production is necessary, but previous studies have not taken material inventory into account sufficiently. This article proposes a scheduling method for civil aircraft distributed production that aims to minimize the production time to complete all the jobs in a large production station under the condition of material inventory replenishment. Firstly, we analyze the factors constraining civil aircraft production efficiency, and formulize the production scheduling problem into the Resource-Constrained Project Scheduling Problem model with Inventory Replenishment (RCPSP-IR). Precedence constraints and resource constraints, especially the inventory constraints, are mainly considered in RCPSP-IR. To solve the corresponding scheduling problem, the Genetic Algorithm (GA) is applied and multiple approaches are introduced to handle the complex constraints and avoid local optimum. Finally, we applied the proposed scheduling method to a case study of a jet twin-engine civil aircraft production of COMAC. The results of the case study show that the proposed method can give a nearly optimal scheduling strategy to be applied to actual civil aircraft production. Full article
(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)
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10 pages, 914 KB  
Article
On Propeties of the LIP Model in the Class of RCPSPs
by Andrey I. Kibzun and Varvara A. Rasskazova
Mathematics 2023, 11(9), 2086; https://doi.org/10.3390/math11092086 - 27 Apr 2023
Viewed by 1108
Abstract
The Resource-Constrained Project Scheduling Problem (RCPSP) is a significant and important issue in the field of project management. It arises during project planning when resources must be allocated among tasks with specific time constraints. Solving this problem enables the optimization of project execution [...] Read more.
The Resource-Constrained Project Scheduling Problem (RCPSP) is a significant and important issue in the field of project management. It arises during project planning when resources must be allocated among tasks with specific time constraints. Solving this problem enables the optimization of project execution time, minimization of resource costs, and increased efficiency of the entire team’s work. Due to the increasing complexity of projects, the development of new methods and algorithms to solve RCPSP is relevant nowadays. The existing methods for obtaining approximate solutions with guaranteed accuracy are characterized by high computational complexity and are often ineffective in considering the specific constraints of the problem. Fast heuristic approaches also have several drawbacks related to fine-tuning algorithm parameters and strong dependence on the quality of the initial solution. This paper investigates the features of the linear integer programming (LIP) model to solve RCPSP. The proposed LIP model is universal and scalable, enabling it to fully consider all specific aspects of the problem. The paper provides a construction algorithm of a functional space of the model and discusses the estimation of complexity. From the estimation of the mentioned algorithm’s complexity, it is observed that the general complexity of the proposed approach is proportional to a controlled parameter of the LIP. Increasing this controlled parameter can significantly reduce the dimensionality of the initial problem, thus leading to the effectiveness of the LIP model-based approach in terms of computational resources. An upper bound for the value of this parameter is obtained for a special case of the RCPSP. Using the obtained balanced value, a numerical experiment was carried out on real-world samples. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
11 pages, 1313 KB  
Article
Complicated Time-Constrained Project Scheduling Problems in Water Conservancy Construction
by Song Zhang, Xiaokang Song, Liang Shen and Lichun Xu
Processes 2023, 11(4), 1110; https://doi.org/10.3390/pr11041110 - 5 Apr 2023
Cited by 4 | Viewed by 3209
Abstract
Water conservancy project scheduling is an extension to the classic resource-constrained project scheduling problem (RCPSP). It is limited by special time constraints called “forbidden time windows” during which certain activities cannot be executed. To address this issue, a specific RCPSP model is proposed, [...] Read more.
Water conservancy project scheduling is an extension to the classic resource-constrained project scheduling problem (RCPSP). It is limited by special time constraints called “forbidden time windows” during which certain activities cannot be executed. To address this issue, a specific RCPSP model is proposed, and an approach is designated for it which incorporates both a priority rule-based heuristic algorithm to obtain an acceptable solution, and a hybrid genetic algorithm to further improve the quality of the solution. In the genetic algorithm, we introduce a new crossover operator for the forbidden time window and adopt double justification and elitism strategies. Finally, we conduct simulated experiments on a project scheduling problem library to compare the proposed algorithm with other priority-rule based heuristics, and the results demonstrate the superiority of our algorithm. Full article
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24 pages, 5684 KB  
Article
Optimization of Apron Support Vehicle Operation Scheduling Based on Multi-Layer Coding Genetic Algorithm
by Jichao Zhang, Xiaolei Chong, Yazhi Wei, Zheng Bi and Qingkun Yu
Appl. Sci. 2022, 12(10), 5279; https://doi.org/10.3390/app12105279 - 23 May 2022
Cited by 14 | Viewed by 3219
Abstract
Operation scheduling of apron support vehicles is an important factor affecting aircraft support capability. However, at present, the traditional support methods have the problems of low utilization rate of support vehicles and low support efficiency in multi-aircraft support. In this paper, a vehicle [...] Read more.
Operation scheduling of apron support vehicles is an important factor affecting aircraft support capability. However, at present, the traditional support methods have the problems of low utilization rate of support vehicles and low support efficiency in multi-aircraft support. In this paper, a vehicle scheduling model is constructed, and a multi-layer coding genetic algorithm is designed to solve the vehicle scheduling problem. In this paper, the apron support vehicle operation scheduling problem is regarded as a Resource-Constrained Project Scheduling Problem (RCPSP), and the support vehicles and their support procedures are adjusted via the sequential sorting method to achieve the optimization goals of shortening the support time and improving the vehicle utilization rate. Based on a specific example, the job scheduling before and after the optimization of the number of support vehicles is simulated using a multi-layer coding genetic algorithm. The results show that compared with the traditional support scheme, the vehicle scheduling time optimized via the multi-layer coding genetic algorithm is obviously shortened; after the number of vehicles is optimized, the support time is further shortened and the average utilization rate of vehicles is improved. Finally, the optimized apron support vehicle number configuration and the best scheduling scheme are given. Full article
(This article belongs to the Topic Artificial Intelligence Models, Tools and Applications)
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18 pages, 3694 KB  
Article
Application of a Genetic Algorithm for Proactive Resilient Scheduling in Construction Projects
by Martina Milat, Snježana Knezić and Jelena Sedlar
Designs 2022, 6(1), 16; https://doi.org/10.3390/designs6010016 - 15 Feb 2022
Cited by 6 | Viewed by 3803
Abstract
During the execution of construction projects, uncertain events, such as delays, prolongations and disruptions of project activities, have the potential to cause a significant deviation between the planned and realized state of a project. As a result, progress on important project objectives can [...] Read more.
During the execution of construction projects, uncertain events, such as delays, prolongations and disruptions of project activities, have the potential to cause a significant deviation between the planned and realized state of a project. As a result, progress on important project objectives can decrease and this leads to critical delays as well as heavy profit loss. For this reason, we propose the implementation of the customized evolutionary algorithm to generate resilient baseline schedules which include a sufficient number of time floats to absorb the negative impact of uncertainty. This way, the baseline solution is searched as a trade-off between project duration, its final profit and the overall baseline stability. The proposed algorithm is applied to real construction project data and the results of the analysis suggest improved stability for resilient baseline schedules. Application of the genetic algorithm to solve the existing multi-objective problem enables practical implementation of new technologies and methods in construction management. Resilient baseline schedules can be used in an uncertain environment to achieve more accurate predictions and support decision making in the areas of construction scheduling and costing. Full article
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21 pages, 10128 KB  
Article
Optimization Model for the Pavement Pothole Repair Problem Considering Consumable Resources
by Shu-Shun Liu, Agung Budiwirawan, Muhammad Faizal Ardhiansyah Arifin, Wei Tong Chen and Ying-Hua Huang
Symmetry 2021, 13(3), 364; https://doi.org/10.3390/sym13030364 - 24 Feb 2021
Cited by 6 | Viewed by 4026
Abstract
When heavy rain strikes Taiwan, it always results in cracks in road pavement, and damages arising from potholes. Tremendously compromising road safety, road users may have fatal accidents caused by untimely repair actions. The road maintenance department needs to take the responsibilities for [...] Read more.
When heavy rain strikes Taiwan, it always results in cracks in road pavement, and damages arising from potholes. Tremendously compromising road safety, road users may have fatal accidents caused by untimely repair actions. The road maintenance department needs to take the responsibilities for road sections in the form of inspections and faces the decision about how to properly allocate available resources to repair pavement damages immediately. When performing pavement repair works, we need to consider the resource consumption behavior and explore the mechanism of replenishing resources and calculating the return time. Therefore, in order to help maintenance units to deal with consumable resource issues, this study proposes a novel approach to offer the mechanism of consumable resource calculation, which is difficult to solve through the traditional vehicle routing problem (VRP) approach. This proposed model treats the pothole repair problem as a resource-constrained project scheduling problem (RCPSP), which is capable of resolving such consumable resource considerations. The proposed model was developed by adopting constraint programming (CP) techniques. Research results showed that the proposed model is capable of providing the optimal decisions of pavement pothole repair tasks and also meets practical requirements to make appropriate adjustment, and helps the maintenance unit to shorten total repair duration and optimize resource assignment decisions of pavement maintenance objectives. Full article
(This article belongs to the Special Issue Symmetry in Civil Engineering)
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23 pages, 1906 KB  
Article
Emergency Repair Scheduling Model for Road Network Integrating Rescheduling Feature
by Shu-Shun Liu, Muhammad Faizal Ardhiansyah Arifin, Wei Tong Chen and Ying-Hua Huang
Appl. Sci. 2021, 11(4), 1447; https://doi.org/10.3390/app11041447 - 5 Feb 2021
Cited by 5 | Viewed by 3006
Abstract
When a natural disaster occurs, road maintenance departments always face the challenge of how to assign repair resources properly to recover damaged road segments as soon as possible. From the literature review, most studies treat such problems as a vehicle routing problem (VRP). [...] Read more.
When a natural disaster occurs, road maintenance departments always face the challenge of how to assign repair resources properly to recover damaged road segments as soon as possible. From the literature review, most studies treat such problems as a vehicle routing problem (VRP). In those studies, repair resources are always dispatched as complete crews, and cannot be divided into smaller scales. Furthermore, each disaster point is only allowed one group of resources to recover it, without considering the possibility of accelerating the production rate subjected to specific objectives. Such limitation restricts required resources in an inflexible manner. Therefore, this study defines all repair works as an emergency repair project and adopts the framework of the Resource-Constrained Project Scheduling Problem (RCPSP), which can resolve such complicated resource assignment issue. A novel emergency repair scheduling model for the road network is proposed based on Constraint Programming (CP) as the searching algorithm to facilitate model formulation. According to the RCPSP concepts, disaster points are set as repair activities and resource travel routes between disaster points are set as transit activities. All the repair activities are linked by transit activities and the required resources are assigned accordingly. In order to consider the second-wave hazard events of where new disaster points may occur, and new resources may be added into emergency repair projects, a rescheduling feature is integrated into the proposed model. Through two case studies, research findings show that this model can be easily modulated to adapt to different situations satisfying practical disaster management goals and solving emergency repair scheduling problems for road networks efficiently. Full article
(This article belongs to the Section Civil Engineering)
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26 pages, 2772 KB  
Article
Two-Stage Optimization Model for Life Cycle Maintenance Scheduling of Bridge Infrastructure
by Shu-Shun Liu, Hsin-Yi Huang and Nevy Risna Dyah Kumala
Appl. Sci. 2020, 10(24), 8887; https://doi.org/10.3390/app10248887 - 12 Dec 2020
Cited by 4 | Viewed by 2939
Abstract
As bridge infrastructure ages, the deterioration of materials and hazard events reduce the service quality and compromise the safety of the structure. Therefore, there is a tremendous need for bridge maintenance planning, and such maintenance studies during recent years have focused on the [...] Read more.
As bridge infrastructure ages, the deterioration of materials and hazard events reduce the service quality and compromise the safety of the structure. Therefore, there is a tremendous need for bridge maintenance planning, and such maintenance studies during recent years have focused on the life cycle aspect. To fulfill the budget requirements of life cycle maintenance, an important issue is to ensure that the limited maintenance budget is utilized in an effective way. However, there are few studies that have aimed to assess the topic of budget allocation and the adjustment of bridge life-cycle maintenance issues. In order to resolve such issues, a two-stage optimization model based on constraint programming (CP) is proposed in this study to deal with maintenance scheduling problems. This is facilitated by adopting the resource-constrained project scheduling problem (RCPSP) framework, in which, three plans according to the maintenance time point are considered (i.e., early, middle, and late plans). According to the RCPSP concepts, this study views the budget ceiling as the resource limit, and maintenance plans as activities, so that the feasibility of each maintenance plan depends on the sufficiency of the budget. As the first stage, Model-I (the life cycle lifespan evaluation model) takes a life cycle perspective, evaluating how long it will take to keep all bridges in a serviceable condition with minimum expenditure over the planning cycle, and evaluates the annual budgets that can be used as a reference for users to draft a budget plan. Based on the planning result from Model-I and the actual annual budget approved for the current year, the second stage, Model-II (the annual budget allocation model) then reallocates the actual budget to take into account the importance of all bridges and different costs and benefits of maintenance plans, and revises the suggested annual budget values obtained by Model-I for the following years. Through a case study, the optimized result demonstrates that annual recursive implementation of this two-stage model satisfies the need to adjust existing budgetary data, and provides management personnel with optimized and realistic maintenance decision support for bridge infrastructure. Full article
(This article belongs to the Section Civil Engineering)
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13 pages, 652 KB  
Article
Evaluating Typical Algorithms of Combinatorial Optimization to Solve Continuous-Time Based Scheduling Problem
by Alexander A. Lazarev, Ivan Nekrasov and Nikolay Pravdivets
Algorithms 2018, 11(4), 50; https://doi.org/10.3390/a11040050 - 17 Apr 2018
Cited by 3 | Viewed by 6013
Abstract
We consider one approach to formalize the Resource-Constrained Project Scheduling Problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original problem into combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and [...] Read more.
We consider one approach to formalize the Resource-Constrained Project Scheduling Problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original problem into combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and has to be resided on the continuous time axis meeting additional restrictions. The simplest case of continuous-time scheduling assumes one-to-one correspondence of resources and operations and corresponds to the linear programming problem setting. However, real scheduling problems include many-to-one relations which leads to the additional combinatorial component in the formulation due to operations competition. We research how to apply several typical algorithms to solve the resulted combinatorial optimization problem: enumeration including branch-and-bound method, gradient algorithm, random search technique. Full article
(This article belongs to the Special Issue Algorithms for Scheduling Problems)
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19 pages, 1284 KB  
Article
A Practical and Robust Execution Time-Frame Procedure for the Multi-Mode Resource-Constrained Project Scheduling Problem with Minimal and Maximal Time Lags
by Angela Hsiang-Ling Chen, Yun-Chia Liang and Jose David Padilla
Algorithms 2016, 9(4), 63; https://doi.org/10.3390/a9040063 - 24 Sep 2016
Cited by 4 | Viewed by 6212
Abstract
Modeling and optimizing organizational processes, such as the one represented by the Resource-Constrained Project Scheduling Problem (RCPSP), improve outcomes. Based on assumptions and simplification, this model tackles the allocation of resources so that organizations can continue to generate profits and reinvest in future [...] Read more.
Modeling and optimizing organizational processes, such as the one represented by the Resource-Constrained Project Scheduling Problem (RCPSP), improve outcomes. Based on assumptions and simplification, this model tackles the allocation of resources so that organizations can continue to generate profits and reinvest in future growth. Nonetheless, despite all of the research dedicated to solving the RCPSP and its multi-mode variations, there is no standardized procedure that can guide project management practitioners in their scheduling tasks. This is mainly because many of the proposed approaches are either based on unrealistic/oversimplified scenarios or they propose solution procedures not easily applicable or even feasible in real-life situations. In this study, we solve a more true-to-life and complex model, Multimode RCPSP with minimal and maximal time lags (MRCPSP/max). The complexity of the model solved is presented, and the practicality of the proposed approach is justified depending on only information that is available for every project regardless of its industrial context. The results confirm that it is possible to determine a robust makespan and to calculate an execution time-frame with gaps lower than 11% between their lower and upper bounds. In addition, in many instances, the solved lower bound obtained was equal to the best-known optimum. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms in Optimization and Applications)
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