Actual Processing Time Research Articles

Single Machine Scheduling with General Learning Functions: Optimal Solutions

In traditional scheduling problems, most literature assumes that the processing time of a job is fixed. However, there are many situations where the processing time of a job depends on the starting time or the position of the job in a sequence. In such situations, the actual processing time of a job may be less than its normal processing time if it is scheduled later. This phenomenon is known as the ''learning effect''. In this study, we introduce general learning functions into a single-machine scheduling problems. We consider the following objective functions: (i) sum of weighted completion times, (ii) maximum lateness (iii) number of tardy jobs (iv) number of weighted tardy jobs. Non-linear programming models are developed for solving these problems.

Fuzzy Learning System for Uncertain Remanufacturing Process Time of Used Components

In view of the uncertainties inherent in remanufacturing process,a fuzzy petri net based remanufacturing process model is proposed to explicitly represent the variations in remanufacturing process routings and process time with respect to product conditions.A fuzzy learning system with an adaptive learning mechanism is designed to estimate the remanufacturing process time of used component under specific conditions,and to dynamically reshape the distributions of actual process time to improve future predictions.The proposed method is illustrated through the remanufacturing of a batch of used lathe spindles with a Matlab-based simulation system.

Single-machine group scheduling with a general learning effect

This paper investigates some single-machine scheduling problems with a general learning effect and the group technology assumption. A setup time is incurred whenever the single machine transfers job processing from a family to another family. By the general learning effect, we mean that the actual group setup time depends not only on the total setup time of the groups already processed but also on its scheduled position, and the actual processing time of a job in a certain group depends not only on the total normal processing time of the jobs already processed in the group but also on its scheduled position. We show that the makespan minimisation problem remains polynomially solvable under the proposed models. We also show that the problems of minimising the total completion time, the total weighted completion time and the discounted total weighted completion time of all jobs have polynomial optimal solutions under certain conditions.

Two-Agent Single-Machine Scheduling of Jobs with Time-Dependent Processing Times and Ready Times

Scheduling involving jobs with time-dependent processing times has recently attracted much research attention. However, multiagent scheduling with simultaneous considerations of jobs with time-dependent processing times and ready times is relatively unexplored. Inspired by this observation, we study a two-agent single-machine scheduling problem in which the jobs have both time-dependent processing times and ready times. We consider the model in which the actual processing time of a job of the first agent is a decreasing function of its scheduled position while the actual processing time of a job of the second agent is an increasing function of its scheduled position. In addition, each job has a different ready time. The objective is to minimize the total completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We propose a branch-and-bound and several genetic algorithms to obtain optimal and near-optimal solutions for the problem, respectively. We also conduct extensive computational results to test the proposed algorithms and examine the impacts of different problem parameters on their performance.

Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness.

Minimizing the Makespan for Scheduling Problems with General Deterioration Effects

This paper investigates the scheduling problems with general deterioration models. By the deterioration models, the actual processing time functions of jobs depend not only on the scheduled position in the job sequence but also on the total weighted normal processing times of the jobs already processed. In this paper, the objective is to minimize the makespan. For the single-machine scheduling problems with general deterioration effects, we show that the considered problems are polynomially solvable. For the flow shop scheduling problems with general deterioration effects, we also show that the problems can be optimally solved in polynomial time under the proposed conditions.

Single machine past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects

This paper studies the single machine past-sequence-dependent (p-s-d) delivery times scheduling with general position-dependent and time-dependent learning effects. By the general position-dependent and time-dependent learning effects we mean that the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job’s scheduled position. We consider the following objective functions: the makespan, the total completion time, the sum of the θth (θ⩾0) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs. We show that the problems of minimization of the makespan, the total completion time, the sum of the θth (θ⩾0) power of job completion times and the total lateness can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, the maximum tardiness minimization problem and the total tardiness minimization problem can be solved in polynomial time under certain conditions.

Single-machine scheduling problems with past-sequence-dependent delivery times and position-dependent processing times

This paper considers single-machine scheduling problems with job delivery times where the actual job processing time of a job is defined by a function dependent on its position in a schedule. We assume that the job delivery time is proportional to the job waiting time. We investigate the minimization problems of the sum of earliness, tardiness, and due-window-related cost, the total absolute differences in completion times, and the total absolute differences in waiting times on a single-machine setting. The polynomial time algorithms are proposed to optimally solve the above objective functions. We also investigate some special cases of the problem under study and show that they can be optimally solved by lower order algorithms.

Single machine scheduling with truncated job-dependent learning effect

In this paper we consider the single machine scheduling problem with truncated job-dependent learning effect. By the truncated job-dependent learning effect, we mean that the actual job processing time is a function which depends not only on the job-dependent learning effect (i.e., the learning in the production process of some jobs to be faster than that of others) but also on a control parameter. The objectives are to minimize the makespan, the total completion time, the total absolute deviation of completion time, the earliness, tardiness and common (slack) due-date penalty, respectively. Several polynomial time algorithms are proposed to optimally solve the problems with the above objective functions.

Single-machine group scheduling with deteriorating jobs and allotted resource

In this paper, we consider single-machine scheduling problems with deteriorating jobs and resource allocation in a group technology environment. In the proposed model of this paper the actual processing time of a job depend on its starting time and the amount of resource allocated to it, and the actual setup time of a group depend on its starting time and the amount of resource allocated. Deterioration effect and two resource allocation functions are examined for minimizing the weighted sum of makespan and total resource cost. For the linear resource allocation function and the convex resource allocation function, we show that the problem remains polynomially solvable under certain conditions.

Scheduling problems with past-sequence-dependent setup times and general effects of deterioration and learning

In this paper we consider the single-machine setup times scheduling with general effects of deterioration and learning. By the general effects of deterioration and learning, we mean that the actual job processing time is a general function of the processing times of the jobs already processed and its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the sum of the δth (δ>0) power of job completion times, the total lateness are polynomially solvable. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness (tardiness) minimization problem, the total tardiness minimization problem can be solved in polynomial time under certain conditions.

Single-machine scheduling problems with an actual time-dependent deterioration

In this paper, we consider the single machine scheduling problems with an actual time-dependent deterioration effect. By the actual time-dependent deterioration effect, we mean that the processing time of a job is defined by increasing function of total actual processing time of jobs in front of it in the sequence. We show that even with the introduction of an actual time-dependent deterioration to job processing times, makespan minimization problem, total completion time minimization problem, the total lateness, and the sum of the quadratic job completion times minimization problem remain polynomially solvable, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, and the total tardiness minimization problem can be solved in polynomial time under certain conditions.

Single machine scheduling with resource allocation and learning effect considering the rate-modifying activity

This paper addresses a single machine scheduling problem in which the actual job processing times are determined by resource allocation function, its position in a sequence and a rate-modifying activity simultaneously. We discuss two objective functions with two resource allocation functions under the consideration of a rate-modifying activity. We show that the problems are solvable in O(n4) time for a linear resource allocation function and are solvable in O(n2logn) time for a convex resource allocation function.

A generalisation model of learning and deteriorating effects on a single-machine scheduling with past-sequence-dependent setup times

This article introduces a general single-machine setup times scheduling model with learning effect and deteriorating jobs simultaneously which is a generalisation of some existing models in the literature. The setup times are proportional to the length of the already processed jobs, i.e. the setup times are past-sequence-dependent (p-s-d). By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The article shows that the problems to minimise the makespan, sum of the kth power of completion times, total lateness and sum of earliness penalties (with common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimise total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with common due date) are polynomially solvable under certain conditions.

Scheduling Due Dates Assignment with Simultaneous Considerations of Time-Dependent and Position-Dependent Deterioration Effects and Deteriorating Maintenance on a Single Machine

The due date assignment has been popular issues related to the interaction between various participants of the supply chain. In this paper, we investigate single machine due dates assignment scheduling problems with deterioration effects and deteriorating maintenance simultaneously. In the proposed model, the actual processing time of a job is not only dependent on the job's scheduled position, it also depends on the time expended by the jobs already processed. To counteract the deterioration effects of the machine, we assume that at most one maintenance is allowed throughout the scheduling horizon. The common due date assignment model and the slack due date assignment model are examined, respectively. The goal is to determine jointly the optimal due dates, the optimal maintenance position, and the optimal schedule to minimize the total penalty function based on earliness, tardiness and due dates. We show that all the problems studied can be optimally solved in polynomial time algorithms.

Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times

The paper deals with single machine scheduling problems with setup time considerations where the actual processing time of a job is not only a non-decreasing function of the total normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (δ ≥ 0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the δ th (δ ≥ 0) power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.

Single machine scheduling with exponential learning functions

In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

Identification of delayed system using instrumental variable method

System identification uses system inputs and outputs to raise mathematical models. Various techniques of system identification exist that offer a nominal model and an uncertainty bound. Many practical systems such as thermal processes & chemical processes have inbuilt time delay. If the time delay used in the system model for controller design does not concur with the actual process time delay, a closed-loop system may be unstable or demonstrate unacceptable transient response characteristics so here the time delay is assumed to be time-invariant.

SCHEDULING DETERIORATING JOBS ON A SINGLE MACHINE WITH RELEASE TIMES AND REJECTION

This paper considers scheduling deteriorating jobs on a single machine with release times and rejection. Deteriorating job means that its actual processing time is a increasing function on its execution starting time. In this situation, jobs can be rejected by paying penalties. Each job is associated with a release time. The objective is to minimize the makespan plus the total penalty incurred by rejecting jobs. We present two dynamic programming algorithms and then design an FPTAS for the considered problem.

Scheduling jobs with a general learning effect model

The paper deals with machine scheduling problems with a general learning effect. By the general learning effect, we mean that the actual processing time of a job is not only a non-increasing function of the total weighted normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence, where the weight is a position-dependent weight. We show that even with the introduction of a general learning effect to job processing times, some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.