Actual Processing Time Research Articles

Estimation of processing time using machine learning and real factory data for optimization of parallel machine scheduling problem

Traditionally, mathematical optimization methods have been applied in manufacturing industries where production scheduling is one of the most important problems and is being actively researched. Extant studies assume that processing times are known or follow a simple distribution. However, the actual processing time in a factory is often unknown and likely follows a complex distribution. Therefore, in this study, we consider estimating the processing time using a machine-learning model. Although there are studies that use machine learning for scheduling optimization itself, it should be noted that the purpose of this study is to estimate an unknown processing time. Using machine-learning models, one can estimate processing times that follow an unknown and complex distribution while further improving the schedule using the computed importance variable. Based on the above, we propose a system for estimating the processing time using machine-learning models when the processing time follows a complex distribution in actual factory data. The advantages of the proposed system are its versatility and applicability to a real-world factory where the processing times are often unknown. The proposed method was evaluated using process information with the processing time for each manufacturing sample provided by research partner companies. The Light gradient-boosted machine (LightGBM) algorithm and Ridge performed the best with MAPE and RMSE. The optimization of parallel machine scheduling using estimated processing time by our method resulted in an average reduction of approximately 30% for the makespan. On the other hands, the results of probabilistic sampling methods which are Kernel Density Estimation, Gamma distribution, and Normal Distribution have shown poorer performance than ML approaches. In addition, machine-learning models can be used to deduce variables that affect the estimation of processing times, and in this study, we demonstrated an example of feature importance computed from experimental data. In addition, machine-learning models can be used to deduce variables that affect the estimation of processing times, and in this study, we demonstrated an example of feature importance computed from experimental data.

Single machine resource allocation scheduling problems with deterioration effect and general positional effect.

This paper investigates single machine scheduling problems where the actual processing time of a job is dependent on its starting time, processing position and the amount of resource allocation. We present two unified models and provide a bicriteria analysis for the general scheduling criteria and the total weighted resource consumption. We consider two different versions for treating the two criteria and show that the unified models can be applied to solve scheduling problems under various due window assignment considerations. We prove that two different versions of the problems can be solved in polynomial time, respectively.

Optimizing batch-processing operations with batch-position-based learning effects

Motivated by applications in porcelain-making companies, we consider a type of optimization problems for batch-processing operations. In production, a single batch-processing machine with a fixed capacity is used to process jobs. Several jobs can be processed together if their total size is no more than the machine capacity. Batch-position-based learning effects are considered because workers become skillful gradually after they perform the processing task repeatedly. The actual processing time of a batch is a decreasing function of its position in production. The objective is to minimize makespan and we consider three different problems. In the first problem, jobs have identical sizes and we present an algorithm which can find optimal solutions in polynomial time. In the second problem, jobs have identical processing times and we show the problem is NP-hard in the strong sense. We propose an approximation algorithm with an absolute performance guarantee of 1.5 and asymptotic performance guarantee of 1.223. In the third problem, jobs have non-identical sizes and processing times simultaneously. We propose an algorithm with an absolute and asymptotic performance guarantee of 2. Besides, we present the evolution of the performance guarantee and provide managerial insights for decision makers of manufacturing companies.

Custom Clearance Processing Time Analysis and Factors Affecting Clearance Time for Goods in Birgunj Custom of Nepal

Trade plays a fundamental role in shaping the country’s economy and for this imported goods must be delivered to the market in the quickest possible time without unnecessary delay. This study covers the freight vehicles, which clears the custom clearance process for Kathmandu and transports the same goods to Kathmandu from Birgunj. In this study average processing time in Birgunj customs areas (Birgunj customs, Birgunj Inland Clearance Depot (ICD) and Birgunj Integrated Check-Post (ICD)) as well as factors affecting processing time in Birgunj customs area has also been explored. Custom Clearance time at the particular points was collected using the trained enumerators. Key Informant Interview (KII) was carried out to explore the factors affecting the processing time and the questionnaire survey was done to identify the factors affecting clearance time. The average processing time for vehicles in Birgunj customs, ICD and ICP for different types of, vehicles, goods and lanes assigned for goods were analyzed. Various factors that are affecting the processing were identified. In Birgunj customs, ICD and ICP in average approximately 30.1 hours, 2.8 hours and 19.2 hours respectively, extra time is being spent by freight vehicle inside the custom yard, other than actual processing time, which shows that there is mainly delay in-between the process other than in actual processing unit and the major factors for this are: owner not clearing the goods on time, due to lack of enough number of agents and unseen syndicate within the freight transportation system.

Effects of OCRA parameters and learning rate on machine scheduling

In this paper, the effects of Occupational Repetitive Actions (OCRA) parameters, learning rate on process times, and machine scheduling were investigated. We propose that Work-Related Musculoskeletal Disorder (WMSD) risks should be taken into account in machine scheduling. To the best of our knowledge, none of the earlier methods simultaneously considered effects of WMSD risks and the learning rate on processing times. The OCRA index method was employed for WMSD risk assessments. In this context, OCRA parameters such as duration, recovery, force, posture, and repetitiveness were analyzed. Observed process times of each factor were obtained from video records. Statistical analysis (ANOVA) revealed a positive (r=0.616) relationship on processing times with OCRA indexes in independent t-tests at significance level 0.05. To investigate the effects of WMSD risk, our Scheduling with Learning Effect under Risk Deterioration (SLE&RD) model was compared with six existing machine scheduling models in the literature. Detailed machine scheduling instances of 9 jobs with WMSD risks revealed that job sequences and makespan varied under different scenarios. This means that WMSD risks and OCRA factors affect machine scheduling with a deterioration effect. The results confirmed that when WMSD risks are included, actual process time and makespan move closer to observed process times. To obtain more accurate machine scheduling, which is close to real-life applications, WMSD risks, and learning rates should be considered simultaneously. The SLE&RD model is promising in machine scheduling for real-life problems and presents a holistic view of machine scheduling and WMSD risks.

Discrete optimization model for permutation flow shop under time-of-use electricity tariffs

The time-of-use electricity tariffs (TOU) which is widely used at home and abroad make the timeline for scheduling to have the attribute of different electricity tariffs. In order to solve the difficulty of coordination between electricity price segmentation and product processing time, this paper proposes a discrete optimization model, which uses central moment method modelling to ensure the continuity of job-processing and the uniqueness of processing time points. A discrete optimization model with maximum completion time and total electricity cost is constructed. According to the instance of the processing workshop and the characteristics of GAMS software, a virtual small-scale case of detection is constructed. By setting 11 groups of experiments with different weights, the total electricity cost is reduced by 30% compared with the traditional scheduling scheme after the electricity cost optimization is considered to avoid the peak arrangement of the electricity price. Although the maximum completion time is increased by nearly 30% on the surface, the downtime of staggering the peak is removed, the actual processing time is 42 minutes, and the total completion time is only increased by 5%.

Two‐agent scheduling with linear resource‐dependent processing times

AbstractThis paper considers a two‐agent scheduling problem with linear resource‐dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is ‐hard in the ordinary sense, and there does not exist a polynomial‐time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.

A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints

Production systems are subject to machine deterioration and resource consumption constraints. The deterioration increases the processing time which leads to an increase in resource consumption. In this study, we investigate and model the behavior of a parallel machine scheduling problem with respect to the processing time. The machine is subject to deterioration and includes two resource consumption constraints. The first resource R1 controls the processing time so that additional amounts of R1 decrease the processing time. The second R2 is controlled by the actual processing time so that R2 consumption is a linear function of the actual processing time. The increment of R1 consumption leads to processing time and so R2 decrement. Solving this problem consists in finding the optimal schedule that will minimize both makespan and resources cost. This paper provides a mathematical programming model. In fact, due to the deterioration effect and the two resource consumptions, solving such a problem may be very difficult and requires a large computational time. In this paper, we introduce a multi objective simulated annealing (MOSA) in order to solve the combinatorial optimization problem related to finding the best combination (machine, job, position, R1). Literally the best jobs assignment and resources allocation so that makespan and resources cost are minimized. In order to improve the quality of the results we also developed a 2-steps algorithm by decomposing the original problem into two sub problems: an assignment problem and a resources allocation problem. Some simulations were performed to analyze the performances of the two algorithms. The results show that the 2-steps algorithm is very efficient and outperforms MOSA.

Improved DE search for competing groups scheduling with deterioration effects

This paper investigates a three-competing group scheduling problem on serial-batching machines considering the setup time of groups and batches, as well as the job-dependent deteriorating effect, where the setup time of groups and batches depends on their own corresponding start time and deterioration rate, and the jobs’ actual processing time depends on their starting time and deterioration rate. In this problem, the jobs in three groups are processed competitively, and the jobs belonging to the same group are processed together on a machine, meanwhile, the jobs from each group are divided into batches. The objective is to minimize the makespan of one group with deterioration effect under the constraint of satisfying the threshold value of another group. Some key structural properties are proposed under the relevant demonstration, and a decision flow chart of scheduling rules is constructed based on these structural properties. Then, an effective improved differential evolution (DE) search algorithm combining the shaking operation from variable neighborhood search is developed to solve the studied scheduling problem. Computational experiments are conducted to evaluate the performance of proposed improved DE algorithm and some other well-known algorithms. The experimental results show that the proposed algorithm is more effective and stable than compared algorithms.

Multitasking scheduling and due date assignment with deterioration effect and efficiency promotion

We investigate a multitasking scheduling and due date assignment problem with position-dependent deterioration effect and efficiency promotion. Multitasking scheduling allows the processing of a primary job being interrupted by the waiting jobs that are available but unfinished. The duration of processing a primary job is comprised of three parts: the processing time of the remaining part of the primary job, the interruption time denoting the time of the partial processing of the waiting jobs, and the switching time denoting the time during which no jobs are processed when the primary job being scheduled. We consider two behavioral factors which may affect the production efficiency. One is the position-dependent deterioration effect on primary jobs, and the other is the linear efficiency promotion on waiting jobs. The position-dependent deterioration effect means that the productivity deteriorates over time due to personnel fatigue, thereby increasing the actual processing times of primary jobs depending on their scheduled positions. The efficiency promotion indicates that switching between different jobs can keep them from being bored, thereby leading to an increase in productivity when operators tackle the interruption parts of waiting jobs. The due dates of jobs are decision variables in two well-known due date assignment models, i.e., the common and unrestricted due date assignment models. We study several scheduling criteria including the makespan, the total completion time, and two due date-related criteria. For each considered problem, we design an efficient polynomial time algorithm, and present the structural properties of the optimal schedules under different conditions considering the relationships between deterioration effect and efficiency promotion.

A hybrid multi-objective evolutionary algorithm to integrate optimization of the production scheduling and imperfect cutting tool maintenance considering total energy consumption

With the increase in awareness of energy conservation and emission reduction in the manufacturing sector, the energy efficiency optimization of the production process is considered an effective way to promote cleaner production and environmentally sustainable development. Moreover, the transportation process and its energy consumption are non-negligible during the entire workshop production process. In practice, cutting tool degradation during operation is inevitable, which causes the actual processing time of work to be extended, so it is necessary to consider the degradation effects and imperfect maintenance. To reduce the total energy consumption in the manufacturing workshop with degradation effects and imperfect maintenance, this paper constructs a novel integrated optimization model including the flexible job-shop scheduling problem (FJSP), forklift transportation and imperfect cutting tool maintenance. First, an imperfect cutting tool maintenance with degradation effect strategy is presented, which makes the actual processing time of each operation more closely approximate the real-world processing situation. Second, an integrated multi-objective optimization model is formulated to simultaneously minimize the makespan, total tardiness, total production cost and total energy consumption. Third, a hybrid multi-objective evolutionary algorithm with Pareto elite storage strategy (HMOEA/P) is proposed to address the model. More precisely, three improved operations are presented: hybrid dominance principle, local search algorithms and Pareto elite preservation strategy. The effectiveness and feasibility of the parameter setting, improved operations and the proposed algorithm are separately demonstrated by the comparative experiments. Last, the superiority of the integrated multi-objective optimization model is proven by comparing different maintenance strategies and energy consumption models.

Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration

This paper addresses a serial-batching scheduling problem where the jobs with arbitrary release times are scheduled on parallel machines with the objective to minimize the makespan. The effects of learning and deterioration are considered simultaneously, and each job’s actual processing time depends on the sum of previous jobs’ processing times and the position of the current job. Each machine can process up to $$ c $$ jobs in the manner of serial batch, i.e., one after another with a setup time for each batch. Structural properties are identified for the special cases of the studied problem. Based on these derived structural properties, we propose a novel hybrid SC-VNS algorithm to solve the studied problem, which combines Society and Civilization (SC) algorithm with Variable Neighborhood Search (VNS). Computational experiments are conducted to evaluate the performance of the proposed hybrid algorithm and some other well-known algorithms. The results demonstrate that the proposed hybrid SC-VNS algorithm performs quite better than the compared algorithms in terms of the solution quality and the required running time.

NSGA‐III for solving dynamic flexible job shop scheduling problem considering deterioration effect

The production process of manufacturing systems is usually not static and always interrupted by stochastic events, such as the deterioration effect of cutting tools. This study focuses on the dynamic flexible job shop-scheduling problem considering the deterioration effect (DFJSP-DE). Two types of disturbances are considered, i.e. the implicit disturbance caused by the deterioration effect and the explicit disturbance caused by the reprocessing of unqualified jobs. Firstly, a step-deterioration effect model is proposed, with which the actual processing time of each operation can be predicted more accurately. A multi-objective optimisation model is formulated for the DFJSP-DE. The makespan, energy consumption, and stability of rescheduling solutions are three objectives to be optimised simultaneously. For this non-deterministic polynominal (NP)-hard problem, the non-dominated sorting genetic algorithm III is employed to search the Pareto solutions for the DFJSP-DE. Finally, the results of three numerical experiments show that the proposed approach can solve DFJSP-DE effectively and efficiently.

Randomized selection algorithm for online stochastic unrelated machines scheduling

We consider an online stochastic unrelated machines scheduling problem. Specifically, a set of jobs arriving online over time must be randomly scheduled on the unrelated machines, which implies that the information of each job, including the release date and the weight, is not known until it is released. Furthermore, the actual processing time of each job is disclosed upon completion of this job. In addition, we focus on unrelated machines, which means that each job has a processing speed on every machine. Our goal is to minimize the expected total weighted completion time of all jobs. In this paper, we present a randomized selection algorithm for this problem and prove that the competitive ratio is a constant. Moreover, we show that it is asymptotic optimal for the online stochastic uniform machines scheduling problem when some parameters are bounded. Moreover, our proof does not require any probabilistic assumption on the job parameters.

Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing time p j of job J j is assumed to be a linear function of its starting time s j , i.e., p j = α j s j , where α j > 0 is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. When m = 1 , we provide the best possible online algorithm with the competitive ratio of ( 1 + α max ) f , where f is the number of job families and α max is the maximum deterioration rate of all jobs. When m ≥ 1 and m = f , we provide the best possible online algorithm with the competitive ratio of 1 + α max .

A unified approach for single machine scheduling with position-dependent workloads and positional penalties

In this paper, we provide unified methods for solving scheduling problems with convex resource allocation, concentrating on objective functions that can be expressed as a scalar product of the actual processing times vector and a job-independent and position-dependent penalties vector. We assume general position-dependent workloads, i.e., the workloads are not restricted to be either monotone functions of the job positions or to specific functions. The first unified method focuses on minimizing a scheduling measure subject to a constraint on the resource consumption, whereas the second addresses the complementary problem of minimizing the consumed resource given an upper bound on the scheduling measure. For each unified approach, we provide a methodical analysis and consequently provide a $$O\left( {n^{3} } \right)$$ solution algorithm. Furthermore, to demonstrate the unified schemes, we solve several scheduling measures that involve earliness and tardiness penalties.

On Applications of the Earliest Due Date Rule in Stochastic Scheduling and in Queueing

We consider an environment with m servers in parallel and n jobs. The n jobs have i.i.d. exponentially distributed processing requirements. The servers operate at different speeds and preemptions are allowed. The jobs have random release dates that are not known in advance, but whenever a job is released, its due date is fixed and becomes known to the scheduler. We first consider three stochastic scheduling problems with three due date related objective functions and consider variations of the Earliest Due Date (EDD) rule, including the preemptive policy that at any point in time assigns the job with the Earliest Due Date to the Fastest Server (EDD-FS). Our optimality results turn out to be examples of stochastic scheduling problems that have relatively simple priority rules that are optimal while their deterministic counterparts do not allow such priority rules to be optimal. We furthermore extend our results to include a priority queueing model with m exponential servers that operate at different speeds and preemptions being allowed. The jobs arrive according to an arbitrary renewal process, and we assume that the utilization factor of the system is less than 1. Upon a job’s arrival the time difference between its due date and arrival date is set by the draw of a random variable from a given distribution. At a job’s arrival date, its due date is immediately fixed and known while its actual processing time only becomes known upon its service completion. We show that for this priority queueing model the preemptive EDD-FS rule also minimizes the limit of several due date related objective functions as the number of jobs converges to infinity.

An Improved Discrete Artificial Bee Colony Algorithm for Flexible Flowshop Scheduling with Step Deteriorating Jobs and Sequence-Dependent Setup Times

This paper studies a flexible flowshop scheduling problem with step-deteriorating jobs and sequence-dependent setup times (FFSP-SDJ&SDST) where there are multiple unrelated parallel machines at each stage. The actual processing time of each job is modeled as a step function of its starting time. An integer programming model is first formulated with the objective of minimizing the total weighted completion time. Since this problem is NP-complete, it becomes an interesting and challenging topic to develop effective approximation algorithms for solving it. The artificial bee colony (ABC) algorithm has been successfully applied to solve both continuous and combinatorial optimization problems with the advantages of fewer control parameters and ease of implementation. So, an improved discrete artificial bee colony algorithm is proposed. In this algorithm, a dynamic generation mechanism of initial solutions is designed based on job permutation encoding. A genetic algorithm and a modified variable neighborhood search are introduced, respectively, to obtain new solutions for the employed and onlooker bees. A greedy heuristic is proposed to generate the solutions of the scout bees. Finally, to verify the performance of the proposed algorithm, an orthogonal test is performed to optimize the parameter settings. Simulation results on different scale problems demonstrate that the proposed algorithm is more effective compared against several presented algorithms from the existing literatures.

Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

We address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

Single machine common flow allowance group scheduling with learning effect and resource allocation

We introduce a single-machine group scheduling job-dependent due date assignment problem with learning effects and resource allocation in which each job is assigned an individual due date based on a common flow allowance. The actual processing time of a job depends not only on its scheduled position but also on its resource allocation. A job completed earlier (later) than its due date will incur an earliness (tardiness) penalty. Our goal is to find the optimal sequence for both the groups and jobs, together with the optimal due date assignment and the optimal resource allocation to minimize the total cost that comprises the earliness and tardiness penalties, and common flow allowance and resource allocation. We give polynomial time algorithm to solve these problems.