Deviation Of Job Completion Times Research Articles

A machine learning-based simulation metamodeling method for dynamic scheduling in smart manufacturing systems

Conventional Digital Twins (DTs) in smart manufacturing rely on complex and time-intensive simulation models, hindering real-time DT-based decision-making. However, the availability of big data in Manufacturing Execution Systems (MES) enables training different Machine Learning (ML) models for fast and accurate predictions and decision assessments. Accordingly, this paper proposes an ML-Based Simulation Metamodeling Method (MLBSM) to facilitate DT-based decision-making for dynamic production scheduling in complex Stochastic Flexible Job Shop (SFJS) environments. The proposed MLBSM integrates three modules: a novel data vectorizing method (SPBM), multi-output Adaptive Boosting Regressor (ABR) models, and a new statistical risk evaluation method. SPBM converts unstructured production log data into numerical vectors for ABR training by calculating numeric penalty scores for each job based on the position of operations in the schedule queue. Each trained ABR predicts mean job completion times for various dynamic scenarios based on shift schedules. The risk evaluation method estimates the standard deviation of job completion times and calculates the delay probability scores for each job, aiding DT in promptly evaluating production schedules. Working seamlessly together, MLBSM modules present a novel way of using production log data for ML training and ultimately bypassing several computationally intensive simulation replications. In this research, a simulation model generates the synthetic MES data, focusing on the machining process at a photolithography workstation in the semiconductor manufacturing. Experiments demonstrate the MLBSM’s accuracy and efficiency, predicting high-risk jobs with over 80% recall and being at least 70 times faster than conventional simulation runs. Sensitivity analyses also confirm the MLBSM’s consistency under different workstation conditions.

An asymptotically optimal solution for the minimization of the variation of job completion times in two-stage proportionate no-wait flow shops

We propose an asymptotically optimal solution for the two-stage no-wait proportionate flow shop scheduling problem with the objective of minimizing the total absolute deviation of job completion times. The proposed solution is within 1% of the optimum for problems with more than 20 jobs. We also show that the problem is solved optimally in constant time for the special case where the two smallest jobs have equal processing times. Our results provide answers to most of the outstanding research questions for this problem.

Results of Parallel-Machine Scheduling Model with Maintenance Activity considering Time-Dependent Deterioration, Delivery Times, and Resource Allocation

This paper investigates parallel-machine scheduling models with maintenance activity, delivery times, time-dependent deterioration, and resource allocation. We consider two forms of the problem: the first is to minimize the sum of total completion times, total machine loads, the total absolute deviation of job completion times, and the total resource allocation; the second is to minimize the sum of total waiting times, total machine loads, the total absolute deviation of job waiting times, and the total resource allocation. The problems are proved to be solvable in polynomial time.

Minimizing total absolute deviation of job completion times on a single machine with maintenance activities using a Lion Optimization Algorithm

Scheduling is a decision-making process that plays an important role in the service and production industries. Effective scheduling can assist companies to survive in the competitive market. Single machine scheduling is an important optimization problem in the scheduling research area. It can be found in a wide range of real-world engineering problems, from manufacturing to computer science. Due to the high complexity of single machine scheduling problems, developing approximation methods, particularly metaheuristic algorithms, for solving them have absorbed considerable attention. In this study, a Lion Optimization Algorithm (LOA) is employed to solve a single machine with maintenance activities, where the objective is to minimize the Total Absolute Deviation of Compilation Times (TADC). In the scheduling literature, TADC as an objective function has hardly been studied. To evaluate the performance of the LOA, it was compared against a set of well-known metaheuristics. Therefore, a set of problem was generated, and a comprehensive experimental analysis was conducted. The results of computational experiments indicate the superiority of the proposed optimization method.

Parallel-Machine Scheduling with DeJong’s Learning Effect, Delivery Times, Rate-Modifying Activity, and Resource Allocation

We investigate parallel-machine scheduling with past-sequence-dependent (p-s-d) delivery times, DeJong’s learning effect, rate-modifying activity, and resource allocation. Each machine has a rate-modifying activity. We consider two versions of the problem to minimize the sum of the total completion times, the total absolute deviation of job completion times, and the total resource allocation and the sum of the total waiting times, the total absolute deviation of job waiting times, and the total resource allocation, respectively. The problems under our present model can be solved in polynomial time.

New results for minimising variation of flow time in two-machine proportionate no-wait flow shops

In this paper, the two-machine no-wait proportionate flow shop problem is analysed with the objective of minimising the total absolute deviation of job completion times. The optimality of V-shaped sequences is extended to problems with 12 jobs and it is shown that an optimal sequence may not be V-shaped with 13 jobs. For problems of larger size, the best V-shaped sequence is determined in linear time without resorting to dynamic programming. For larger size problems, it is shown that the number of non-dominated potentially optimal semi-V-shaped sequences increases rapidly. This indicates that derivation of optimal solutions in low order polynomial time is unlikely with a large number of jobs. Finally, the findings are extended to the corresponding problem with the objective of minimising the total absolute differences in waiting times.

A filtered beam search method for the m-machine permutation flowshop scheduling problem minimizing the earliness and tardiness penalties and the waiting time of the jobs

This paper addresses the minimization of the absolute deviation of job completion times from a common due date in a flowshop scheduling problem. Besides this main objective, the minimization of the waiting time of the jobs in the production environment, that can be seen as an intermediate inventory cost, is also considered. Initially, a mixed integer programming model for this problem is proposed and, due to its complexity, heuristic approaches are developed. A list-scheduling algorithm for the approached problem is introduced. Moreover, a filtered beam search method that explores specific characteristics of the considered environment is proposed. Numerical experiments show that the presented methods can be successfully applied to this problem.

Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion

The problem of minimising total absolute deviation of job completion times in a two-machine no-wait proportionate flow shop has been recently studied. It was shown that the LPT (largest processing time first) job sequence is optimal if the number of jobs n does not exceed 7, and that the LPT sequence is not optimal for instances with . We prove that there exists an optimal semi-V-shaped job sequence, in which the first job has the largest processing time, a certain number, greater than n / 2, of the following jobs appear in the LPT order, and jobs following job with the minimum processing time are sequenced in the SPT (shortest processing time first) order. We also present an time dynamic programming algorithm to find the best V-shaped job sequence, in which the jobs on the left of the job with the minimum processing time are sequenced in the LPT order and those on the right of this job are sequenced in the SPT order.

A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection

We study a scheduling problem with the objective of minimizing total absolute deviation of completion times (TADC). TADC is considered here in the most general form studied so far: the machine setting is that of parallel unrelated, job processing time are assumed to be position-dependent with no restrictions on the functional form, and the option of processing only a subset of the jobs (i.e., job-rejection) is allowed. We show that minimizing TADC in this very general form remains polynomially solvable in the number of jobs.

Minimizing total absolute deviation of job completion times on a single machine with cleaning activities

This paper considers a new single machine scheduling problem with several unavailability periods, where the machine has to be stopped in order to remove the dirt. The problem appears in the process in wafer manufacturing company. During the processing of a wafer on a specific machine, the dirt, including particle, organic materials and metal-salts, etc., on the surface of the wafer while processing, has to be taken away by a cleaning agent. Once the accumulation of dirt is over a threshold value, it is necessary to interrupt the machine processing and replace the cleaning agent in order to avoid damaging the wafer. The objective is to minimize the total absolute deviation of job completion times (TADC). The problem integrates production scheduling and cleaning activities and is strongly NP-hard. Many properties for solving the problem efficiently are explored. A mixed binary integer programming model is developed to find the optimal solution. Based on the properties explored, symmetry of the V-shaped rule, and the dynamic programming on scheduling the cleaning activities, an effective heuristic is developed. Computational results indicate that the performance of the heuristic is robust and significantly outperforms the modified TADC solution in the literature. Furthermore, the efficiency of the mixed binary integer programming model and the impact of the dirt accumulation as well as cleaning time are explored in detail.

Parallel-Machine Scheduling with Delivery Times and Deteriorating Maintenance

In this paper, we consider parallel-machine scheduling with past-sequence-dependent (p-s-d) delivery times and deteriorating maintenance. The delivery time of a job is proportional to its waiting time in the system. Each machine has a deteriorating maintenance activity, i.e., delaying the maintenance increases the time required to perform it. We consider three versions of the problem to minimize the total absolute deviation of job completion times, the total load on all the machines, and the total completion time. We develop polynomial-time algorithms to solve them.

Parallel-Machine Scheduling Problems with Past-Sequence-Dependent Delivery Times and Aging Maintenance

We consider parallel-machine scheduling problems with past-sequence-dependent (psd) delivery times and aging maintenance. The delivery time is proportional to the waiting time in the system. Each machine has an aging maintenance activity. We develop polynomial algorithms to three versions of the problem to minimize the total absolute deviation of job completion times, the total load, and the total completion time.

A note on minimising total absolute deviation of job completion times on a two-machine no-wait proportionate flowshop

A popular measure used in service systems is that of total absolute deviation of job completion times (TADC). It is relevant to settings where the objective is to balance the level of service provided to different customers. During the last decade, TADC has been studied in various machine settings, and under various assumptions on the job processing times. In this note, we study TADC on a two-machine no-wait proportionate flow shop, i.e. a flow shop with machine-independent processing times, and with no buffer between the machines. A very surprising and unique result is introduced: a simple index policy (the well-known largest processing time (LPT) first sequence) is shown to be optimal for instances of no more than seven jobs. This property does not hold for larger instances. We show that for instances of eight and nine jobs, there are exactly two schedules which are candidates for optimality. For the 10-job instance, the number of candidates increases. This uncommon behaviour of the optimal solution and, consequently, the complexity of the problem studied here, remain open questions, and are challenging topics for future research.

Single machine just‐in‐time scheduling problems with two competing agents

In scheduling problems with two competing agents, each one of the agents has his own set of jobs to be processed and his own objective function, and both share a common processor. In the single‐machine problem studied in this article, the goal is to find a joint schedule that minimizes the total deviation of the job completion times of the first agent from a common due‐date, subject to an upper bound on the maximum deviation of job completion times of the second agent. The problem is shown to be NP‐hard even for a nonrestrictive due‐date, and a pseudopolynomial dynamic program is introduced and tested numerically. For the case of a restrictive due‐date (a sufficiently small due‐date that may restrict the number of early jobs), a faster pseudopolynomial dynamic program is presented. We also study the multiagent case, which is proved to be strongly NP‐hard. A simple heuristic for this case is introduced, which is tested numerically against a lower bound, obtained by extending the dynamic programming algorithm. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 1–16, 2014

An exact algorithm to minimize mean squared deviation of job completion times about a common due date

We consider a deterministic n-job, single machine scheduling problem with the objective of minimizing the Mean Squared Deviation (MSD) of job completion times about a common due date (d). The MSD measure is non-regular and its value can decrease when one or more completion times increases. MSD problem is connected with the Completion Time Variance (CTV) problem and has been proved to be NP-hard. This problem finds application in situations where uniformity of service is important. We present an exact algorithm of pseudo-polynomial complexity, using ideas from branch and bound and dynamic programming. We propose a dominance rule and also develop a lower bound on MSD. The dominance rule and lower bound are effectively combined and used in the development of the proposed algorithm. The search space is explored using the breadth first branching strategy. The asymptotic space complexity of the algorithm is O(nd). Irrespective of the version of the problem – tightly constrained, constrained or unconstrained – the proposed algorithm provides optimal solutions for problem instances up to 1000 jobs size under different due date settings.

Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect

This paper considers identical parallel-machine scheduling problem with past-sequence-dependent (psd) delivery times and learning effect. In electronic manufacturing industry, an electronic component may be exposed to certain electromagnetic field and requires an extra time for eliminating adverse effect after the main processing. The extra time is modeled as past-sequence-dependent delivery time in the literature, which is proportional to the waiting time in the system. It is also observed that the learning process reflects a decrease in the processing time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. In practice, one often has to deal with the scheduling problems with psd delivery times and learning effect. Identical parallel-machine setting is considered because the occurrence of resources in parallel is common in the real world. In this paper, three objectives are the minimization of the total absolute deviation of job completion times, the total load on all machines and the total completion time. We develop polynomial algorithms to optimally solve these problems.

Minimizing weighted mean absolute deviation of job completion times from their weighted mean

We address a single-machine scheduling problem where the objective is to minimize the weighted mean absolute deviation of job completion times from their weighted mean. This problem and its precursors aim to achieve the maximum admissible level of service equity. It has been shown earlier that the unweighted version of this problem is NP-hard in the ordinary sense. For that version, a pseudo-polynomial time dynamic program and a 2-approximate algorithm are available. However, not much (except for an important solution property) exists for the weighted version. In this paper, we establish the relationship between the optimal solution to the weighted problem and a related one in which the deviations are measured from the weighted median (rather than the mean) of the job completion times; this generalizes the 2-approximation result mentioned above. We proceed to give a pseudo-polynomial time dynamic program, establishing the ordinary NP-hardness of the problem in general. We then present a fully-polynomial time approximation scheme as well. Finally, we report the findings from a limited computational study on the heuristic solution of the general problem. Our results specialize easily to the unweighted case; they also lead to an approximation of the set of schedules that are efficient with respect to both the weighted mean absolute deviation and the weighted mean completion time.

Some unrelated parallel machine scheduling problems with past-sequence-dependent setup time and learning effects

In this paper, we study an unrelated parallel machine scheduling problem with setup time and learning effects simultaneously. The setup time is proportional to the length of the already processed jobs. That is, the setup time of each job is past-sequence-dependent. The objectives are to minimize the total absolute deviation of job completion times and the total load on all machines, respectively. We show that the proposed problem is polynomially solvable. We also discuss two special cases of the problem and show that they can be optimally solved by lower order algorithms.

Minimising mean squared deviation of job completion times about a common due date in multimachine systems

In this paper we consider the problem of scheduling n jobs on two identical parallel machines in order to minimise the mean squared deviation (MSD) of job completion times about a given common due date. When due dates are small and large deviations of job completion times from the due dates are undesirable, it becomes necessary to consider parallel machines. MSD comes under the category of non-regular performance measures, which penalises jobs that are early as well as late. In this paper we develop a lower bound on MSD for a given partial schedule and present a branch and bound algorithm to solve the problem. Optimal solutions for problem instances up to 35 jobs have been obtained for different values of due dates and the results of computational testing are presented. Based on our experiments we observe that when the due date exceeds a certain value the second machine becomes undesirable. We also propose a heuristic to provide quick solutions for problems of larger size.

Parallel-machine scheduling with setup and removal times under consideration of the learning effect

This article aims to study the problems related to identical parallel-machine scheduling with setup, processing, and removal times under consideration of the learning effect. The objectives are to minimize the total completion time, total load, and total absolute deviation of job completion times (TADC) on all the machines. We show that these problems can be solved in time if the jobs satisfy an agreeable condition, i.e. implies that and for any two jobs Ji and Jj , , where n denotes the number of jobs, m denotes the number of machines, and Pi , si , and ri , respectively, denote the normal processing, setup, and removal times of job Ji . For the case where all jobs have a common learning factor for job processing, setup, and removal times, we prove that these problems can also be solved in time. In addition, we extend the problem under study to an unrelated parallel-machine environment and show that all the problems studied can be formulated as assignment problems and hence can be solved in time.