Job Splitting Research Articles

An effective multi-stage evolutionary algorithm for distributed scheduling with splitting jobs in heterogeneous factories

This article examines an alliance of heterogeneous factories operating as a production network, in which jobs can be divided into several sub-jobs and independently processed in distributed factories. This problem is considered as a distributed unrelated parallel machine scheduling with splitting jobs (DUPMSP/S). A mathematical model and an effective multi-stage evolutionary algorithm (EMSEA) are proposed, aiming to minimize the total tardiness and total cost of production and transportation. In the EMSEA, the optimization process is divided into three stages according to the population in each generation, and four problem-based initial methods and three knowledge-based local exploitation strategies are embedded to improve its performance. Extensive experiments are conducted to compare the EMSEA with four other algorithms and to compare the scheduling model with no splitting jobs. The results demonstrate that EMSEA is the most promising method in solving the DUPMSP/S, and the job splitting mode is effective.

Job splitting on the ALICE grid, introducing the new job optimizer for the ALICE grid middleware

This contribution introduces the job optimizer service for the nextgeneration ALICE Grid middleware, JAliEn (Java Alice Environment). It is a continuous service running on central machines and is essentially responsible for splitting jobs into subjobs, to then be distributed and executed on the ALICE grid. There are several ways of creating subjobs based on various strategies relevant to the aim of any particular grid job. Therefore a user has to explicitly declare that a job is to be split, and also define the strategy to be used. The new job optimizer service aims to retain the old ALICE grid middleware functionalities from the user’s point of view while increasing the performance and throughput. One aspect of increasing performance is looking at how the job optimizer interacts with the job queue database. A different way of describing subjobs in the database is presented, to minimize resource usage. There is also a focus on limiting communications with the database, as this is already a congested area. Furthermore, a new solution to splitting based on the locality of job input data will be presented, aiming to split into subjobs more efficiently, therefore making better use of resources on the grid to further increase throughput. Added options for the user regarding splitting by locality, such as setting a minimum limit for a subjob size, will also be explored.

Improved multi-objective artificial bee colony algorithm for parallel machine lot-streaming scheduling problem with limited and unequal sub-lots

Job splitting is a full-time effective measure used to improve corporate competitiveness, especially when the lot size of jobs is considerably large. This work investigates a parallel machine lot-streaming scheduling problem, where unequal sub-lot is considered and the number of sub-lots is strictly limited by that of cutters. Focus on this problem, a mixed-integer linear programming model is formulated to minimize makespan and due time deviation simultaneously, to scrutinize the coupling relationship among decision variables, i.e., the number and size of sub-lots, the machine allocation, and the processing order of all sub-lots. Then, an improved multi-objective artificial bee colony algorithm (IMOABC) with two categories of improvements is developed to obtain high-quality Pareto front solutions. Specifically, a semi-random initialization is proposed to balance the workload as evenly as possible, which includes a half-normal distribution strategy for determining the number of utilized sub-lots, an equal-probability lot-splitting strategy for determining the size of each sub-lots, and a machine allocation strategy to synchronize the completion time of all machines. Besides, a multipoint preservative crossover is designed to enhance diversity in the employed bee phase, a sub-lot adjustment operator is proposed to implement objective-oriented local search in the onlooker bee phase, and an individual restart mechanism is adopted to avoid being trapped in local optimum in the scout bee phase. Extensive experiment results demonstrate that IMOABC significantly outperforms the other six state-of-the-art algorithms in terms of diversity and convergence.

Self-growth learning-based machine scheduler to minimize setup time and tardiness in OLED display semiconductor manufacturing

This paper focuses on a scheduling problem of the evaporation and encapsulation (EVEN) line in organic light-emitting diode (OLED) display manufacturing towards minimizing total setup time and tardiness of allocated jobs. This scheduling problem is an unrelated dedicated parallel machine scheduling (UDPMS) problem with practical complex constraints including machine availability, family setup, preventive maintenance (PM), and job splitting. There are three major points to this problem. First, the processing of a job on a machine should be completed before its due date. Second, setups should be reduced to minimize labor costs. Finally, a job is able to be split into one or more sub-jobs for processing on machines independently. To obtain a schedule to minimize total setup time and tardiness of allocated jobs, we suggest two novel machine schedulers such as deep learning-based and self-growth learning-based schedulers, called DLS and SGLS, respectively. Although the structure of the proposed schedulers is identical, especially, SGLS incrementally learns to explore more effective allocation patterns by preserving the obtained knowledge from the trained DLS based on self-growth learning. The comprehensive experiments show that SGLS produces satisfactory schedules in terms of minimizing total setup time and tardiness. In particular, when the number of jobs and the ratio of job sizes are larger, SGLS achieves a schedule with both less setup time and tardiness compared to others.

Optimal Scheduling of Rainwater Collection Vehicles: Mixed Integer Programming and Genetic Algorithms

Due to climate change, some areas in the world witnessed higher levels of heavy rain than the capacity of the wastewater system of the streets. Therefore, water tankers are used for the dewatering process to take the extra rainwater from the streets to keep a smooth flow of vehicles and to use the water in agriculture and industry. Water is taken to a water treatment plant. Performing the dewatering process as fast as possible, especially in crowded streets, was ignored by researchers. In this study, at first, the problem was solved using two mixed integer programming (MIP) models. A new variant of identical parallel machine scheduling with job splitting is proposed for the first time, where one or at most two tankers can work at the same flood location at the same time. This is performed in the second model. However, the first model considers dividing the dewatering processes into two phases, where the first one, which is more urgent, is to reduce the amount of floodwater. The second one is for dewatering the rest of the water. Then two genetic algorithms (GAs) were used to solve faster the two MIP models, which are NP-hard problems. At first, the MIP and GA models were applied to small-sized problems. Then GA was used for large practical data sets. Results showed that for small problems, MIP and GA gave optimal solutions in a reasonable number of iterations, while for larger problems, good solutions were obtained in a reasonable number of iterations.

Job scheduling for maximum revenue on uniform, parallel machines with major and minor setups and job splitting

We consider a revenue maximization scheduling problem where jobs can be split on parallel, uniform machines. By assuming that only major and minor setups exist between jobs and that these can be grouped into families, we reformulate the scheduling problem as a continuous knapsack problem with setup time. We then create the Revenue Rate Heuristic to solve the maximum revenue scheduling problem for both the partial and binary revenue cases. This makes use of a revenue rate – the ratio between total revenue that can be obtained from a job and the time required to achieve the revenue. The Revenue Rate Heuristic schedules the job with the highest revenue rate first and updates all the revenue rates accordingly based on existing scheduled families and remaining capacity. In cases where there are no setup times or if there is only one machine and an ordering of job revenue and production time, we are able to show that the Revenue Rate Heuristic is optimal. Numerical studies show that the Revenue Rate Heuristic performs well with an average optimality gap of 3.47% across a large set of parameters and when the setup times across families are different from each other. In a case study based on firm-level data, we also show that the average optimality gap remains small.

Scheduling unrelated machines with job splitting, setup resources and sequence dependency

ABSTRACT We examine the parallel machine scheduling problem where a set of jobs are to be processed by a set of unrelated parallel machines. We examine the most general among the variations for which an exact method has been proposed regarding makespan minimisation. This is because, apart from unrelated machines, we allow for (i) job splitting: each job's quantity can be split and processed by multiple machines simultaneously; (ii) sequence- and machine-dependent setup times: the setup time when job j succeeds k is different than the time when k succeeds j and varies also per machine m; and (iii) setup resource constraints: the number of setups that can be performed simultaneously on different machines is restricted. We present novel lower bound formulations and a heuristic that solves instances of up to 1000 jobs in a few minutes at an average gap of less than . Then, we propose a logic-based Benders decomposition, which, coupled with our heuristic, solves instances of up to 200 jobs and 20 machines to near optimality in less than two hours. Our method is used for a broad range of instances from textile manufacturing, thus yielding valuable managerial insights on makespan's versatility under varying machines or resources.

Unrelated Parallel Machine Scheduling with Job Splitting, Setup Time, Learning Effect, Processing Cost and Machine Eligibility

This work investigates an unrelated parallel machine scheduling problem in the shared manufacturing environment. Based on practical production complexity, five job and machine-related factors, including job splitting, setup time, learning effect, processing cost and machine eligibility constraint, are integrated into the considered problem. Parallel machines with uniform speed but non-identical processing capabilities are shared on a sharing service platform, and jobs with different types can only be processed by the machines with matching eligibilities. The platform pays an amount of processing cost for using any machine to process the jobs. To balance the processing cost paid and the satisfaction of customers, we aim to minimize the weighted sum of total processing cost and total completion time of jobs in the considered problem. We establish a mixed integer linear programming model, and provide a lower bound by relaxing the machine eligibility constraint. The CPLEX solver is employed to generate optimal solutions for small-scale instances. For large-scale instances, we propose an efficient heuristic algorithm. Experimental results demonstrate that for various instance settings, the proposed algorithm can always produce near optimal solutions. We further present several managerial insights for the shared manufacturing platform.

Unrelated parallel machine scheduling with processing cost, machine eligibility and order splitting

Under the background of the emerging of shared manufacturing economics, this work addresses a new production order scheduling problem on unrelated parallel machines. Customer orders with release times are of various types depending on their specific product demands. Unrelated machines may be rented for processing orders via one cloud manufacturing service platform. It occurs a uniform processing cost once any machine is rented (via contract) for a given length time duration to process the orders. Each machine is generally able to process some but not all types of orders, i.e., machine eligibility is considered. Orders can be split into sub-orders and processed on their eligible machines simultaneously. For the objective of minimizing the weighted sum of total completion time of orders and total processing cost of machines being used, we establish a mixed integer linear programming model. We provide a lower bound of the considered problem by constraint relaxation, and present the pseudocode of an approach to obtain the lower bound. CPLEX is employed to generate optimal solutions for small-scale instances. For large-scale instances, two heuristic algorithms named Type-Based Greedy and Improved Differential Evolution are developed. The former algorithm selects a smallest set of machines to process the jobs and makes use of job splitting as much as possible, while the latter one is to acquire a best local optimal solution via finite times random global search in the feasible region. Computational experiments are carried out to demonstrate the efficiency and effectiveness of the proposed heuristics.

Scheduling problem in seru production system considering DeJong’s learning effect and job splitting

Scheduling problem in seru production system considering DeJong’s learning effect and job splitting

A green model for identical parallel machines scheduling problem considering tardy jobs and job splitting property

• A bi-objective green model has been formulated to solve the problem of scheduling parallel machines considering job splitting property. • The first objective function minimizes the total number of tardy jobs while the second objective function is minimization of total energy consumption. • An augmented ε-constraint method has been deployed for solving small-scale problems. • To solve large-scale problems, an efficient simulated annealing algorithm has been developed. • A harmony search algorithm has also been applied to examine the quality of the proposed SA algorithm. • Random generated problems have been used to compare the results of three deployed algorithms. In most organizations, especially order-oriented ones meeting deadlines are crucial. Job shop environments could be mentioned as an example where decision makers are try to schedule all jobs in such a way that tardy jobs (TJ) are minimized. Indeed, manufacturers are received customers’ orders and required to deliver them no later than the determined due dates. Otherwise, penalties should be paid to customers and it can lead to a huge amount of financial loss. Also, regarding global warming and climate changes manufacturers should redesign their processes from an eco-friendly perspective. Motivated by these issues, in this paper, a green bi-objective model has been formulated to solve the problem of scheduling parallel machines considering TJ and job splitting property (JSP). In the proposed model, the first objective function minimizes the total number of TJ while the second objective function is minimization of total energy consumption. An augmented ε-constraint method has been deployed for solving small-scale problems. However, to solve large-scale problems, an efficient Simulated Annealing (SA) algorithm has been developed while a Harmony Search (HS) algorithm has also been applied to examine the quality of the proposed SA algorithm. Random generated problems have been used to compare the results of three deployed algorithms. Results approved that the proposed SA algorithm outperforms others significantly. In particular, SA solved the problems sooner than others while its solutions were closer to solutions of the augmented ε-constraint method.

Work Allocating Strategy Using a Powerful Prioritized Tasks in Mobile Cloud Computing Atmosphere

Abstract: In recent times, users necessitate and expect more demanding criteria to perform computational in-depth applications on their mobile devices. Based on the mobile device limitations such as processing power and battery life, Mobile Cloud Computing (MCC) is turned to be a more attractive choice to influence these drawbacks as a mobile computation can be provided to the cloud, which is coined as Mobile computation deceive. Prevailing researches on mobile computation offloading determines offloading mobile computation to single cloud. Moreover, in real time environment, computation service can be offered by multiple clouds for every computation services. Therefore, a novel and an interesting research crisis in mobile computation offloading begins with, how to choose a computation service for every tasks of mobile computation like computation time, energy consumption and cost of using these computation services. This is also termed as multi-site computation offloading in mobile cloud computation. In this examination deceive computation to diverse cloudlets/data centres with respect to task scheduling is formulated for examination. So, a Searching algorithm known as Accelerated Cuckoo Search Algorithm based job splittingis designed to attain higher data transmission rate in the MCC. The results of the certain method outperform the prevailing methods in terms of effectual job splitting; transmission speed, Bandwidth used, execution time of a job, transmission value, through put value, buffering overhead and reduced waiting time. The simulation was carried out in Clouds environment for good output. Keywords: Computation Deceive, Mobile Cloud Computing, Scheduling, Searching Algorithm, WorkSplitting.

Planning Production and Equipment Qualification under High Process Flexibility

We present and solve a joint production and qualification planning problem for a manufacturing environment with high process flexibility. Various factors contribute to the complexity of the problem, one of which is product‐machine mapping: Each machine may be qualified to produce multiple products and each product can be produced on multiple machines. To meet a build‐plan, the factory needs to not only determine a multi‐machine multi‐product production schedule that accounts for sequence‐dependent setup time, but also a qualification schedule which prescribes whether and when a machine should undergo a qualification process such that it is ready to produce a product. We consider processing characteristics including sequence‐dependent setups, job splitting, and machine eligibility in addition to qualification. We formulate the mathematical model as an MILP problem that minimizes the total weighted delay. In this study, we describe two heuristic solution approaches developed for this complex decision setting and the application at Intel. We compare our approach with Intel's current approach which is a spreadsheet‐based manual approach that relies on the experience of the factory planner. The results indicate that our approach, which we call the GS approach, dominates in terms of minimizing the delay. Our approach performs well when capacity is tight and additional qualifications are considered while the Intel approach may perform better on reducing the setup and qualification time in certain problem instances, particularly those with loose capacity. As a result, an integrated approach which selects the better solution from both approaches is proposed, which shows significant reduction over the current approach in both the weighted delay and the setup and qualification time.

Secure Coded Multi-Party Computation for Massive Matrix Operations

In this article, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are not reliable. Some of them may collude to gain information about the input data (semi-honest workers). The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, each share's size is assumed to be at most 1/k fraction of the input matrix, for some k ∈ \mathbb N. The objective is to minimize the number of workers needed to perform the computation task correctly, such that even if an arbitrary subset of t-1 workers, for some t ∈ \mathbb N, collude, they cannot gain any information about the input matrices. We propose a sharing scheme, called polynomial sharing, and show that it admits basic operations such as adding and multiplication of matrices and transposing a matrix. By concatenating the procedures for basic operations, we show that any polynomial function of the input matrices can be calculated, subject to the problem constraints. We show that the proposed scheme can offer order-wise gain in terms of the number of workers needed, compared to the approaches formed by the concatenation of job splitting and conventional MPC approaches.

A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators

We examine a parallel machine scheduling problem with a job splitting property, sequence-dependent setup times, and limited setup operators, for minimizing makespan. Jobs are split into arbitrary (job) sections that can be processed on different machines simultaneously. When a job starts to be processed on a machine, a setup that requires an operator is performed, and the setup time is sequence-dependent. The number of setup operators is limited, and hence not all of the machines can be set up at the same time. For this problem, we propose a mathematical programming model and analyze a lower bound. We then develop a simple but efficient heuristic algorithm so that it can be used in practice, and analytically derive a worst-case bound of the algorithm. We finally evaluate the performance of the proposed algorithm numerically with various scenarios.

Scheduling uniform parallel dedicated machines with job splitting, sequence-dependent setup times, and multiple servers

We address a uniform parallel machine scheduling problem with machine eligibility, job splitting, sequence-dependent setup times, and limited setup servers, which has been defined from a real application of piston manufacturing in Korea. The objective is to minimize the makespan. We first propose a mathematical programming model and derive four lower bounds. We then develop an efficient heuristic algorithm that assigns jobs to machines by considering processing times, setup times, and machine eligibility constraints, and then balances machine workloads by splitting jobs. We analyze a worst-case bound of the algorithm and perform extensive experiments with various scenarios. The gap from a lower bound is not significant for practical cases.

Insertion of new idle time for unrelated parallel machine scheduling with job splitting and machine breakdowns

In real production systems, there are some uncertainties such as failure uncertainty and uncertain processing time. This paper addresses predictable scheduling and rescheduling, considering machine breakdown and eligibility in the unrelated parallel machines environment with job splitting including textile industry and printed circuit board (PCB) manufacturing. We propose a new approach to achieving robust and stable schedule to minimize expected maximum completion time and expected total deviation between the jobs' planned start times and actual start times simultaneously. In the first step of the approach, we present a predictable scheduling algorithm using the insertion of new idle time considering job splitting. In the next step, we present a schedule repair rule considering job splitting for rescheduling. The computational experiments show that the proposed algorithm outperforms alternative algorithms.

Parallel machine scheduling with multiple processing alternatives and sequence-dependent setup times

This paper examines a parallel machine scheduling problem in which jobs can be processed either in multiple parts or in a complete form and the number of possible job splitting alternatives of jobs is more than one. There are sequence-dependent setup times between different jobs (or parts), and the objective is to minimise makespan by choosing an appropriate processing alternative for each job, assigning parts (or jobs) to machines, and determining the sequence of parts on the machines. This work is motivated from a 3D printer-based manufacturing system that produces customised products for individuals or start-up companies. When 3D printers are used as processing machines, a product can be printed in diverse forms composed of different parts. To address the problem, we first propose a mixed integer programming model and then develop a hybrid genetic algorithm which is combined with a travelling salesman problem-based heuristic algorithm. The experimental results show that the average gap between a solution from the proposed algorithm and an optimal one solved with CPLEX or a lower bound is very small. The paired t-test shows that there is a significant improvement for processing jobs with multiple alternatives.

Two-step approach for scheduling jobs to non-related parallel machines with sequence dependent setup times applying job splitting

This paper investigates the problem of manufacturing processes by bar-turning machine. The scenario is modeled as a problem of scheduling jobs to non-related parallel machines with sequence dependent setup times applying batch splitting. In order to optimize this problem, we propose a mixed integer linear programming model (MILP). However, as shown in numerical result, it is limited to solve only small instances. Hence, a two-step approach is presented to solve real-size instances. This method uses a relaxed version of the MILP model proposed, however, allowing solutions with sub-tour. Afterwards, a heuristic algorithm is presented to adjust these solutions. The numerical results analyze 20 instances with different sizes, compositions of demand and set of machines. Some general rules to characterize good solutions were presented after investigating the results. These rules associate the quantity of pieces for each demand and the type of machine used, and the complexity of the piece demanded for the type of machine.

Iterative job splitting algorithms for parallel machine scheduling with job splitting and setup resource constraints

This paper examines a parallel machine scheduling problem with job splitting and setup resource constraints for makespan minimization. Jobs can be split into multiple sections, and such sections can be processed simultaneously on different machines. It is necessary to change setups between the processes of different jobs on a machine, and the number of setups that can be performed simultaneously is restricted due to limited setup operators. To solve this problem, we propose a mathematical programming model and develop iterative job splitting algorithms that improve a feasible initial solution step by step, taking into account job splitting, setup times, and setup resources. We derive a worst-case performance ratio of the algorithms and evaluate the performance of the proposed heuristics on a large number of randomly generated instances. We finally provide a case study of piston manufacturing in Korea.