Scheduling: Algorithms and Applications

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Combinatorial Optimization, Graph, and Network Algorithms".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 28572

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Guest Editor
Faculty of Mathematics, Otto-von-Guericke-University, P.O. Box 4120, D-39016 Magdeburg, Germany
Interests: scheduling, in particular development of exact and approximate algorithms; stability investigations is discrete optimization; scheduling with interval processing times; complexity investigations for scheduling problems; train scheduling; graph theory; logistics; supply chains; packing; simulation and applications
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Special Issue Information

Dear Colleagues,

We invite you to submit your latest research in the area of the development of scheduling algorithms to this Special Issue, “Scheduling: Algorithms and Applications”. We are looking for innovative approaches for solving scheduling problems or interesting applications in the scheduling area. High-quality papers are solicited to address both theoretical and practical scheduling aspects. Submissions are welcome both for traditional scheduling problems and new applications. Potential topics include, but are not limited to, single-criterion and multi-criteria scheduling problems with additional constraints such as e.g. setup times/costs, precedence constraints, batching/lot sizing, resource constraints, as well as scheduling algorithms for problems arising in emerging applications, such as healthcare, transport, and energy management.

Prof. Dr. Frank Werner
Guest Editor

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Keywords

  • enumerative scheduling algorithms
  • approximate scheduling algorithms
  • online algorithms
  • scheduling heuristics, metaheuristics, matheuristics and evolutionary algorithms
  • complexity of scheduling algorithms
  • algorithms for multi-criteria scheduling
  • scheduling in manufacturing systems
  • scheduling algorithms for supply chains
  • scheduling algorithms for problems in logistics, transport, timetabling, healthcare, and energy management
  • resource-constrained project scheduling problems
  • assembly line balancing and scheduling
  • railway scheduling
  • agent-based scheduling
  • scheduling under uncertainty

Published Papers (13 papers)

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Editorial

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3 pages, 163 KiB  
Editorial
Special Issue “Scheduling: Algorithms and Applications”
by Frank Werner
Algorithms 2023, 16(6), 268; https://doi.org/10.3390/a16060268 - 27 May 2023
Cited by 2 | Viewed by 977
Abstract
This special issue of Algorithms is dedicated to recent developments of scheduling algorithms and new applications [...] Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)

Research

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14 pages, 3872 KiB  
Article
Hybrid Genetic and Spotted Hyena Optimizer for Flow Shop Scheduling Problem
by Toufik Mzili, Ilyass Mzili, Mohammed Essaid Riffi and Gaurav Dhiman
Algorithms 2023, 16(6), 265; https://doi.org/10.3390/a16060265 - 25 May 2023
Cited by 4 | Viewed by 1477
Abstract
This paper presents a new hybrid algorithm that combines genetic algorithms (GAs) and the optimizing spotted hyena algorithm (SHOA) to solve the production shop scheduling problem. The proposed GA-SHOA algorithm incorporates genetic operators, such as uniform crossover and mutation, into the SHOA algorithm [...] Read more.
This paper presents a new hybrid algorithm that combines genetic algorithms (GAs) and the optimizing spotted hyena algorithm (SHOA) to solve the production shop scheduling problem. The proposed GA-SHOA algorithm incorporates genetic operators, such as uniform crossover and mutation, into the SHOA algorithm to improve its performance. We evaluated the algorithm on a set of OR library instances and compared it to other state-of-the-art optimization algorithms, including SSO, SCE-OBL, CLS-BFO and ACGA. The experimental results show that the GA-SHOA algorithm consistently finds optimal or near-optimal solutions for all tested instances, outperforming the other algorithms. Our paper contributes to the field in several ways. First, we propose a hybrid algorithm that effectively combines the exploration and exploitation capabilities of SHO and GA, resulting in a balanced and efficient search process for finding near-optimal solutions for the FSSP. Second, we tailor the SHO and GA methods to the specific requirements of the FSSP, including encoding schemes, objective function evaluation and constraint handling, which ensures that the hybrid algorithm is well suited to address the challenges posed by the FSSP. Third, we perform a comprehensive performance evaluation of the proposed hybrid algorithm, demonstrating its effectiveness in terms of solution quality and computational efficiency. Finally, we provide an in-depth analysis of the behavior of the hybrid algorithm, discussing the roles of the SHO and GA components and their interactions during the search process, which can help understand the factors contributing to the success of the algorithm and provide insight into potential improvements or adaptations to other combinatorial optimization problems. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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14 pages, 730 KiB  
Article
A Scheduling Solution for Robotic Arm-Based Batching Systems with Multiple Conveyor Belts
by Kasper Gaj Nielsen, Inkyung Sung, Mohamed El Yafrani, Deniz Kenan Kılıç and Peter Nielsen
Algorithms 2023, 16(3), 172; https://doi.org/10.3390/a16030172 - 21 Mar 2023
Cited by 1 | Viewed by 1615
Abstract
In this study, we tackle a key scheduling problem in a robotic arm-based food processing system, where multiple conveyors—an infeed conveyor that feeds food items to robotic arms and two tray lane conveyors, on which trays to batch food items are placed—are implemented. [...] Read more.
In this study, we tackle a key scheduling problem in a robotic arm-based food processing system, where multiple conveyors—an infeed conveyor that feeds food items to robotic arms and two tray lane conveyors, on which trays to batch food items are placed—are implemented. The target scheduling problem is to determine what item on an infeed conveyor belt is picked up by which robotic arm at what position, and on which tray the picked up item will be placed. This problem involves critical constraints, such as sequence-dependent processing time and dynamic item and tray positions. Moreover, due to the speed of the infeed conveyor and latency in the information about entering items into the system, this scheduling problem must be solved in near real time. To address these challenges, we propose a scheduling solution that first decomposes the original scheduling problem into sub-problems, where a sub-problem formulated as a goal program schedules robotic arms only for a single tray. The performance of the proposed solution approach is then tested under a simulation environment, and from the experiments, the proposed approach produces acceptable performance. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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17 pages, 5821 KiB  
Article
Comparison of Single-Lane Roundabout Entry Degree of Saturation Estimations from Analytical and Regression Models
by Ana Čudina Ivančev, Maja Ahac, Saša Ahac and Vesna Dragčević
Algorithms 2023, 16(3), 164; https://doi.org/10.3390/a16030164 - 18 Mar 2023
Cited by 2 | Viewed by 1811
Abstract
Roundabout design is an iterative process consisting of a preliminary geometry design, geometry performance checks, and the estimation of intersection functionality (based on the results of analytical or regression models). Since both roundabout geometry design procedures and traffic characteristics vary around the world, [...] Read more.
Roundabout design is an iterative process consisting of a preliminary geometry design, geometry performance checks, and the estimation of intersection functionality (based on the results of analytical or regression models). Since both roundabout geometry design procedures and traffic characteristics vary around the world, the discussion on which functionality estimation model is more appropriate is ongoing. This research aims to reduce the uncertainty in decision-making during this final roundabout design stage. Its two objectives were to analyze and compare the results of roundabout performance estimations derived from one analytical and one regression model, and to quantify the model results’ susceptibility to changes in roundabout geometric parameters. For this, 60 four-legged single-lane roundabout schemes were created, varying in size and leg alignment. Their geometric parameters resulted from the assumption of their location in a suburban environment and chosen design vehicle swept path analysis. To compare the models’ results, the degree of saturation of roundabout entries was calculated based on presumed traffic flows. The results showed that the regression model estimates higher functionality and that this difference (both between the two models and regression models applied on different schemes) is more pronounced as the outer radius and angle between the legs increase. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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18 pages, 530 KiB  
Article
A Hybrid Exact–Local Search Approach for One-Machine Scheduling with Time-Dependent Capacity
by Christos Valouxis, Christos Gogos, Angelos Dimitsas, Petros Potikas and Anastasios Vittas
Algorithms 2022, 15(12), 450; https://doi.org/10.3390/a15120450 - 29 Nov 2022
Cited by 3 | Viewed by 1339
Abstract
Machine scheduling is a hard combinatorial problem having many manifestations in real life. Due to the schedule followed, the possibility of installations of machines operating sub-optimally is high. In this work, we examine the problem of a single machine with time-dependent capacity that [...] Read more.
Machine scheduling is a hard combinatorial problem having many manifestations in real life. Due to the schedule followed, the possibility of installations of machines operating sub-optimally is high. In this work, we examine the problem of a single machine with time-dependent capacity that performs jobs of deterministic durations, while for each job, its due time is known in advance. The objective is to minimize the aggregated tardiness in all tasks. The problem was motivated by the need to schedule charging times of electric vehicles effectively. We formulate an integer programming model that clearly describes the problem and a constraint programming model capable of effectively solving it. Due to the usage of interval variables, global constraints, a powerful constraint programming solver, and a heuristic we have identified, which we call the “due times rule”, the constraint programming model can reach excellent solutions. Furthermore, we employ a hybrid approach that exploits three local search improvement procedures in a schema where the constraint programming part of the solver plays a central role. These improvement procedures exhaustively enumerate portions of the search space by exchanging consecutive jobs with a single job of the same duration, moving cost-incurring jobs to earlier times in a consecutive sequence of jobs or even exploiting periods where capacity is not fully utilized to rearrange jobs. On the other hand, subproblems are given to the exact constraint programming solver, allowing freedom of movement only to certain parts of the schedule, either in vertical ribbons of the time axis or in groups of consecutive sequences of jobs. Experiments on publicly available data show that our approach is highly competitive and achieves the new best results in many problem instances. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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27 pages, 1237 KiB  
Article
The Assignment Problem and Its Relation to Logistics Problems
by Milos Seda
Algorithms 2022, 15(10), 377; https://doi.org/10.3390/a15100377 - 16 Oct 2022
Cited by 3 | Viewed by 3082
Abstract
The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations [...] Read more.
The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software’s applicability. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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15 pages, 665 KiB  
Article
A Static Assignment Algorithm of Uniform Jobs to Workers in a User-PC Computing System Using Simultaneous Linear Equations
by Xudong Zhou, Nobuo Funabiki, Hein Htet, Ariel Kamoyedji, Irin Tri Anggraini, Yuanzhi Huo and Yan Watequlis Syaifudin
Algorithms 2022, 15(10), 369; https://doi.org/10.3390/a15100369 - 07 Oct 2022
Cited by 1 | Viewed by 1524
Abstract
Currently, the User-PC computingsystem (UPC) has been studied as a low-cost and high-performance distributed computing platform. It uses idling resources of personal computers (PCs) in a group. The job-worker assignment for minimizing makespan is critical to determine the performance of the UPC system. [...] Read more.
Currently, the User-PC computingsystem (UPC) has been studied as a low-cost and high-performance distributed computing platform. It uses idling resources of personal computers (PCs) in a group. The job-worker assignment for minimizing makespan is critical to determine the performance of the UPC system. Some applications need to execute a lot of uniform jobs that use the identical program but with slightly different data, where they take the similar CPU time on a PC. Then, the total CPU time of a worker is almost linear to the number of assigned jobs. In this paper, we propose a static assignment algorithm of uniform jobs to workers in the UPC system, using simultaneous linear equations to find the lower bound on makespan, where every worker requires the same CPU time to complete the assigned jobs. For the evaluations of the proposal, we consider the uniform jobs in three applications. In OpenPose, the CNN-based keypoint estimation program runs with various images of human bodies. In OpenFOAM, the physics simulation program runs with various parameter sets. In code testing, two open-source programs run with various source codes from students for the Android programming learning assistance system (APLAS). Using the proposal, we assigned the jobs to six workers in the testbed UPC system and measured the CPU time. The results show that makespan was reduced by 10% on average, which confirms the effectiveness of the proposal. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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20 pages, 2794 KiB  
Article
A Practical Staff Scheduling Strategy Considering Various Types of Employment in the Construction Industry
by Chan Hee Park and Young Dae Ko
Algorithms 2022, 15(9), 321; https://doi.org/10.3390/a15090321 - 09 Sep 2022
Cited by 2 | Viewed by 2191
Abstract
The Korean government implemented a 52-h workweek policy for employees’ welfare. Consequently, companies face workforce availability reduction with the same number of employees. That is, labor-dependent companies suffer from workforce shortage. To handle the workforce shortage, they increase irregular employees who are paid [...] Read more.
The Korean government implemented a 52-h workweek policy for employees’ welfare. Consequently, companies face workforce availability reduction with the same number of employees. That is, labor-dependent companies suffer from workforce shortage. To handle the workforce shortage, they increase irregular employees who are paid relatively less. However, the problem of ‘no-show’, due to the stochastic characteristics of irregular employee’s absence, happens. Therefore, this study aims to propose a staff scheduling strategy considering irregular employee absence and a new labor policy by using linear programming. By deriving a deterministic staff schedule through system parameters derived from the features and rules of an actual company in the numerical experiment, the practicality and applicability of the developed mathematical model are proven. Furthermore, through sensitivity analysis and simulation considering the stochastic characteristics of absences, various proactive cases are provided. Through the proactive cases, the influence of the change of the average percent of irregular employees’ absences on the total labor costs and staff schedules and the expected number who would not come to work could be given when assuming the application in practice. This finding can help decision-makers prepare precautious measures, such as assigning extra employees in case of an irregular employee’s absence. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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13 pages, 2190 KiB  
Article
Parallel Hybrid Particle Swarm Algorithm for Workshop Scheduling Based on Spark
by Tianhua Zheng, Jiabin Wang and Yuxiang Cai
Algorithms 2021, 14(9), 262; https://doi.org/10.3390/a14090262 - 30 Aug 2021
Cited by 3 | Viewed by 2049
Abstract
In hybrid mixed-flow workshop scheduling, there are problems such as mass production, mass manufacturing, mass assembly and mass synthesis of products. In order to solve these problems, combined with the Spark platform, a hybrid particle swarm algorithm that will be parallelized is proposed. [...] Read more.
In hybrid mixed-flow workshop scheduling, there are problems such as mass production, mass manufacturing, mass assembly and mass synthesis of products. In order to solve these problems, combined with the Spark platform, a hybrid particle swarm algorithm that will be parallelized is proposed. Compared with the existing intelligent algorithms, the parallel hybrid particle swarm algorithm is more conducive to the realization of the global optimal solution. In the loader manufacturing workshop, the optimization goal is to minimize the maximum completion time and a parallelized hybrid particle swarm algorithm is used. The results show that in the case of relatively large batches, the parallel hybrid particle swarm algorithm can effectively obtain the scheduling plan and avoid falling into the local optimal solution. Compared with algorithm serialization, algorithm parallelization improves algorithm efficiency by 2–4 times. The larger the batches, the more obvious the algorithm parallelization improves computational efficiency. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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23 pages, 2584 KiB  
Article
Efficient Dynamic Cost Scheduling Algorithm for Financial Data Supply Chain
by Alia Al Sadawi, Abdulrahim Shamayleh and Malick Ndiaye
Algorithms 2021, 14(7), 211; https://doi.org/10.3390/a14070211 - 14 Jul 2021
Cited by 1 | Viewed by 2149
Abstract
The financial data supply chain is vital to the economy, especially for banks. It affects their customer service level, therefore, it is crucial to manage the scheduling of the financial data supply chain to elevate the efficiency of banking sectors’ performance. The primary [...] Read more.
The financial data supply chain is vital to the economy, especially for banks. It affects their customer service level, therefore, it is crucial to manage the scheduling of the financial data supply chain to elevate the efficiency of banking sectors’ performance. The primary tool used in the data supply chain is data batch processing which requires efficient scheduling. This work investigates the problem of scheduling the processing of tasks with non-identical sizes and different priorities on a set of parallel processors. An iterative dynamic scheduling algorithm (DCSDBP) was developed to address the data batching process. The objective is to minimize different cost types while satisfying constraints such as resources availability, customer service level, and tasks dependency relation. The algorithm proved its effectiveness by allocating tasks with higher priority and weight while taking into consideration customers’ Service Level Agreement, time, and different types of costs, which led to a lower total cost of the batching process. The developed algorithm proved effective by testing it on an illustrative network. Also, a sensitivity analysis is conducted by varying the model parameters for networks with different sizes and complexities to study their impact on the total cost and the problem under study. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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22 pages, 4082 KiB  
Article
A Multicriteria Simheuristic Approach for Solving a Stochastic Permutation Flow Shop Scheduling Problem
by Eliana Maria Gonzalez-Neira, Jairo R. Montoya-Torres and Jose-Fernando Jimenez
Algorithms 2021, 14(7), 210; https://doi.org/10.3390/a14070210 - 14 Jul 2021
Cited by 6 | Viewed by 2186
Abstract
This paper proposes a hybridized simheuristic approach that couples a greedy randomized adaptive search procedure (GRASP), a Monte Carlo simulation, a Pareto archived evolution strategy (PAES), and an analytic hierarchy process (AHP), in order to solve a multicriteria stochastic permutation flow shop problem [...] Read more.
This paper proposes a hybridized simheuristic approach that couples a greedy randomized adaptive search procedure (GRASP), a Monte Carlo simulation, a Pareto archived evolution strategy (PAES), and an analytic hierarchy process (AHP), in order to solve a multicriteria stochastic permutation flow shop problem with stochastic processing times and stochastic sequence-dependent setup times. For the decisional criteria, the proposed approach considers four objective functions, including two quantitative and two qualitative criteria. While the expected value and the standard deviation of the earliness/tardiness of jobs are included in the quantitative criteria to address a robust solution in a just-in-time environment, this approach also includes a qualitative assessment of the product and customer importance in order to appraise a weighted priority for each job. An experimental design was carried out in several study instances of the flow shop problem to test the effects of the processing times and sequence-dependent setup times, obtained through lognormal and uniform probability distributions with three levels of coefficients of variation, settled as 0.3, 0.4, and 0.5. The results show that both probability distributions and coefficients of variation have a significant effect on the four decision criteria selected. In addition, the analytical hierarchical process makes it possible to choose the best sequence exhibited by the Pareto frontier that adjusts more adequately to the decision-makers’ objectives. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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27 pages, 11845 KiB  
Article
Energy Management of a Multi-Source Power System
by Omar Salah, Abdulrahim Shamayleh and Shayok Mukhopadhyay
Algorithms 2021, 14(7), 206; https://doi.org/10.3390/a14070206 - 07 Jul 2021
Cited by 4 | Viewed by 1965
Abstract
This work focuses on energy management for a system operated by multiple energy sources which include batteries, super capacitors, a hydrogen fuel cell, and a photovoltaic cell. The overall objective is to minimize the power consumption from all sources needed to satisfy the [...] Read more.
This work focuses on energy management for a system operated by multiple energy sources which include batteries, super capacitors, a hydrogen fuel cell, and a photovoltaic cell. The overall objective is to minimize the power consumption from all sources needed to satisfy the system’s power demand by optimizing the switching between the different energy sources. A dynamic mathematical model representing the energy sources is developed taking into account the different constraints on the system, i.e., primarily the state-of-charge of the battery and the super capacitors. In addition to the model, a heuristic approach is developed and compared with the mathematical model. Both approaches were tested on a multi-energy source ground robot as a prototype. The novelty of this work is that the scheduling of an energy system consisting of four different types of sources is compared by performing analysis via dynamic programming, and a heuristic approach. The results generated using both methods are analyzed and compared to a standard mode of operation. The comparison validated that the proposed approaches minimize the average power consumption across all sources. The dynamic modeling approach performs well in terms of optimization and provided a superior switching sequence, while the heuristic approach offers the definite advantages in terms of ease of implementation and simple computation requirements. Additionally, the switching sequence provided by the dynamic approach was able to meet the power demand for all simulations performed and showed that the average power consumption across all sources is minimized. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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Review

Jump to: Editorial, Research

43 pages, 506 KiB  
Review
Assembly and Production Line Designing, Balancing and Scheduling with Inaccurate Data: A Survey and Perspectives
by Yuri N. Sotskov
Algorithms 2023, 16(2), 100; https://doi.org/10.3390/a16020100 - 10 Feb 2023
Cited by 4 | Viewed by 3064
Abstract
Assembly lines (conveyors) are traditional means of large-scale and mass-scale productions. An assembly line balancing problem is needed for optimizing the assembly process by configuring and designing an assembly line for the same or similar types of final products. This problem consists of [...] Read more.
Assembly lines (conveyors) are traditional means of large-scale and mass-scale productions. An assembly line balancing problem is needed for optimizing the assembly process by configuring and designing an assembly line for the same or similar types of final products. This problem consists of designing the assembly line and distributing the total workload for manufacturing each unit of the fixed product to be assembled among the ordered workstations along the constructed assembly line. The assembly line balancing research is focused mainly on simple assembly line balancing problems, which are restricted by a set of conditions making a considered assembly line ideal for research. A lot of published research has been carried out in order to describe and solve (usually heuristically) more realistic generalized assembly line balancing problems. Assembly line designing, balancing and scheduling problems with not deterministic (stochastic, fuzzy or uncertain) parameters have been investigated in many published research works. This paper is about the design and optimization methods for assembly and disassembly lines. We survey the recent developments for designing, balancing and scheduling assembly (disassembly) lines. New formulations of simple assembly line balancing problems are presented in order to take into account modifications and uncertainties characterized by real assembly productions. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Applications)
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