Search results for: makespan

Authors: Sanjay Kumar Parjapati, Ajai Jain

Abstract:

This paper presents optimization of makespan for ‘n’ jobs and ‘m’ machines flexible job shop scheduling problem with sequence dependent setup time using genetic algorithm (GA) approach. A restart scheme has also been applied to prevent the premature convergence. Two case studies are taken into consideration. Results are obtained by considering crossover probability (pc = 0.85) and mutation probability (pm = 0.15). Five simulation runs for each case study are taken and minimum value among them is taken as optimal makespan. Results indicate that optimal makespan can be achieved with more than one sequence of jobs in a production order.

Keywords: flexible job shop, genetic algorithm, makespan, sequence dependent setup times

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

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The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: flow-shop scheduling problem, makespan, Petri nets, state equation

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Authors: S. S. Bendib, L. W. Mouss, S. Kalla

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This paper proposes a self-organization-based approach for real-time systems design. The addressed issue is the mapping of an application onto an architecture of heterogeneous processors while optimizing both makespan and reliability. Since this problem is NP-hard, a heuristic algorithm is used to obtain efficiently approximate solutions. The proposed approach takes into consideration the quality as well as the diversity of solutions. Indeed, an alternate treatment of the two objectives allows to produce solutions of good quality while a self-organization approach based on the neighborhood structure is used to reorganize solutions and consequently to enhance their diversity. Produced solutions make different compromises between the makespan and the reliability giving the user the possibility to select the solution suited to his (her) needs.

Keywords: embedded real-time systems design, makespan, reliability, self-organization, compromises

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Authors: Mohsen Ziaee

Abstract:

Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: M. Duran Toksari, Berrin Ucarkus

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In this paper, we propose two algorithms to optimally solve makespan and total completion time scheduling problems with learning effect and job dependent delivery times in a single machine environment. The delivery time is the extra time to eliminate adverse effect between the main processing and delivery to the customer. In this paper, we introduce the job dependent delivery times for some single machine scheduling problems with position dependent learning effect, which are makespan are total completion. The results with respect to two algorithms proposed for solving of the each problem are compared with LINGO solutions for 50-jobs, 100-jobs and 150-jobs problems. The proposed algorithms can find the same results in shorter time.

Keywords: delivery Times, learning effect, makespan, scheduling, total completion time

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

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This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm

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Authors: Ali Allahverdi

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The m-machine no-wait flowshop scheduling problem is addressed in this paper. The objective is to minimize total completion time subject to the constraint that the makespan value is not greater than a certain value. Setup times are treated as separate from processing times. Several recent algorithms are adapted and proposed for the problem. An extensive computational analysis has been conducted for the evaluation of the proposed algorithms. The computational analysis indicates that the best proposed algorithm performs significantly better than the earlier existing best algorithm.

Keywords: scheduling, no-wait flowshop, algorithm, setup times, total completion time, makespan

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Authors: Safia Rabaaoui, Héla Hachicha, Ezzeddine Zagrouba

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Nowadays, cloud computing is becoming the more popular technology to various companies and consumers, which benefit from its increased efficiency, cost optimization, data security, unlimited storage capacity, etc. One of the biggest challenges of cloud computing is resource allocation. Its efficiency directly influences the performance of the whole cloud environment. Finding an effective method to address these critical issues and increase cloud performance was necessary. This paper proposes a mobile agents-based framework for dynamic resource allocation in cloud computing to minimize both the cost of using virtual machines and the makespan. Furthermore, its impact on the best response time and power consumption has been studied. The simulation showed that our method gave better results than here.

Keywords: cloud computing, multi-agent system, mobile agent, dynamic resource allocation, cost, makespan

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Authors: Lei Wang, Jiahao Zhou

Abstract:

The development of heterogeneous computing clusters provides a strong computility guarantee for large-scale workflows (e.g., scientific computing, artificial intelligence (AI), etc.). However, the tasks within large-scale workflows have also gradually become heterogeneous due to different demands on computing resources, which leads to the addition of a task resource-restricted constraint to the workflow scheduling problem on heterogeneous computing platforms. In this paper, we propose a heterogeneous constrained minimum makespan scheduling algorithm based on the idea of greedy strategy, which provides an efficient solution to the heterogeneous workflow scheduling problem in a heterogeneous platform. In this paper, we test the effectiveness of our proposed scheduling algorithm by randomly generating heterogeneous workflows with heterogeneous computing platform, and the experiments show that our method improves 15.2% over the state-of-the-art methods.

Keywords: heterogeneous computing, workflow scheduling, constrained resources, minimal makespan

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Authors: Mohsen Ziaee

Abstract:

In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: scheduling, flexible job shop, makespan, mixed integer linear programming

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Authors: Majid Khalili

Abstract:

This paper deals with a bi-objective hybrid no-wait flowshop scheduling problem minimizing the makespan and total weighted tardiness, in which we consider transportation times between stages. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper presents a new multi-objective variable neighborhood algorithm (MOVNS). A set of experimental instances are carried out to evaluate the algorithm by advanced multi-objective performance measures. The algorithm is carefully evaluated for its performance against available algorithm by means of multi-objective performance measures and statistical tools. The related results show that a variant of our proposed MOVNS provides sound performance comparing with other algorithms.

Keywords: no-wait hybrid flowshop scheduling; multi-objective variable neighborhood algorithm; makespan; total weighted tardiness

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Authors: Abdelhadi Adel, Kadri Ouahab

Abstract:

This paper proposes an improved approach based on MAS Architecture and Heuristic Algorithm for systematic maintenance to minimize makespan. We have implemented a problem-solving approach for optimizing the processing time, methods based on metaheuristics. The proposed approach is inspired by the behavior of the human body. This hybridization is between a multi-agent system and inspirations of the human body, especially genetics. The effectiveness of our approach has been demonstrated repeatedly in this paper. To solve such a complex problem, we proposed an approach which we have used advanced operators such as uniform crossover set and single point mutation. The proposed approach is applied to three preventive maintenance policies. These policies are intended to maximize the availability or to maintain a minimum level of reliability during the production chain. The results show that our algorithm outperforms existing algorithms. We assumed that the machines might be unavailable periodically during the production scheduling.

Keywords: multi-agent systems, emergence, genetic algorithm, makespan, systematic maintenance, scheduling, hybrid flow shop scheduling

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Authors: Ebrahim Asadi-Gangraj

Abstract:

Hybrid flow shop scheduling problem (HFS) contains sequencing in a flow shop where, at any stage, there exist one or more related or unrelated parallel machines. This production system is a common manufacturing environment in many real industries, such as the steel manufacturing, ceramic tile manufacturing, and car assembly industries. In this research, a mixed integer linear programming (MILP) model is presented for the hybrid flow shop scheduling problem, in which, the objective consists of minimizing the maximum completion time (makespan). For this purpose, a Benders Decomposition (BD) method is developed to solve the research problem. The proposed approach is tested on some test problems, small to moderate scale. The experimental results show that the Benders decomposition approach can solve the hybrid flow shop scheduling problem in a reasonable time, especially for small and moderate-size test problems.

Keywords: hybrid flow shop, mixed integer linear programming, Benders decomposition, makespan

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Authors: Abdelhadi Adel, Kadri Ouahab

Abstract:

This paper proposes a hybrid algorithm for the integration of systematic preventive maintenance policies in hybrid flow shop scheduling to minimize makespan. We have implemented a problem-solving approach for optimizing the processing time, methods based on metaheuristics. The proposed approach is inspired by the behavior of the human body. This hybridization is between a multi-agent system and inspirations of the human body, especially genetics. The effectiveness of our approach has been demonstrated repeatedly in this paper. To solve such a complex problem, we proposed an approach which we have used advanced operators such as uniform crossover set and single point mutation. The proposed approach is applied to three preventive maintenance policies. These policies are intended to maximize the availability or to maintain a minimum level of reliability during the production chain. The results show that our algorithm outperforms existing algorithms. We assumed that the machines might be unavailable periodically during the production scheduling.

Keywords: multi-agent systems, emergence, genetic algorithm, makespan, systematic maintenance, scheduling, hybrid flow shop scheduling

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Authors: Hwang Ho Kim, Do Gyun Kim, Jin Young Choi, Sang Chul Park

Abstract:

Since tire production process is very complicated, company-wide management of it is very difficult, necessitating considerable amounts of capital and labors. Thus, productivity should be enhanced and maintained competitive by developing and applying effective production plans. Among major processes for tire manufacturing, consisting of mixing component preparation, building and curing, the mixing process is an essential and important step because the main component of tire, called compound, is formed at this step. Compound as a rubber synthesis with various characteristics plays its own role required for a tire as a finished product. Meanwhile, scheduling tire mixing process is similar to flexible job shop scheduling problem (FJSSP) because various kinds of compounds have their unique orders of operations, and a set of alternative machines can be used to process each operation. In addition, setup time required for different operations may differ due to alteration of additives. In other words, each operation of mixing processes requires different setup time depending on the previous one, and this kind of feature, called sequence dependent setup time (SDST), is a very important issue in traditional scheduling problems such as flexible job shop scheduling problems. However, despite of its importance, there exist few research works dealing with the tire mixing process. Thus, in this paper, we consider the scheduling problem for tire mixing process and suggest an efficient particle swarm optimization (PSO) algorithm to minimize the makespan for completing all the required jobs belonging to the process. Specifically, we design a particle encoding scheme for the considered scheduling problem, including a processing sequence for compounds and machine allocation information for each job operation, and a method for generating a tire mixing schedule from a given particle. At each iteration, the coordination and velocity of particles are updated, and the current solution is compared with new solution. This procedure is repeated until a stopping condition is satisfied. The performance of the proposed algorithm is validated through a numerical experiment by using some small-sized problem instances expressing the tire mixing process. Furthermore, we compare the solution of the proposed algorithm with it obtained by solving a mixed integer linear programming (MILP) model developed in previous research work. As for performance measure, we define an error rate which can evaluate the difference between two solutions. As a result, we show that PSO algorithm proposed in this paper outperforms MILP model with respect to the effectiveness and efficiency. As the direction for future work, we plan to consider scheduling problems in other processes such as building, curing. We can also extend our current work by considering other performance measures such as weighted makespan or processing times affected by aging or learning effects.

Keywords: compound, error rate, flexible job shop scheduling problem, makespan, particle encoding scheme, particle swarm optimization, sequence dependent setup time, tire mixing process

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Authors: Hernández Eva Selene, Reyna Mary Carmen, Rivera Héctor, Barragán Irving

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We propose an approach that jointly addresses the layout of a facility and the scheduling of a sequence of jobs. In real production, these two problems are interrelated. However, they are treated separately in the literature. Our approach is an extension of the job shop problem with transportation delay, where the location of the machines is selected among possible sites. The model minimizes the makespan, using the short processing times rule with two algorithms; the first one considers all the permutations for the location of machines, and the second only a heuristic to select some specific permutations that reduces computational time. Some instances are proved and compared with literature.

Keywords: layout problem, job shop scheduling problem, concurrent scheduling and layout problem, metaheuristic

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Authors: Fawaz Abdulmalek

Abstract:

The two-stage flowshop assembly scheduling problem is considered in this paper. There are more than one parallel machines at stage one and an assembly machine at stage two. The jobs will be processed into the flowshop based on Johnson rule and two extensions of Johnson rule. A simulation model of the two-stage flowshop is constructed where both machines at stage one are subject to random failures. Three simulation experiments will be conducted to test the effect of the three job ranking rules on the makespan. Johnson Largest heuristic outperformed both Johnson rule and Johnson Smallest heuristic for two performed experiments for all scenarios where each experiments having five scenarios.

Keywords: flowshop scheduling, random failures, johnson rule, simulation

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

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The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: job-shop scheduling, classification, constraints, objective functions

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Authors: Mohammed Ali

Abstract:

A flexible manufacturing system has been studied under different manufacturing strategies. The aim of this paper is to test the impact of number of pallets and routing flexibility (design strategy) on system performance operating at different sequencing and dispatching rules (control strategies) at unbalanced load condition (planning strategies). A computer simulation model is developed to evaluate the effects of aforementioned strategies on the make-span time, which is taken as the system performance measure. The impact of number of pallets is shown with the different levels of routing flexibility. In this paper, the same manufacturing system is modeled under different combination of sequencing and dispatching rules. The result of the simulation shows that there is definite range of pallets for each level of routing flexibility at which the systems performs satisfactorily.

Keywords: flexible manufacturing system, manufacturing, strategy, makespan

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid Hopfield neural network is proposed for the dynamic, flexible job shop scheduling problem. A new heuristic based and easy to implement energy function is designed for the Hopfield neural network, which penalizes the constraints violation and decreases makespan. Moreover, for enhancing the performance, several heuristics are integrated to it that achieve active, and non-delay schedules also, prevent early convergence of the neural network. The suggested algorithm that is designed as a generalization of the previous studies for the flexible and dynamic scheduling problems can be used for solving real scheduling problems. Comparison of the presented hybrid method results with the previous studies results proves its efficiency.

Keywords: dynamic flexible job shop scheduling, neural network, heuristics, constrained optimization

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Authors: Arshad Mehmood Ch, Riaz Ahmad, Imran Ali Ch, Waqas Durrani

Abstract:

This study deals with the application of Ant Colony Optimization (ACO) approach to solve no-wait flowshop scheduling problem (NW-FSSP). ACO algorithm so developed has been coded on Matlab computer application. The paper covers detailed steps to apply ACO and focuses on judging the strength of ACO in relation to other solution techniques previously applied to solve no-wait flowshop problem. The general purpose approach was able to find reasonably accurate solutions for almost all the problems under consideration and was able to handle a fairly large spectrum of problems with far reduced CPU effort. Careful scrutiny of the results reveals that the algorithm presented results better than other approaches like Genetic algorithm and Tabu Search heuristics etc; earlier applied to solve NW-FSSP data sets.

Keywords: no-wait, flowshop, scheduling, ant colony optimization (ACO), makespan

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Authors: Anju Bala, Inderveer Chana

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Task scheduling is the key concern for the execution of performance-driven workflow applications. As efficient scheduling can have major impact on the performance of the system, task scheduling is often chosen for assigning the request to resources in an efficient way based on cloud resource characteristics. In this paper, priority based task scheduling algorithm has been proposed that prioritizes the tasks based on the length of the instructions. The proposed scheduling approach prioritize the tasks of Cloud applications according to the limits set by six sigma control charts based on dynamic threshold values. Further, the proposed algorithm has been validated through the CloudSim toolkit. The experimental results demonstrate that the proposed algorithm is effective for handling multiple task lists from workflows and in considerably reducing Makespan and Execution time.

Keywords: cloud computing, priority based scheduling, task scheduling, VM allocation

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Authors: Gagandeep Kaur

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Cloud computing uses various computing resources such as CPU, memory, processor etc. which is used to deliver service over the network and is one of the emerging fields for large scale distributed computing. In cloud computing, execution of large number of tasks with available resources to achieve high performance, minimal total time for completion, minimum response time, effective utilization of resources etc. are the major research areas. In the proposed research, an algorithm has been proposed to achieve high performance in load balancing and resource utilization. The proposed algorithm is used to reduce the makespan, increase the resource utilization and performance cost for independent tasks. Further scheduling metrics based on algorithm in cloud computing has been proposed.

Keywords: resource utilization, response time, load balancing, performance cost

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Authors: Trapti Sharma, Devesh Kumar Srivastava

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This paper is basically a analysis study of above MapReduce implementation and also to verify and validate the MapReduce solution model for Parallel K-Mediod algorithm on Hadoop Cluster. MapReduce is a programming model which authorize the managing of huge amounts of data in parallel, on a large number of devices. It is specially well suited to constant or moderate changing set of data since the implementation point of a position is usually high. MapReduce has slowly become the framework of choice for “big data”. The MapReduce model authorizes for systematic and instant organizing of large scale data with a cluster of evaluate nodes. One of the primary affect in Hadoop is how to minimize the completion length (i.e. makespan) of a set of MapReduce duty. In this paper, we have verified and validated various MapReduce applications like wordcount, grep, terasort and parallel K-Mediod clustering algorithm. We have found that as the amount of nodes increases the completion time decreases.

Keywords: hadoop, mapreduce, k-mediod, validation, verification

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Authors: Nhat-To Huynh, Chen-Fu Chien

Abstract:

Textile batch dyeing scheduling problem is complicated which includes batch formation, batch assignment on machines, batch sequencing with sequence-dependent setup time. Most manufacturers schedule their orders manually that are time consuming and inefficient. More power methods are needed to improve the solution. Motivated by the real needs, this study aims to propose approaches in which genetic algorithm is developed with multi-subpopulation and hybridised with estimation of distribution algorithm to solve the constructed problem for minimising the makespan. A heuristic algorithm is designed and embedded into the proposed algorithms to improve the ability to get out of the local optima. In addition, an empirical study is conducted in a textile company in Taiwan to validate the proposed approaches. The results have showed that proposed approaches are more efficient than simulated annealing algorithm.

Keywords: estimation of distribution algorithm, genetic algorithm, multi-subpopulation, scheduling, textile dyeing

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Authors: Fahad Y. Al-dawish

Abstract:

The current trend by a large number of organizations and individuals to use cloud computing. Many consider it a significant shift in the field of computing. Cloud computing are distributed and parallel systems consisting of a collection of interconnected physical and virtual machines. With increasing request and profit of cloud computing infrastructure, diverse computing processes can be executed on cloud environment. Many organizations and individuals around the world depend on the cloud computing environments infrastructure to carry their applications, platform, and infrastructure. One of the major and essential issues in this environment related to allocating incoming tasks to suitable virtual machine (cloud task scheduling). Cloud task scheduling is classified as optimization problem, and there are several meta-heuristic algorithms have been anticipated to solve and optimize this problem. Good task scheduler should execute its scheduling technique on altering environment and the types of incoming task set. In this research project a cloud task scheduling methodology based on ant colony optimization ACO algorithm, we call it ACO-TS Ant Colony Optimization for Task Scheduling has been proposed and compared with different scheduling algorithms (Random, First Come First Serve FCFS, and Fastest Processor to the Largest Task First FPLTF). Ant Colony Optimization (ACO) is random optimization search method that will be used for assigning incoming tasks to available virtual machines VMs. The main role of proposed algorithm is to minimizing the makespan of certain tasks set and maximizing resource utilization by balance the load among virtual machines. The proposed scheduling algorithm was evaluated by using Cloudsim toolkit framework. Finally after analyzing and evaluating the performance of experimental results we find that the proposed algorithm ACO-TS perform better than Random, FCFS, and FPLTF algorithms in each of the makespaan and resource utilization.

Keywords: cloud Task scheduling, ant colony optimization (ACO), cloudsim, cloud computing

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Authors: Huan Ting Liao

Abstract:

In a typical manufacturing environment, computer numerical control (CNC) machining is essential for automating production through precise computer-controlled tool operations, significantly enhancing efficiency and ensuring consistent product quality. However, traditional CNC production lines often rely on manual loading and unloading, limiting operational efficiency and scalability. Although automated loading systems have been developed, they frequently lack sufficient intelligence and configuration efficiency, requiring extensive setup adjustments for different products and impacting overall productivity. This research addresses the job shop scheduling problem (JSSP) in CNC machining environments, aiming to minimize total completion time (makespan) and maximize CNC machine utilization. We propose a novel approach using reinforcement learning (RL), specifically the Q-learning algorithm, to optimize scheduling decisions. The study simulates the JSSP, incorporating robotic arm operations, machine processing times, and work order demand allocation to determine optimal processing sequences. The Q-learning algorithm enhances machine utilization by dynamically balancing workloads across CNC machines, adapting to varying job demands and machine states. This approach offers robust solutions for complex manufacturing environments by automating decision-making processes for job assignments. Additionally, we evaluate various layout configurations to identify the most efficient setup. By integrating RL-based scheduling optimization with layout analysis, this research aims to provide a comprehensive solution for improving manufacturing efficiency and productivity in CNC-based job shops. The proposed method's adaptability and automation potential promise significant advancements in tackling dynamic manufacturing challenges.

Keywords: job shop scheduling problem, reinforcement learning, operations sequence, layout optimization, q-learning

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Authors: Tommaso Adamo, Gianpaolo Ghiani, Antonio Domenico Grieco, Emanuela Guerriero

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Batch production plants provide a wide range of scheduling problems. In pharmaceutical industries a batch process is usually described by a recipe, consisting of an ordering of tasks to produce the desired product. In this research work we focused on pharmaceutical production processes requiring the culture of a microorganism population (i.e. bacteria, yeasts or antibiotics). Several sources of uncertainty may influence the yield of the culture processes, including (i) low performance and quality of the cultured microorganism population or (ii) microbial contamination. For these reasons, robustness is a valuable property for the considered application context. In particular, a robust schedule will not collapse immediately when a cell of microorganisms has to be thrown away due to a microbial contamination. Indeed, a robust schedule should change locally in small proportions and the overall performance measure (i.e. makespan, lateness) should change a little if at all. In this research work we formulated a constraint programming optimization (COP) model for the robust planning of antibiotics production. We developed a discrete-time model with a multi-criteria objective, ordering the different criteria and performing a lexicographic optimization. A feasible solution of the proposed COP model is a schedule of a given set of tasks onto available resources. The schedule has to satisfy tasks precedence constraints, resource capacity constraints and time constraints. In particular time constraints model tasks duedates and resource availability time windows constraints. To improve the schedule robustness, we modeled the concept of (a, b) super-solutions, where (a, b) are input parameters of the COP model. An (a, b) super-solution is one in which if a variables (i.e. the completion times of a culture tasks) lose their values (i.e. cultures are contaminated), the solution can be repaired by assigning these variables values with a new values (i.e. the completion times of a backup culture tasks) and at most b other variables (i.e. delaying the completion of at most b other tasks). The efficiency and applicability of the proposed model is demonstrated by solving instances taken from Sanofi Aventis, a French pharmaceutical company. Computational results showed that the determined super-solutions are near-optimal.

Keywords: constraint programming, super-solutions, robust scheduling, batch process, pharmaceutical industries

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Authors: Ajit Rai, Hamza Deroui, Blandine Vacher, Khwansiri Ninpan, Arthur Aumont, Francesco Vitillo, Robert Plana

Abstract:

Large-scale critical industrial scheduling problems are based on Resource-Constrained Project Scheduling Problems (RCPSP), that necessitate integration with other optimization problems (e.g., vehicle routing, supply chain, or unique industrial ones), thus requiring practical solutions (i.e., modular, computationally efficient with feasible solutions). To the best of our knowledge, the current industrial state of the art is not addressing this holistic problem. We propose an original modular solution that answers the issues exhibited by the delivery of complex projects. With three interlinked entities (project, task, resources) having their constraints, it uses a greedy heuristic with a dynamic cost function for each task with a situational assessment at each time step. It handles large-scale data and can be easily integrated with other optimization problems, already existing industrial tools and unique constraints as required by the use case. The solution has been tested and validated by domain experts on three use cases: outage management in Nuclear Power Plants (NPPs), planning of future NPP maintenance operation, and application in the defense industry on supply chain and factory relocation. In the first use case, the solution, in addition to the resources’ availability and tasks’ logical relationships, also integrates several project-specific constraints for outage management, like, handling of resource incompatibility, updating of tasks priorities, pausing tasks in a specific circumstance, and adjusting dynamic unit of resources. With more than 20,000 tasks and multiple constraints, the solution provides a feasible schedule within 10-15 minutes on a standard computer device. This time-effective simulation corresponds with the nature of the problem and requirements of several scenarios (30-40 simulations) before finalizing the schedules. The second use case is a factory relocation project where production lines must be moved to a new site while ensuring the continuity of their production. This generates the challenge of merging job shop scheduling and the RCPSP with location constraints. Our solution allows the automation of the production tasks while considering the rate expectation. The simulation algorithm manages the use and movement of resources and products to respect a given relocation scenario. The last use case establishes a future maintenance operation in an NPP. The project contains complex and hard constraints, like on Finish-Start precedence relationship (i.e., successor tasks have to start immediately after predecessors while respecting all constraints), shareable coactivity for managing workspaces, and requirements of a specific state of "cyclic" resources (they can have multiple states possible with only one at a time) to perform tasks (can require unique combinations of several cyclic resources). Our solution satisfies the requirement of minimization of the state changes of cyclic resources coupled with the makespan minimization. It offers a solution of 80 cyclic resources with 50 incompatibilities between levels in less than a minute. Conclusively, we propose a fast and feasible modular approach to various industrial scheduling problems that were validated by domain experts and compatible with existing industrial tools. This approach can be further enhanced by the use of machine learning techniques on historically repeated tasks to gain further insights for delay risk mitigation measures.

Keywords: deterministic scheduling, optimization coupling, modular scheduling, RCPSP

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