Makespan Minimization Research Articles

Ruzicka Indexive Throttled Deep Neural Learning for Resource-Efficient Load Balancing in a Cloud Environment

Cloud Computing (CC) is a prominent technology that permits users as well as organizations to access services based on their requirements. This computing method presents storage, deployment platforms, as well as suitable access to web services over the internet. Load balancing is a crucial factor for optimizing computing and storage. It aims to dispense workload across every virtual machine in a reasonable manner. Several load balancing techniques have been conventionally developed and are available in the literature. However, achieving efficient load balancing with minimal makespan and improved throughput remains a challenging issue. To enhance load balancing efficiency, a novel technique called Ruzicka Indexive Throttle Load Balanced Deep Neural Learning (RITLBDNL) is designed. The primary objective of RITLBDNL is to enhance throughput and minimize the makespan in the cloud. In the RITLBDNL technique, a deep neural learning model contains one input layer, two hidden layers, as well as one output layer to enhance load balancing performance. In the input layer, the number of cloud user tasks is collected and sent to hidden layer 1. In that layer, the load balancer in the cloud server analyzes the virtual machine resource status depending on energy, bandwidth, memory, and CPU using the Ruzicka Similarity Index. Then, it is classified VMs as overloaded, less loaded, or balanced. The analysis results are then transmitted to hidden layer 2, where Throttled Load Balancing is performed to dispense the workload of weighty loaded virtual machines to minimum loaded ones. The cloud server efficiently balances the workload between the virtual machines in higher throughput and lower response time and makespan for handling a huge number of incoming tasks. To evaluate experiments, the proposed technique is compared with other existing load balancing methods. The result shows that the proposed RITLBDNL provides better performance of higher load balancing efficiency of 7%, throughput of 46% lesser makespan of 41%, and response time of 28% than compared to conventional methods.

Online makespan minimization for MapReduce scheduling on multiple parallel machines

Abstract In this work, we investigate the online MapReduce processing problem on m m uniform parallel machines, aiming at minimizing the makespan. Each job consists of two sets of tasks, namely, the map tasks and the reduce tasks. A job’s map tasks can be arbitrarily split and processed on different machines simultaneously, while its reduce tasks can only be processed after all its map tasks have been completed. We assume that the reduce tasks are preemptive, but cannot be processed on different machines in parallel. We provide a new lower bound for this problem and present an online algorithm with a competitive ratio of 2 − 1 m 2-\frac{1}{m} ( m m is the number of machines) when the speeds of the machines are 1.

Efficient arc-flow formulations for makespan minimisation on parallel machines with a common server

Efficient arc-flow formulations for makespan minimisation on parallel machines with a common server

Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear

The scheduling of parallel machines with and without a job-splitting property, deterministic demand,and sequence-independent setup time with the goal of minimizing makespan is examined in this work.For simultaneous processing by multiple machines, single-stage splitable jobs are broken into random(job) sections. When a job starts to be processed on a machine, an operator has to setup the machinefor an hour. By creating two Mixed Integer Linear Programming models, this work proposes amathematical programming strategy (MILP). A MILP model takes the job-splitting property intoaccount. Another model, however, does not include the job-splitting property. This study investigatesthe performance of the proposed models using Gurobi solver. These programs' numerical calculationsare based on actual problems in the Indonesian city of Bandung's plastics industry. On four identicalparallel injection molding machines, 318 jobs must be finished in 22 periods. The real schedulingmethod is contrasted with these two MILP models. The maximum workload imbalance, the maximumrelative percentage of imbalance, and the makespan of these three scheduling systems are used toevaluate their effectiveness. Without the job-splitting property, MILP can handle the real issue ofscheduling identical parallel machines on injection molding machines to reduce makespan, resultingin a 36% average decrease. The MILP model's job-splitting property can reduce makespan by anadditional 2.40%. The order of relative ranking is MILP with job-splitting property, MILP withoutjob-splitting property, and actual scheduling based on the makespan minimization, workloadimbalance, and relative percentage of imbalance.

Identical Parallel Machine Scheduling to Minimize Makespan Using Suggested Algorithm Method at XYZ Company

XYZ company produce the various shape of motor spare parts product. The company has threeidentical parallel spot welding machines that use a random method of production scheduling, basedon machine capacity without any sequence of jobs, and only use daily production targets given tooperators. Based on the data, the actual scheduling of the machines has a very large completion timedifference between each machine, or the machine loading is uneven. As a result, the makespanbecomes longer with a value of 440000 seconds (26 days). This research aims to minimize the existingmakespan by giving proposed scheduling, using the suggested algorithm method, which has a smallnumber of iterations and has an optimal result. The method begins with the longest processing timesequence rule which is used as the upper bound for the first iteration, then continued to calculate thelower bound and machine workload. The calculation stops at the 15th iteration because the completiontime value exceeds the lower and upper bound so that the optimal scheduling taken is scheduled inthe 14th iteration with a makespan value of 914412 seconds (16 days). The proposed scheduling canminimize the makespan from the actual schedule by 38%.

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

Minimising the makespan on parallel identical machines with log-linear position-dependent processing times

This article studies the minimum makespan scheduling problem on parallel identical machines with the log-linear learning/ageing effect, also known as polynomial positional learning/ageing effect. To develop a Fully Polynomial Time Approximation Scheme to the problem, we start with an intermediate artificial variant that rounds the values to integers and restricts the solutions to instances sorted in the shortest/longest processing time order. To this end, we propose a dynamic programming algorithm and show that the difference between its returned value and the minimum makespan of the original problem is independent of the processing times. This then leads to an algorithm with provable guaranteed ϵ-additive approximation and pseudo-polynomial running time algorithm, resulting in the desired fully polynomial time approximation solution to the original, not restricted problem.

Integration of MILP and discrete-event simulation for flow shop scheduling using Benders cuts

Optimization-based scheduling in the chemical industry is highly beneficial but also highly difficult due to its combinatorial complexity. Different modeling and optimization techniques exist, each with individual strengths. We propose Benders decomposition to integrate mixed-integer linear programming (MILP) and discrete-event simulation (DES) to solve flow shop scheduling problems with makespan minimization objective. The basic idea is to generate valid Benders cuts based on sensitivity information of the DES sub problem, which can be found in the critical paths of DES solutions. For scaled literature flow shops, our approach requires at least an order of magnitude fewer iterations than a genetic algorithm and provides optimality gap information. For a real-world case study, our approach finds good solutions very quickly, making it a powerful alternative to established methods. We conclude that the Benders-DES algorithm is a promising approach to combine rigorous MILP optimization capabilities with high-fidelity DES modeling capabilities.

A Combined Discrete Event Simulation and Factorial Design Experiment for the Scheduling Problem in a Hybrid Flow Shop

Production plants have always been confronted with the problem of scheduling, as this has a direct impact on production time and therefore on production costs. This is especially true in today's world, where it is necessary to produce a quality product at a low price and in a short time, while at the same time responding flexibly to customer demands. Due to the complexity and for economic reasons, testing different variants in a real production environment is insufficient and ineffective. For this reason, this paper proposes a new method that combines discrete event simulation and factorial design experiment to find the optimal schedule in hybrid flow shop. It was tested with the goal of achieving the minimum makespan. The results show that this method makes it possible to find improved solution very quickly. Compared to the original production schedule, the makespan could be reduced by 3 hours and 31 minutes which is reduction of 16.3%. The proposed methodology can be used in many discrete and process production plants.

A novel and efficient mathematical optimization model for multi-stage assembly flow shop considering post-processing

ABSTRACT We addressed the multistage assembly flow shop problem with post-processing and makespan minimization, a production environment commonly encountered in diverse industries such as automotive, dental, medical equipment, and clothing manufacturing. In this context, we presented an innovative mixed-integer linear programming model with a position-based strategy. Our proposed formulation demonstrated remarkable efficiency when compared to the model of the literature. It achieved optimal solutions in 77.16% of instances, with an average optimality gap of 10.59%. This study constitutes a significant contribution to the efficient resolution of a practical and frequently encountered scheduling problem that has received relatively limited attention in existing literature. The findings highlight the crucial role of mathematical optimization models as valuable decision-making tools for scheduling within the addressed production system.

Efficiency and energy consumption of the automated container yard with twin rail-mounted gantry cranes considering crane scheduling strategies and handshake area designs

This study investigates the effects of twin rail-mounted gantry crane (RMG) scheduling strategies and handshake area designs on container yard efficiency and energy consumption. A handshake area is set for temporary storage of containers within each block, enabling the cooperation and interference avoidance of twin RMGs. Considering the complexity and dynamics, we establish a simulation model for the twin RMG operations with agent-based and discrete event simulation modeling. Container relocation, microscopic movements of RMGs, and stochastic arrivals of automated guided vehicles (AGVs) and external trucks (ETs) are simulated, and the corresponding efficiency and energy consumption are quantitatively estimated. By testing the six RMG scheduling strategies and thirteen handshake area designs, the results show that the 2-OPT RMG scheduling strategy (an optimization heuristic that attempts to find the schedule with the minimum makespan) outperforms the other strategies in terms of efficiency. However, the optimal RMG strategy for minimal energy consumption depends on the ratio of landside and seaside requests and handshake area settings. Furthermore, the location of the handshake area significantly affects the efficiency and power consumption of AGVs and RMGs. This study can provide decision support to improve the efficiency and reduce energy consumption of the twin RMGs by selecting a specified combination of the RMG scheduling strategy and the handshake area design.

Scheduling stochastic distributed flexible job shops using an multi-objective evolutionary algorithm with simulation evaluation

The trend of reverse globalisation prompts manufacturing enterprises to adopt distributed structures with multiple factories for improving production efficiency, meeting customer requirements, and responding disturbance events. This study focuses on scheduling a distributed flexible job shop with random job processing time to achieve minimal makespan and minimal total tardiness. First, a stochastic programming model is established to formulate the concerned problems. Second, in accordance with the natures of two objectives and randomness, an evolutionary algorithm incorporating an evaluation method is designed. In it, population-based and external archive-based search processes are developed for searching candidate solutions, and the evaluation method integrates stochastic simulation and discrete event simulation to calculate objective values of acquired solutions. Finally, a mathematical optimisation solver, CPLEX, is employed to validate the developed model and optimisation approach. A set of cases is solved to verify the performance of the proposed method. The comparisons and discussions show the superiority of the proposed method for handling the problems under study.

New bounds for single-machine time-dependent scheduling with uniform deterioration

We consider the single-machine time-dependent scheduling problem with linearly deteriorating jobs arriving over time. Each job i is associated with a release time ri and a processing time pi(si)=αi+βisi, where αi,βi>0 are parameters and si is the job's start time. In this setting, the approximability of both single-machine minimum makespan and total completion time problems remains open. We develop new bounds and approximation results for the special case of the problems with uniform deterioration, i.e. βi=β, for each i. The main contribution is a O(1+1/β)-approximation algorithm for the makespan problem and a O(1+1/β2) approximation algorithm for the total completion time problem. Further, we propose greedy constant-factor approximation algorithms for instances with β=O(1/n) and β=Ω(n), where n is the number of jobs. Our analysis is based on an approach for comparing computed and optimal schedules via bounding pseudomatchings.

Synchronisation of operations and maintenance in distributed unrelated parallel machine systems: a hierarchical optimisation framework

ABSTRACT Synchronisation of operations and maintenance means that production and maintenance departments work together effectively to achieve integrated optimisation of production scheduling and maintenance activities. This paper addresses such an integrated optimisation problem towards distributed unrelated parallel machine systems, where deteriorating processing time and machine failures are considered. For the trade-off between production and maintenance to obtain a minimal makespan in the worst-case scenario, a hierarchical optimisation framework with reinforcement learning-based encoder and knowledge-based intelligent optimiser (HOFRK) is developed. Experimental results show that HOFRK can be treated as an excellent optimiser for enterprise information systems to solve the proposed problem.

Makespan minimization for workflows with multiple privacy levels

With the advanced development of Metaverse, various service requests are required to be processed as soon as possible which contains a series of tasks with topology structure (workflow) and different privacy constraints. Due to the diversity and complex hierarchical structure of resources, how to rent suitable resources from cloud, edge, and local nodes to minimize the makespan of workflows is currently one of the key issues in service computing scenarios. Due to the limited computing resources of local devices, tasks need to be offloaded to edge or cloud servers. Based on task privacy constraints, it is challenging to determine the appropriate offloading nodes for each task in the workflow. In this paper, for workflows with multi-privacy level tasks, a privacy-preserving workflow scheduling algorithm based on clustering (PWCSA) is proposed to minimize the workflow makespan with limited bandwidth. Multiple tasks of different privacy levels are clustered into one task pipeline to reduce the data transmission time caused by limited bandwidth, thereby reducing workflow makespan. After statistically calibrating algorithm parameters over a comprehensive set of workflow instances, the proposed algorithms are compared with the state-of-the-art algorithms over five workflow-type instances. The results indicate that the proposed PWCSA algorithm outperforms other algorithms with acceptable computational time. Through a number of workflow instances, the system parameters are verified by analysis of variance methods.

Q-learning guided algorithms for bi-criteria minimization of total flow time and makespan in no-wait permutation flowshops

Combining Deep Reinforcement Learning and meta-heuristic techniques represents a new research direction for enhancing the search capabilities of meta-heuristic methods in the context of production scheduling. Q-learning is a prominent reinforcement learning in which its utilization aims to direct the selection of actions, thus preventing the necessity for a random exploration in the iterative process of the metaheuristics. In this study, we provide Q-learning guided algorithms for the Bi-Criteria No-Wait Flowshop Scheduling Problem (NWFSP). The problem is treated as a bi-criteria combinatorial optimization problem where total flow time and makespan are optimized simultaneously. Firstly, a deterministic mixed-integer linear programming (MILP) model is provided. Then, Q-learning guided algorithms are developed: Bi-Criteria Iterated Greedy Algorithm with Q-Learning (BC-IGQL). Bi-Criteria Block Insertion Heuristic Algorithm with Q-Learning (BC-BIHQL). Moreover, the performance of the proposed Q-learning guided algorithms is compared over a collection of Bi-Criteria Genetic Local Search Algorithms (BC-GLS), Bi-Criteria Iterated Greedy Algorithm (BC-IG), Bi-Criteria Iterated Greedy Algorithm with a Local Search (BC-IGALL) and Bi-Criteria Variable Block Insertion Heuristic Algorithm (BC-VBIH). The complete computational experiment, performed on 480 problem instances of Vallada et al. (2015), which is known as the VRF benchmark set, indicates that the BC-BIHQL and the BC-IGQL algorithms outperform the BC-GLS, BC-IG, BC-IGALL, and BC-VBIH algorithms in comparative performance metrics. More specifically, the proposed BC-BIHQL and BC-IGQL algorithms can yield more non-dominated bi-criteria solutions with the most substantial competitiveness than the remaining algorithms. At the same time, both are competitive with each other on the benchmark problems. Moreover, the BC-IGQL algorithm dominates almost 97% and 99% of the solutions reached by the BC-IG, BC-IGALL, and BC-VBIH algorithms in small and large datasets. Similarly, The BC-BIHQL algorithm dominates almost 98% and 99% of the solutions reached by the BC-IG, BC-IGALL, and BC-VBIH algorithms in small and large datasets, respectively. This means that, among all the features that have been compared, the Q-learning-guided algorithms demonstrate the highest level of competitiveness. The outcomes of this study encourage us to discover many more bi-criteria NWFSPs to reveal the trade-off between other conflicting objectives, such as makespan & the number of early jobs, to overcome various industries' problems.

Multi-policy deep reinforcement learning for multi-objective multiplicity flexible job shop scheduling

This study considers the simultaneous minimization of makespan and total tardiness for the multi-objective multiplicity flexible job shop scheduling problem (MOMFJSP). A deep reinforcement learning framework employing a multi-policy proximal policy optimization algorithm (MPPPO) is developed to solve MOMFJSP. The MOMFJSP is treated as a Markov decision process, allowing an intelligent agent to make sequential decisions based on the current production status. This framework involves multiple policy networks with different objective weight vectors. Using MPPPO, these networks are optimized simultaneously to obtain a set of high-quality Pareto-optimal policies. Moreover, a fluid model is introduced to extract state features and devise composite dispatching rules as discrete actions. A multi-policy co-evolution mechanism (MPCEM) is proposed to facilitate collaborative evolution among policy networks, supported by a reward mechanism that considers the objective weights. A training algorithm based on MPPPO is designed for learning across multiple policy networks. The effectiveness and superiority of the proposed method are confirmed through comparisons with composite dispatching rules and other scheduling methods.

Effective social spider optimization algorithms for distributed assembly permutation flowshop scheduling problem in automobile manufacturing supply chain

This paper presents a novel distributed assembly permutation flowshop scheduling problem (DAPFSP) based on practical problems in automobile production. Different from the existing research on DAPFSP, this study considers that each component of the final product is composed of more than one part. Components are processed in a set of identical components manufacturing factories and are assembled into products in the assembly factory. The integration of manufacturing processes is an important objective of Industry 4.0. For solving this problem with the minimum makespan criterion, we introduce a three-level representation and a novel initialization method. To enhance the search ability of the proposed algorithms, we design three local search methods and two restart procedures according to characteristics of the problem. Then, by incorporating the problem specific knowledge with the social spider optimization algorithm (SSO), we propose three SSO variants: the SSO with hybrid local search strategies (HSSO), the HSSO with restart procedures (HSSOR), and the HSSOR with self-adaptive selection probability (HSSORP). Finally, 810 extended instances based on the famous instances are used to test the proposed algorithms. In most cases, HSSOR performs the best, with an average comparison metric value of 0.158% across three termination conditions, while the average comparison metric value for the best comparison method is 2.446%, which is 15.481 times that of HSSOR. Numerical results demonstrate that the proposed algorithms can solve the problem efficiently.

Dynamic Load Balancing in Cloud Computing: Optimized RL-Based Clustering with Multi-Objective Optimized Task Scheduling

Dynamic load balancing in cloud computing is crucial for efficiently distributing workloads across available resources, ensuring optimal performance. This research introduces a novel dynamic load-balancing approach that leverages a deep learning model combining Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) to calculate load values for each virtual machine (VM). The methodology aims to enhance cloud performance by optimizing task scheduling and stress distribution. The proposed model employs a dynamic clustering mechanism based on computed loads to categorize VMs into overloaded and underloaded clusters. To improve clustering efficiency, the approach integrates Reinforcement Learning (RL) with a sophisticated Hybrid Lyrebird Falcon Optimization (HLFO) algorithm. HLFO merges the Lyrebird Optimization Algorithm (LOA) and Falcon Optimization Algorithm (FOA), enhancing the effectiveness of load balancing. A Multi-Objective Hybrid Optimization model is introduced to optimize task scheduling while considering Quality of Service (QoS) parameters, including makespan minimization, energy consumption reduction, balanced CPU utilization, efficient memory usage, and task prioritization. The implementation, conducted in Python and CloudSim, demonstrates the model’s ability to effectively allocate work between virtual machines (VMs) and physical machines (PMs), resulting in improved resource utilization, shortened makespan, enhanced CPU usage, and rigorous assessments affirming its efficacy. This research addresses the complexity of dynamic load balancing in cloud environments by combining deep learning, reinforcement learning, and hybrid optimization techniques, offering a comprehensive solution to optimize cloud performance under varying workloads and resource conditions.

EPTAS for parallel identical machine scheduling with time restrictions

We consider the non-preemptive scheduling problem on identical machines where there is a parameter B and each machine in every unit length time interval can process up to B different jobs. The goal function we consider is the makespan minimization and we develop an EPTAS for this problem. Prior to our work a PTAS was known only for the case of one machine and constant values of B, and even the case of non-constant values of B on one machine was not known to admit a PTAS.