Single-machine Group Scheduling Research Articles

Group Scheduling With Nonperiodical Maintenance and Deteriorating Effects

In this paper, we consider single-machine group scheduling with nonperiodical maintenance and deteriorating effects. Nonperiodical maintenance, which has unfixed maintaining interval or the number of jobs in each group is unfixed, results in a variable number of groups. Deteriorating effects lead to longer processing times of which the deterioration index depends on job grouping. This problem is of significance in different production settings and is much more difficult than and general that other simpler single-machine group scheduling problems. Making use of historical processing times, we construct the actual processing time model for jobs. We prove that the problem under study is NP-hard. By transforming the optimization objective, properties are discovered and two batch-based heuristics are presented for small size problems. To further improve the effectiveness for large size problems, an iterated greedy algorithm is proposed being its main advantages simplicity and effectiveness. The proposed methods are evaluated over a large number of random instances with calibrated parameters and components. Comprehensive computational and statistical analyses demonstrate the superiority of the methods proposed over adapted existing approaches.

Single-machine group scheduling with new models of position-dependent processing times

Abstract We propose new models of position-dependent processing times for single-machine group scheduling problems. The two objectives of the scheduling problems are to minimize the makespan and the total completion time, respectively. We present polynomial-time algorithms to solve the problems.

Single-machine group scheduling problems with deteriorating and learning effect

The concepts of deteriorating jobs and learning effects have been individually studied in many scheduling problems. However, most studies considering the deteriorating and learning effects ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as ‘group technology’ in the literature. In this paper, a new group scheduling model with deteriorating and learning effects is proposed, where learning effect depends not only on job position, but also on the position of the corresponding job group; deteriorating effect depends on its starting time of the job. This paper shows that the makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, a polynomial optimal solution is also presented to minimise the maximum lateness problem under certain agreeable restriction.

Single-Machine Group Scheduling Problems with Variable Job Processing Times

This paper considers two resource constrained single-machine group scheduling problems. These problems involve variable job processing times (general position-dependent learning effects and deteriorating jobs); that is, the processing time of a job is defined by the function that involves its starting time and position in the group, and groups’ setup time is a positive strictly decreasing continuous function of the amount of consumed resource. Polynomial time algorithms are proposed to optimally solve the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Single-machine bicriterion group scheduling with deteriorating setup times and job processing times

This paper considers a group scheduling problem with two ordered criteria where both setup times and job-processing times are increasing functions of their starting times. It is assumed that the jobs be classified into several groups and the jobs of the same group have to be processed contiguously. We consider two objectives where the primary criterion is the total weighted completion time and the secondary criterion is the maximum cost. A polynomial time algorithm is presented to solve this bicriterion group scheduling problem with deteriorating setup times and job-processing times. This algorithm can also solve single-machine group scheduling problems with deteriorating setup times and job-processing times in several ordered maximum cost and arbitrary precedence.

Single-machine group scheduling problem considering learning, forgetting effects and preventive maintenance

An integrated single-machine group scheduling model is proposed, which incorporates both learning and forgetting effects and preventive maintenance (PM) planning. The objective is to minimise the expected makespan by optimising job sequence and PM decisions. This model contains sequence-dependent set-up time, actual processing time, planned PM time and expected minimal repair time simultaneously. Based on the properties of group production, three learning functions under different circumstances are proposed to deduce the variable processing time of each part, considering the learning effect when consecutively producing identical or similar parts, together with the forgetting effect when transferring jobs interrupts the production process and makes retrogress in learning. Both run-based maintenance and minimal repair policies are specified to handle the uncertainty of machine breakdowns. The search algorithm for the model is developed, and the numerical example is studied. The computational results and sensitivity analysis show that this improved group scheduling model can well balance the machine resource requirements from different practical manufacturing-related activities.

Group scheduling and job-dependent due window assignment based on a common flow allowance

We study a single-machine group scheduling and job-dependent due window assignment problem in which each job is assigned an individual due window based on a common flow allowance. In the group technology environment, the jobs are divided into groups in advance according to their processing similarities and all the jobs of the same group are processed consecutively in order to improve production efficiency. A sequence-independent machine setup time precedes the processing of the first job of each group. A job completed earlier (later) than its due window 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 window assignment, to minimize the total cost that comprises the earliness and tardiness penalties, and the due window starting time and due window size costs. We give an O(nlogn)time algorithm to solve this problem.

Single machine group scheduling with time and position dependent processing times

In the paper two resource constrained single-machine group scheduling problems with time and position dependent processing times are considered. By time and position dependent processing times and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Single-machine group scheduling with time-dependent learning effect and position-based setup time learning effect

As to learning effect, it may be more appropriate to assume that position-based learning takes place during machine setups only, while sum-of-processing-time-based learning occurs in considering the experience that workers have gained from producing jobs. Thus, in this paper, we consider sum-of-processing-time-based learning on job processing time and position-based learning on setup time in single-machine group scheduling problems. The objectives are to minimize the makespan and the total completion time, respectively. We provide two polynomial time algorithms to solve the makespan minimization problems. On the other hand, we also provide two polynomial time algorithms to solve the total completion time minimization problems under certain conditions.

Heuristic Model for Dynamic Single Machine Group Scheduling in Laser Cutting Job Shop to Minimize the Makespan

In today’s highly competitive market, laser cutting which has a characteristic of “make to order” and high product variety is under pressure to reduce costs, to increase productivity and to respond to the rapidly changing demands from customers. To maintain the competitive advantage, companies need to have a real-time dynamic scheduling system, which can handle large combinations of jobs, allowing sequencing of jobs to achieve multi-objective goals. Motivated by a real-life scheduling problem in a sheet metal processing company in Malaysia, this research addressed single machine scheduling problem with sequence-dependent setup times and group technology assumption to minimize makespan and with the secondary objective of minimizing setup times. The focus of this paper is on developing a simple heuristic algorithm based dynamic scheduling system. This algorithm has been coded in vb.net and is integrated with a database system. The scheduling system developed is verified and validated by comparing to the actual production run. Results show that the algorithm model can find good solutions within short computational time.

Single-machine group scheduling with general deterioration and learning effects

In this paper we consider single-machine group scheduling problems with effects of learning and deterioration at the same time. By effects of learning and deterioration, we mean that the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent and time-dependent learning effects. The objective of scheduling problems is to minimize the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.

Single-machine group scheduling with both learning effects and deteriorating jobs

In the paper two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered. By learning effects, deteriorating jobs and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Note on “A note on single-machine group scheduling problems with position-based learning effect”

In a recent paper, Lee and Wu [W.-C. Lee, C.-C. Wu, A note on single-machine group scheduling problems with position-based learning effect, Appl. Math. Model. 33 (2009) 2159–2163] proposed a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. They investigate the makespan and the total completion time minimization problems on a single-machine. As for the total completion time minimization problem, they assumed that the numbers of jobs in each group are the same and the group normal setup and the job normal processing times are agreeable. Under the assumption conditions, they showed that the total completion time minimization problem can be optimally solved in polynomial time solution. However, the assumption conditions for the total completion time minimization problem do not reflect actual practice in many manufacturing processes. Hence, in this note, we propose other agreeable conditions and show that the total completion time minimization problem remains polynomially solvable under the agreeable conditions.

Single-machine group scheduling problems under the effects of deterioration and learning

This paper investigates single-machine group scheduling problems with simultaneous considerations of deteriorating and learning effects to minimize the makespan and the total completion time of all jobs. The group setup time is assumed to follow a simple linear time-dependent deteriorating model. Two models of learning for the job processing time are examined in this study. We provided polynomial time solutions for the makespan minimization problems. We also showed that the total completion time minimization problems remain polynomially solvable under agreeable conditions.

Single-machine group scheduling problems with deteriorated and learning effect

In many realistic situation, a job processed later consumes more time than the same job when it is processed earlier, this phenomenon is known as deteriorated effect. The skills of workers continuously improve when repeating the same or similar tasks, this phenomenon is as the ''learning effect'' in the literature. However, most studies considering the deteriorated and learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known ''group technology'' in the literature. In this paper, we propose a new group scheduling with deteriorated and learning model where the learning effect not only depends on job position, but also depends on the group position; the deteriorated effect depends on its starting time of the job. We then show that the single-machine makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, we show the maximum lateness have a polynomial optimal solution under certain agreeable restriction.

A note on single-machine group scheduling problems with position-based learning effect

In many situations, the skills of workers continuously improve when repeating the same or similar tasks. This phenomenon is known as the “learning effect” in the literature. However, most studies considering the learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as “group technology” in the literature. In this paper, we propose a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. We then show that the makespan and the total completion time problems remain polynomially solvable under the proposed model.

Single-machine group scheduling problems with deteriorating jobs

This paper investigates single-machine scheduling problems with deteriorating jobs and the group technology (GT) assumption. By deteriorating jobs and the group technology assumption, we mean that the group setup times and job processing times are both increasing functions of their starting times, i.e., the group setup times and job processing times are both described by a function which is proportional to a linear function of time. The two objectives of scheduling problems are to minimize the makespan and the total weighted completion time, respectively. We show that these problems remain solvable in polynomial time when deterioration and group technology are considered simultaneously.

Single machine group scheduling under decreasing linear deterioration

This paper considers single machine scheduling problems with group technology (GT) and deteriorating jobs. A sequence independent setup is required to process a job from a different group and jobs in each group are processed together. We consider the case of jobs whose processing times are a decreasing function of their starting time. The objectives of scheduling problems are to minimize the makespan and the total completion time, respectively. We also provide polynomial time algorithms to solve these problems.

Single-machine group scheduling problems with deterioration consideration

In many realistic situations, a job processed later consumes more time than the same job when it is processed earlier; this phenomenon is known as deteriorating jobs. However, job deterioration is relatively unexplored in the context of group technology. In this paper, we consider deterioration in the framework of minimizing the makespan and the total completion time in single-machine group scheduling problems. We show that these problems remain polynomially solvable when deterioration is considered.

A single-machine group schedule with fuzzy setup and processing times

Group technology is a popular concept in production activities. It is assumed that all jobs are classified into several groups and the jobs within a group must be processed contiguously on the same machines. A sequence-independent setup time is incurred between two consecutive scheduling groups. Traditionally, both group setup times and job processing times have been assumed to be crisp numbers. This paper presents a single-machine groupscheduling problem when the group setup times and job processing times are treated as fuzzy numbers. A solution is provided to find a group sequence and a job sequence that minimizes the centroid values of these jobs. A total fuzzy flow time is then calculated for the decision makers. An example is given to illustrate this approach.