Rate-modifying Activity Research Articles

복구조정 활동과 복구조정 후 시간경과에 따라 퇴화하는 작업시간을 갖는 단일기계의 일정계획에 관한 연구

We consider the single machine scheduling problem with a rate-modifying activity and time-dependent deterioration after the activity. The class of scheduling problems with rate-modifying activities and the class of scheduling problems with time-dependent processing times have been studied independently. However, the integration of these classes is motivated by human operators of tasks who has fatigue while carrying out the operation of a series of tasks. This situation is also applicable to machines that experience performance degradation over time due to mal-position or mal-alignment of jobs, abrasion of tools, and scraps of operations, etc. In this study, the integration of the two classes of scheduling problems is considered. We present a mathematical model to determine job-sequence and a position of a rate-modifying activity for the integration problem. Since the model is difficult to solve as the size of real problem being very large, we propose genetic algorithms. The performance of the algorithms are compared with optimal solutions with various problems.

Unrelated parallel-machine scheduling problems with multiple rate-modifying activities

In this article we investigate scheduling problems with multiple rate-modifying activities on an unrelated parallel-machine setting. We assume that each machine may have multiple rate-modifying activities. The goal is to determine jointly the optimal rate-modifying activity frequencies, the optimal rate-modifying activity positions, and the optimal schedule to minimize the total completion time and the total machine load, respectively. If the number of machines is fixed, we propose two efficient polynomial time algorithms for solving both problems no matter what the processing time of a job scheduled after a rate-modifying activity is greater or less than its processing time scheduled before the rate-modifying activity.

Single-Machine Scheduling with Due-Window Assignment and Rate-Modifying-Activities under a Deteriorating Maintenance

This paper studies single-machine scheduling problems with a due-window assignment and a rate-modifying activity under a deteriorating maintenance consideration simultaneously. Jobs completed within the due-window incur no penalties, other jobs incur either earliness or tardiness penalties. The maintenance activity can be scheduled immediately after any one of the completed jobs. We assume that once the maintenance activity has been completed, the machine efficiency will be improved and the machine maintenance duration depends on its starting time. The objective is to find the optimal maintenance position as well as the optimal size and location of the due-window, and the sequence of jobs to minimize a cost function based on the window size and window location and the earliness and tardiness of the jobs. We propose a polynomial time algorithm to solve the problem optimally.

Single Machine Problem with Multi-Rate-Modifying Activities under a Time-Dependent Deterioration

The single machine scheduling problem with multi-rate-modifying activities under a time-dependent deterioration to minimize makespan is studied. After examining the characteristics of the problem, a number of properties and a lower bound are proposed. A branch and bound algorithm and a heuristic algorithm are used in the solution, and two special cases are also examined. The computational experiments show that, for the situation with a rate-modifying activity, the proposed branch and bound algorithm can solve situations with 50 jobs within a reasonable time, and the heuristic algorithm can obtain the near-optimal solution with an error percentage less than 0.053 in a very short time. In situations with multi-rate-modifying activities, the proposed branch and bound algorithm can solve the case with 15 jobs within a reasonable time, and the heuristic algorithm can obtain the near-optimal with an error percentage less than 0.070 in a very short time. The branch and bound algorithm and the heuristic algorithm are both shown to be efficient and effective.

Genetic algorithms for single machine scheduling with time-dependent deterioration and rate-modifying activities

In this paper, the integration of two emerging classes of scheduling problems, the class of scheduling problems with time-dependent deterioration and the class of scheduling problems with rate-modifying activities, are addressed. The scheduling problems have been studied independently. However, the integration of these classes is motivated by human operators of tasks who have fatigue while carrying out the operation of a series of tasks. This situation is also applicable to machines that experience performance degradation over time due to mal-position or mal-alignment of jobs, abrasion of tools, and scraps of operations, etc. It requires maintenance in order to sustain acceptable production rates. We consider the single machine scheduling problem with time-dependent deterioration and multiple RMAs. A mathematical model for an optimal solution to minimize the makespan is derived and genetic algorithms are proposed. The performance of the genetic algorithms is evaluated using randomly generated examples.

Machine scheduling in the presence of sequence-dependent setup times and a rate-modifying activity

Rate modifying activity (RM) is a type of maintenance after which the processing rate of the machine increases. RM is a very new topic in academic studies. However, it is very common in real world situations. In this paper, we study the integrated problem of assigning a common due-date to all jobs, scheduling the jobs and making decisions about the position of RM in a single machine environment in which the setup times are sequence dependent. The objective is minimising the summation of earliness costs, tardiness costs and due date related costs. This problem has never been studied in the literature with any arbitrary criterion. We construct a time-dependent travelling salesman problem (TDTSP) formulation for this problem. The position of the optimal common due date and some dominance properties for the position of RM are presented. A branch and bound (B&B) procedure is developed to solve the problem optimally. Numerical results justify the effectiveness of the B&B method for small problems. For larger problems, two robust metaheuristics are proposed.

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.

Unrelated parallel-machine scheduling simultaneously with rate-modifying activities and earliness and tardiness penalties

In this paper, we consider a scheduling problem simultaneously with rate-modifying activities and earliness and tardiness penalties on an unrelated parallel-machine setting. We assume that each machine has at most one rate-modifying activity to improve its production efficiency during the scheduling horizon and all the jobs have a common due-date. The objective is to determine jointly the optimal positions of rate-modifying activities, the optimal common due-date of all jobs, and the optimal schedule to minimize the sum of earliness and tardiness costs. We show that the problem can be optimally solved in polynomial time.

Note on “A unique integer mathematical model for scheduling deteriorating jobs with rate-modifying activities on a single machine”

In this note, we study scheduling problems with simultaneous considerations of deteriorating jobs and rate-modifying activities on a single machine. The job-dependent deterioration effect and the job-independent deterioration effect models are examined with the objective of minimizing the makespan. We propose polynomial time solutions for all the studied problems.

Common due date assignment and scheduling with a rate-modifying activity to minimize the due date, earliness, tardiness, holding, and batch delivery cost

e consider a single-machine batch delivery scheduling and common due date assignment problem. In addition to making decisions on sequencing the jobs, determining the common due date, and scheduling job delivery, we consider the option of performing a rate-modifying activity on the machine. The processing time of a job scheduled after the rate-modifying activity decreases depending on a job-dependent factor. Finished jobs are delivered in batches. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find a common due date for all the jobs, a location of the rate-modifying activity, and a delivery date for each job to minimize the sum of earliness, tardiness, holding, due date, and delivery cost. We provide some properties of the optimal schedule for the problem and present polynomial algorithms for some special cases.

Single-Machine Total Completion Time Scheduling with Position-Based Deterioration and Multiple Rate-Modifying Activities

In this paper, we study a single-machine scheduling problem with deteriorating processing time of jobs and multiple rate-modifying activities which reset deteriorated processing time to the original processing time. In this situation, the objective function is to minimize total completion time. First, we formulate an integer programming model. Since the model is difficult to solve as the size of real problem being very large, we design an improved genetic algorithm called adaptive genetic algorithm (AGA) with spontaneously adjusting crossover and mutation rate depending upon the status of current population. Finally, we conduct some computational experiments to evaluate the performance of AGA with the conventional GAs with various combinations of crossover and mutation rates.

Parallel-machine scheduling with deteriorating jobs and rate-modifying activities to minimize total completion time

This article explores the parallel-machine scheduling problems in which the processing time of a job is a linear function of its starting time and the job-independent deterioration rates are identical for all jobs. We implemented a rate-modifying activity to change the processing time of the jobs that followed this activity on each machine. Therefore, the actual processing time of a job varied given that it depended not only on its starting time but also on whether it was scheduled before or after the rate-modifying activity. Hence, the objective of this study was to determine the job sequence on each machine and the position of rate-modifying activity on each machine so that the total completion time was minimized. We showed that the problem could be solved in polynomial time when the number of machines was fixed.

SINGLE MACHINE SCHEDULING WITH A LEARNING EFFECT AND A RATE-MODIFYING ACTIVITY

In the paper, single machine scheduling problems with a learning effect and a rate-modifying activity are considered. Under the learning effect, the processing time of a job is a decreasing function of its position in the sequence. The rate-modifying activity is an event that can change the speed of the machine, and hence the processing time of jobs after the activity. The following objective functions are considered: the makespan, the total earliness, tardiness and completion time penalty, and the total earliness, tardiness, due-window starting time and due-window size penalty. Polynomial time algorithms are proposed to optimally solve the problems.

Single machine common flow allowance scheduling with a fuzzy rate-modifying activity

The fuzzy scheduling is a new approach presented in this paper. In classic scheduling, it was assumed that the machines are always available. So, no maintenance time was considered for calculations. Also, assumed that all given times are exact and there is no uncertainty, however in the real word accurate calculation is impossible and always faced with uncertainty. Therefore, scheduling calculations would not be accurate and an optimal solution would not be reached. In this study, rate-modifying activity time considered as the fuzzy number and the optimal solution was calculated in uncertainty condition. A novel type of fuzzy scheduling model is presented. A ROG algorithm for ranking fuzzy numbers was introduced and example was solved to show the effectiveness of the proposed approach. Keywords: Fuzzy algorithm; machine scheduling; job scheduling rate-modifying activity; single machine..

Unrelated parallel-machine scheduling with rate-modifying activities to minimize the total completion time

Zhao et al. (2009) [24] study the m identical parallel-machine scheduling problem with rate-modifying activities to minimize the total completion time. They show that the problem can be solved in O( n 2 m+3 ) time. In this study we extend the scheduling environment to the unrelated parallel-machine setting and present a more efficient algorithm to solve the extended problem. For the cases where the rate-modifying rate is (i) larger than 0 and not larger than 1, and (ii) larger than 0, we show that the problem can be solved in O( n m+3 ) and O( n 2 m+2 ) time, respectively.

A unique integer mathematical model for scheduling deteriorating jobs with rate-modifying activities on a single machine

In this paper, we consider the scheduling a set of deteriorating jobs on a single processor. We propose a model which reflects real life situations in which the processing time of jobs change depending on its initial processing time (deteriorating jobs) and activities, such as machine maintenance or a break for workers. A rate-modifying activity (rma) is a maintenance activity given to a machine to restore it to its original state. The general problem we deal with in this study is to determine the job sequence, the number of rmas, and rma positions within the work sequence. We formulate a unique integer program to solve this model for makespan and total completion time objectives. We also propose efficient heuristic algorithms for solving large size problems for both makespan and total completion time objectives.

Parallel machine scheduling with a deteriorating maintenance activity and total absolute differences penalties

In this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity. In this model, each machine has a deteriorating maintenance activity, that is, delaying the maintenance increases the time required to perform it. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remain polynomially solvable under the proposed model.

Single machine common flow allowance scheduling with a rate-modifying activity

In this paper we consider single machine SLK due date assignment scheduling problem with a rate-modifying activity. In this model, the machine has a rate-modifying activity that can change the processing rate of machine under consideration. Hence the actual processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. We need to make a decision on when to schedule the rate-modifying activity, the optimal common flow allowance and the sequence of jobs to minimize total earliness, tardiness and common flow allowance cost. We introduce an efficient (polynomial time) solution for this problem.

Scheduling with job-dependent learning effects and multiple rate-modifying activities

We consider a scheduling problem with job-dependent learning effects and multiple rate-modifying activities. The learning effects manifest such that the processing time of a job is a decreasing function of its position in a sequence. By job-dependent learning effects, we mean that the learning of the jobs is different. A rate-modifying activity is an activity that changes the production rate of a machine. So the actual processing time of a job in our problem is a variable, which depends not only on its position in a sequence but also on whether it is scheduled before or after a rate-modifying activity. We assume that each machine may have multiple rate-modifying activities. The objective is to minimize the total completion time. We show that all the cases of the problem are polynomially solvable.

A note to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity

This note considers a single machine scheduling and due-window assignment problem, in which the processing time of a job is a linear function of its starting time and the job-independent deterioration rates are identical for all jobs. We allow an option for performing a rate-modifying activity for changing the normal processing times of the jobs following this activity. The objective is to schedule the jobs, the due-window and the rate-modifying activity so as to minimize the sum of earliness, tardiness and due-window starting time and due-window size costs. We introduce a polynomial solution for the problem.