Job Sizes Research Articles

Single machine parallel-batch scheduling under time-of-use electricity prices: New formulations and optimisation approaches

Electricity costs account for a relatively large proportion of total production costs in many energy-intensive manufacturing industries. And energy-efficient scheduling is getting increasing attention from researchers owing to its wide real-world applications and computational challenges. In this study, the single-machine parallel-batch scheduling problem with non-identical job sizes under time-of-use electricity prices is investigated. The objective is to minimise the total energy consumption cost such that the makespan does not exceed a given deadline. First, an improved time-slot-indexed formulation is proposed to eliminate symmetric solutions. Subsequently, a new set partition-based formulation is developed. To the best of our knowledge, there is no exact algorithm for this problem, except for some formulations solved by off-the-shelf solvers. To address this problem, a branch-and-price algorithm is developed with a novel and efficient branching rule. In addition, a column-generation-based heuristic is proposed to solve larger-scale instances. Extensive numerical experiments show that the efficiency of the branch-and-price algorithm is significantly better than that of off-the-shelf solvers, and many instances with up to 100 jobs could be solved to optimality within a 20-minute computational time limit for the first time. The column-generation-based heuristic can efficiently provide better solutions than existing heuristics (2.75% average gap in three minutes on instances with 100 jobs and 3.12% average gap in ten minutes on instances with 200 jobs).

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.

EPTAS for load balancing problem on parallel machines with a non-renewable resource

The problem considered is the non-preemptive scheduling of independent jobs that consume a resource (which is non-renewable and replenished regularly) on parallel uniformly related machines. The input defines the speed of machines, size of jobs, the quantity of the resource required by the jobs, the replenished quantities, and replenishment dates of the resource. Every job can start processing only after the required quantity of the resource is allocated to the job. The objective function is a generalization of makespan minimization and minimization of the lp-norm of the vector of loads of the machines. We present an EPTAS for this problem. Prior to our work only a PTAS was known in this non-renewable resource settings only for the special case of our problem of makespan minimization on identical machines.

Effective league championship algorithm and lower bound procedure for scheduling a single batch-processing machine with non-identical job sizes and job rejection

We address the scheduling problem of a set of non-identical size jobs on a single batch-processing machine (SBPM) wherein the scheduler can make decision whether to schedule a job in batches or not to schedule it with a job-dependent penalty. The processing time of a batch is the greatest job processing time in that batch (parallel batching or p-batching). The scheduler wants to minimize a given objective function f, where f is the total rejection penalties of the rejected jobs (rejection cost) plus the makespan of the scheduled ones. We formulate the aforementioned problem as a 0–1 mixed integer programming model. We also apply an effective dynamic programming algorithm (DPA) to calculate a lower bound (LB) on the optimal cost of the problem. To tackle the problem, we propose a grouping algorithm, based on league championship algorithm (LCA), with new updating equations maintaining the major characteristics of the original updating equations of the LCA and well-suited to the structure of the problem. For small problems, performance of the proposed LCA is compared with GAMS/CPLEX solver. For large-scale instances, a genetic algorithm is adopted as a basis for comparison. Simulated experiments confirm the performance of the proposed methods.

Performance Analysis of Modified SRPT in Multiple-Processor Multitask Scheduling

In this paper we study the multiple-processor multitask scheduling problem in both deterministic and stochastic models, where each job have several tasks and is complete only when all its tasks are finished. We consider and analyze Modified Shortest Remaining Processing Time (M-SRPT) scheduling algorithm, a simple modification of SRPT, which always schedules jobs according to SRPT whenever possible, while satisfying the non-preemptive constraint. The M-SRPT algorithm is proved to achieve a competitive ratio of θ(log α + β) for minimizing response time, where α denotes the ratio between maximum job workload and minimum job workload, β represents the ratio between maximum non-preemptive task workload and minimum job workload. In addition, the competitive ratio achieved is shown to be optimal (up to a constant factor), when there are constant number of machines. We further consider the problem under Poisson arrival and general workload distribution (i. e., M/GI/N system), and show that M-SRPT achieves asymptotic optimal mean response time when the traffic intensity ρ approaches 1, if job size distribution has finite support. Beyond finite job workload, the asymptotic optimality of M-SRPT also holds for infinite job size distributions with certain probabilistic assumptions, for example, M/M/N system with finite task workload.

Group Technology Scheduling with Due-Date Assignment and Controllable Processing Times

This paper investigates common (slack) due-date assignment single-machine scheduling with controllable processing times within a group technology environment. Under linear and convex resource allocation functions, the cost function minimizes scheduling (including the weighted sum of earliness, tardiness, and due-date assignment, where the weights are position-dependent) and resource-allocation costs. Given some optimal properties of the problem, if the size of jobs in each group is identical, the optimal group sequence can be obtained via an assignment problem. We then illustrate that the problem is polynomially solvable in O(℘3) time, where ℘ is the number of jobs.

A tabu-based adaptive large neighborhood search for scheduling unrelated parallel batch processing machines with non-identical job sizes and dynamic job arrivals

A tabu-based adaptive large neighborhood search for scheduling unrelated parallel batch processing machines with non-identical job sizes and dynamic job arrivals

Scheduling Policies for Stability and Optimal Server Running Cost in Cloud Computing Platforms

We propose throughput and cost optimal job scheduling algorithms in cloud computing platforms offering Infrastructure as a Service. We first consider online job migration and propose job scheduling algorithms to minimize job migration and server running costs. We consider algorithms that assume knowledge of job-size on the arrival of jobs. We characterize the optimal cost subject to system stability. We develop a drift-plus-penalty framework based algorithm that can achieve optimal cost arbitrarily closely. Specifically, this algorithm yields a tradeoff between delay and costs. We then relax the job-size knowledge assumption and give an algorithm that uses readily offered service to the jobs. We show that this algorithm gives order-wise identical cost as the job size based algorithm. Later, we consider offline job migration that incurs migration delays. We again present throughput optimal algorithms that minimize server running cost. We illustrate the performance of the proposed algorithms and compare these to the existing algorithms via simulation.

A Hybrid Large Neighborhood Search Method for Minimizing Makespan on Unrelated Parallel Batch Processing Machines with Incompatible Job Families

This paper studies a scheduling problem with non-identical job sizes, arbitrary job ready times, and incompatible family constraints for unrelated parallel batch processing machines, where the batches are limited to the jobs from the same family. The scheduling objective is to minimize the maximum completion time (makespan). The problem is important and has wide applications in the semiconductor manufacturing industries. This study proposes a mixed integer programming (MIP) model, which can be efficiently and optimally solved by commercial solvers for small-scale instances. Since the problem is known to be NP-hard, a hybrid large neighborhood search (HLNS) combined with tabu strategy and local search is proposed to solve large-scale problems, and a lower bound is proposed to evaluate the effectiveness of the proposed algorithm. The proposed algorithm is evaluated on numerous compatible benchmark instances and newly generated incompatible instances. The results of computational experiments indicate that the HLNS outperforms the commercial solver and the lower bound for incompatible problems, while for compatible problems, the HLNS outperforms the existing algorithm. Meanwhile, the comparison results indicate the effectiveness of the tabu and local search strategies.

A machine learning-based study of multifactor susceptibility and risk control of induced seismicity in unconventional reservoirs

A comprehensive dataset from 594 fracturing wells throughout the Duvernay Formation near Fox Creek, Alberta, is collected to quantify the influences of geological, geomechanical, and operational features on the distribution and magnitude of hydraulic fracturing-induced seismicity. An integrated machine learning-based investigation is conducted to systematically evaluate multiple factors that contribute to induced seismicity. Feature importance indicates that a distance to fault, a distance to basement, minimum principal stress, cumulative fluid injection, initial formation pressure, and the number of fracturing stages are among significant model predictors. Our seismicity prediction map matches the observed spatial seismicity, and the prediction model successfully guides the fracturing job size of a new well to reduce seismicity risks. This study can apply to mitigating potential seismicity risks in other seismicity-frequent regions.

Lot streaming of hybrid flowshops with variable lot sizes and eligible machines

Hybrid flowshops are a special type of manufacturing systems, in which a stage may contain identical or unrelated parallel machines. This paper deals with a more practical approach for lot streaming hybrid flowshop in which the sublot sizes of jobs can vary from one stage to the next according to machines' speed. Two models of mixed-integer nonlinear programming are developed to minimise the make-span of two different hybrid flowshop systems. The first model deals with unrelated parallel machines with eligibility, independent setup time, and variable sublot sizes. The second model is a special case of the hybrid flowshop as it consists of multi-stages comprising one machine at the stages preceding the final stage, while the final stage includes unrelated parallel machines. The first model was studied and the data gathered were analysed using ANOVA test to evaluate the factors' effect on system. The factors are number of jobs, maximum number of batches, setup time, and machine's configuration. The analysis revealed that all the factors were effective. The second model was compared to benchmarking published paper and it gets better results.

Financing practices of Micro and Small Entrepreneurs using WSM MCDM Method

A small or micro enterprise is usually a one-person show. A partnership is held by a firm or corporation Even in small units, operations are mainly carried out by shareholders or Carried out by one of the directors. In practice, others are sleeping partners or directors, essentially helping out financing. A company is classified If the paid up capital is less than or equal to 20,000 Birr As micro. Similarly, a company has its paid-up capital when less than or equal to Birr 500,000 considered small. However, it is the size of jobs or number of employees in MSE Does not provides information about Key Differences between Small Business and Small Business are scale and size. A small business is a type of small a business employing less than 10 persons, small Businesses with up to 500 employees including Haksever has fewer than 500 employees Define and characterizes a small business with shows following characteristics Management is independent; usually the manager is also the owner. Working Stress Design Method Reinforced A concrete design method is used Concrete is elastic, whereas steel and concrete are elastic in nature, in which the relationship between loads and stresses is linear. Working pressure method (WSM) This traditional design is perfect.

Optimal Scheduling in the Multiserver-job Model under Heavy Traffic

Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Essentially all of the theoretical work on multiserver-job systems focuses on maximizing utilization, with almost nothing known about mean response time. In simpler settings, such as various known-size single-server-job settings, minimizing mean response time is merely a matter of prioritizing small jobs. However, for the multiserver-job system, prioritizing small jobs is not enough, because we must also ensure servers are not unnecessarily left idle. Thus, minimizing mean response time requires prioritizing small jobs while simultaneously maximizing throughput. Our question is how to achieve these joint objectives. We devise the ServerFilling-SRPT scheduling policy, which is the first policy to minimize mean response time in the multiserver-job model in the heavy traffic limit. In addition to proving this heavy-traffic result, we present empirical evidence that ServerFilling-SRPT outperforms all existing scheduling policies for all loads, with improvements by orders of magnitude at higher loads. Because ServerFilling-SRPT requires knowing job sizes, we also define the ServerFilling-Gittins policy, which is optimal when sizes are unknown or partially known.

On the Stochastic and Asymptotic Improvement of First-Come First-Served and Nudge Scheduling

Recently it was shown that, contrary to expectations, the First-Come-First-Served (FCFS) scheduling algorithm can be stochastically improved upon by a scheduling algorithm called Nudge for light-tailed job size distributions. Nudge partitions jobs into 4 types based on their size, say small, medium, large and huge jobs. Nudge operates identical to FCFS, except that whenever a small job arrives that finds a large job waiting at the back of the queue, Nudge swaps the small job with the large one unless the large job was already involved in an earlier swap. In this paper, we show that FCFS can be stochastically improved upon under far weaker conditions. We consider a system with 2 job types and limited swapping between type-1 and type-2 jobs, but where a type-1 job is not necessarily smaller than a type-2 job. More specifically, we introduce and study the Nudge- K scheduling algorithm which allows type-1 jobs to be swapped with up to K type-2 jobs waiting at the back of the queue, while type-2 jobs can be involved in at most one swap. We present an explicit expression for the response time distribution under Nudge- K when both job types follow a phase-type distribution. Regarding the asymptotic tail improvement ratio (ATIR), we derive a simple expression for the ATIR, as well as for the K that maximizes the ATIR. We show that the ATIR is positive and the optimal K tends to infinity in heavy traffic as long as the type-2 jobs are on average longer than the type-1 jobs.

Job grade camouflage: When low gender pay gap does not mean equal pay

“Equal pay for equal work” is one of the backbone principles of Responsible Leadership. It is also deeply incorporated in legislation, mostly in developed countries. In recent decades, the gender pay gap has been put forward as a general indicator of equality by policy makers and researches alike. Yet, the research outcomes are disturbingly unsettled in comparison to bold political proclamations that are often based on simplified statistics. In our article we show, that gender pay gap shrinks substantially if firm-level job grades (based on Hay methodology) are used. The methodology used is gender neutral and focuses solely on the job size, not on the incumbent. Moreover, we show that the gender pay gap is not reflecting the idea of “equal pay for equal work” well. In fact, we conclude that people are being paid unequally regardless their gender. Low or non-existent gender pay gap then might just camouflage real inequalities leading managers and stakeholders to false feeling that company follows responsible leadership principles as defined by Steve Kempster (2016).

Well-behaved online load balancing against strategic jobs

In the online load balancing problem on related machines, we have a set of jobs (with different sizes) arriving online, and the task is to assign each job to a machine immediately upon its arrival, so as to minimize the makespan, i.e., the maximum completion time. In classic mechanism design problems, we assume that the jobs are controlled by selfish agents, with the sizes being their private information. Each job (agent) aims at minimizing its own cost, which is its completion time plus the payment charged by the mechanism. Truthful mechanisms guaranteeing that every job minimizes its cost by reporting its true size have been well studied (Aspnes et al. JACM 44(3):486–504, 1997, Feldman et al. in: EC, 2017). In this paper, we study truthful online load balancing mechanisms that are well-behaved (machine with higher speed has larger workload). Good behavior is important as it guarantees fairness between machines and implies truthfulness in some cases when machines are controlled by selfish agents. Unfortunately, existing truthful online load balancing mechanisms are not well behaved. We first show that to guarantee producing a well-behaved schedule, any online algorithm (even non-truthful) has a competitive ratio at least \(\varOmega (\sqrt{m})\), where m is the number of machines. Then, we propose a mechanism that guarantees truthfulness of the online jobs and produces a schedule that is almost well-behaved. We show that our algorithm has a competitive ratio of \(O(\log m)\). Moreover, for the case when the sizes of online jobs are bounded, the competitive ratio of our algorithm improves to O(1). Interestingly, we show several cases for which our mechanism is actually truthful against selfish machines.

Graduating college students apply here: Communicating family firm ownership and firm size

Attracting business college graduates is a major challenge for the growth and transgenerational success of family firms. Moreover, the institutional context of countries is critical in explaining family firms’ potential advantages and/or disadvantages in attracting nonfamily talent. This study aims to elucidate how communicating firm ownership (family vs. nonfamily), firm size (large vs. small), and type of job offered (professional vs. nonprofessional) influences the perceptions and attitudes of Latin American business graduates toward working in such firms. In an experimental study that uses job advertisement stimuli, we found that communicating family ownership positively influences career development’s perceptions of firm prestige. Large (vs. small) firm size also has a positive influence on job seekers’ perceptions of firms. Importantly, both firm prestige and career development positively influence the attraction of working in family firms. In this paper, we discuss the differences in the results among countries and professional vs. nonprofessional job positions advertised. The results have several implications for family firm owners and managers.

Fork–join and redundancy systems with heavy-tailed job sizes

We investigate the tail asymptotics of the response time distribution for the cancel-on-start (c.o.s.) and cancel-on-completion (c.o.c.) variants of redundancy-d scheduling and the fork–join model with heavy-tailed job sizes. We present bounds, which only differ in the pre-factor, for the tail probability of the response time in the case of the first-come first-served discipline. For the c.o.s. variant, we restrict ourselves to redundancy-d scheduling, which is a special case of the fork–join model. In particular, for regularly varying job sizes with tail index-nu the tail index of the response time for the c.o.s. variant of redundancy-d equals -min {d_{mathrm {cap}}(nu -1),nu }, where d_{mathrm {cap}} = min {d,N-k}, N is the number of servers and k is the integer part of the load. This result indicates that for d_{mathrm {cap}} < frac{nu }{nu -1} the waiting time component is dominant, whereas for d_{mathrm {cap}} > frac{nu }{nu -1} the job size component is dominant. Thus, having d = lceil min {frac{nu }{nu -1},N-k} rceil replicas is sufficient to achieve the optimal asymptotic tail behavior of the response time. For the c.o.c. variant of the fork–join (n_{mathrm {F}},n_{mathrm {J}}) model, the tail index of the response time, under some assumptions on the load, equals 1-nu and 1-(n_{mathrm {F}}+1-n_{mathrm {J}})nu , for identical and i.i.d. replicas, respectively; here, the waiting time component is always dominant.

Burnout and work-privacy conflict – are there differences between full-time and part-time physicians?

BackgroundChanges in everyday work with regard to working time models have reached the medical profession. The number of physicians working part-time is steadily increasing. At the same time, however, the population's need for care is also rising. This can reinforce the impending shortage of doctors in the future. The aim was to investigate differences in work-privacy conflict and burnout among physicians working full-time or part-time.MethodThe present study includes data from a baseline survey of the long-term study of physicians with different medical backgrounds. The analysis focused on a sub-sample of 598 physicians (not self-employed). The two main outcomes under investigation—burnout and work-privacy conflict—were measured using the Copenhagen Burnout Inventory adapted for health care professionals, as well as the associated subscale of the Copenhagen Psychosocial Questionnaire (COPSOQ). Data analyses included descriptive statistics followed by regression models.ResultsDescriptive analyses show, that 31.8% of physicians are working part-time, whereas 68.2% are working full-time. The part-time subsample is significantly older, and female physicians are more likely to work part-time. With regard to workload and work-privacy conflict, significant differences between part-time and full-time physicians were only observed in terms of work-privacy-conflict. However, regression analysis underline the importance of possible confounding variables (such as medical setting) within the relationship between job size and job-related well-being.DiscussionDifferences in working hour arrangements (full-time or part-time work) are only accompanied by less work-privacy conflict. No differences with regard to burnout (patient-related, work-related or personal) could be obtained. Rather, the data suggests that other job-related variables may play a role and should be further investigated.

Comparative Analysis of USA Green Industries and Green Jobs in Colorado and Pennsylvania

This paper estimates and forecasts the green economies and green jobs in the USA states of Colorado and Pennsylvania. The industry distribution of green jobs in each state is estimated by NAICS code. The occupational distribution of green jobs in each state is estimated by detailed occupational classification and skill levels. Green jobs for each state are forecast for the coming decade. We find substantial differences in the size, structure, distribution, and forecasts of green jobs in each state. We determine that the number of future green jobs in a state is determined by the increasing portion of total jobs in the state comprised of green jobs and the rate of growth of employment in the state, and that green jobs in Colorado are forecast to increase much more rapidly than in Pennsylvania in both percentage and absolute terms. We determine that these changes will alter the future distribution of U.S. green jobs among the states. We also find that the distribution of green jobs among industry sectors in the two states differs significantly. Finally, we find that there are substantial differences in the industrial and occupational distributions of green jobs in Colorado and Pennsylvania. We discuss the implications for Colorado, Pennsylvania, and other states seeking to implement ambitious green initiatives.