Scheduling problems with general effects of deterioration and learning

Scheduling with deteriorating jobs or learning effects has been widely studied recently. There are situations where both the deterioration and learning effects might exist at the same time. However, the research with the consideration of both the effects is relatively limited. Furthermore, the forms of the effects are specific functions in the literature. In this paper, we introduce a general scheduling model in the sense that the form of the function is unspecified. Under the proposed model, the actual job processing time is a general function on the processing times of the jobs already processed and its scheduled position. The optimal solutions for some single-machine problems are provided.     

Scheduling problems with deteriorating jobs and learning effects including proportional setup times

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered setup times. We introduce a new scheduling model in which job deterioration and learning, and setup times are considered simultaneously. In the proposed model, the actual processing time of a job is defined as a function of the setup and processing times of the jobs already processed and the job’s own scheduled position in a sequence. In addition, the setup times are assumed to be proportional to the actual processing times of the already scheduled jobs. We derive polynomial-time optimal solutions for some single-machine problems with or without the presence of certain conditions.     

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.     

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.     

Some scheduling problems with deteriorating jobs and learning effects

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper, we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. For the single-machine case, we derive polynomial-time optimal solutions for the problems to minimize makespan and total completion time. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. For the case of an m-machine permutation flowshop, we present polynomial-time optimal solutions for some special cases of the problems to minimize makespan and total completion time.     

Single-machine scheduling problems with deteriorating jobs and learning effects

In this paper, we introduce a new scheduling model in which deteriorating jobs and learning effect are both considered simultaneously. By deterioration and the learning effect, we mean that the actual processing time of a job depends not only on the processing time of the jobs already processed but also on its scheduled position. For the single-machine case, we show that the problems of makespan, total completion time and the sum of the quadratic job completion times remain polynomially solvable, respectively. In addition,we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain conditions.     

Exact and parallel metaheuristic algorithms for the single processor total weighted completion time scheduling problem with the sum-of-processing-time based models

In this paper, the single processor scheduling problem to minimize the total weighted completion times is analysed, where the processing times of jobs are described by functions dependent on the sum of the normal processing times of previously processed jobs, which can model learning or aging (deteriorating) effects. We construct the exact pseudopolynomial time algorithm based on the dynamic programming, which solves the problem, where the processing time of each job is described by an arbitrary stepwise function. Moreover, the parallel metaheuristic algorithms are provided for the general version of the problem with arbitrary sum-of-processing time based models. The efficiency of the proposed algorithms is evaluated during numerical analysis.     

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.     

Some scheduling problems with general position-dependent and time-dependent learning effects

In scheduling problems with learning effects, most of the research is based on specific learning functions. In this paper, we develop a general model with learning effects where 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. In particular, it is shown that some single machine scheduling problems and m-machine permutation flowshop problems are still polynomially solvable under the proposed model. These results are significant extensions of some of the existing results on learning effects in the literature.     

Single-machine scheduling with a nonlinear deterioration function

In deteriorating job scheduling problems, most of the researchers assume that the actual job processing time is a function of its starting time. In this paper, we propose a new deterioration model in which the actual job processing time is a general function of the normal processing time of jobs already processed and its scheduled position at the same time. We show that some single-machine scheduling problems remain polynomially solvable.     

Flowshop scheduling of deteriorating jobs on dominating machines

In this paper we consider the general, no-wait and no-idle permutation flowshop scheduling problem with deteriorating jobs, i.e., jobs whose processing times are increasing functions of their starting times. We assume a linear deterioration function with identical increasing rates for all the jobs and there are some dominating relationships between the machines. We show that the problems to minimize the makespan and the total completion time remain polynomially solvable when deterioration is considered, although these problems are more complicated than their classical counterparts without deterioration.     

Single-machine scheduling with deteriorating jobs under a series–parallel graph constraint

This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series–parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.     

Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations

Scheduling with learning effects has attracted growing attention of the scheduling research community. A recent survey classifies the learning models in scheduling into two types, namely position-based learning and sum-of-processing-times-based learning. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases in the first model and when the normal job processing times are large in the second model. Motivated by this observation, we propose a new learning model where the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. The use of the logarithm function is to model the phenomenon that learning as a human activity is subject to the law of diminishing return. Under the proposed learning model, we show that the scheduling problems to minimize the makespan and total completion time can be solved in polynomial time. We further show that the problems to minimize the maximum lateness, maximum tardiness, weighted sum of completion times and total tardiness have polynomial-time solutions under some agreeable conditions on the problem parameters.     

Single-machine scheduling with learning effect and deteriorating jobs

In this paper we consider the single-machine scheduling problems with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their starting times and positions in the sequence. It is shown that even with the introduction of learning effect and deteriorating jobs to job processing times, single machine makespan and sum of completion times (square) minimization problems remain polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion times and the maximum lateness, this paper proves that the WSPT rule and the EDD rule can construct the optimal sequence under some special cases, respectively.     

Some single-machine scheduling problems with a truncation learning effect

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called “sum-of processing-times-based learning” in which the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, we propose a truncation learning model where the actual job processing time is a function which depends not only on the processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. Under the proposed learning model, we show that some single-machine scheduling problems can be solved in polynomial time. In addition, we further provide the worst-case error bounds for the problems to minimize the maximum lateness and total weighted completion time.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

Single-machine scheduling with deteriorating jobs and setup times to minimize the maximum tardiness

In many realistic production situations, a job processed later consumes more time than the same job when it is processed earlier. Production scheduling in such an environment is known as scheduling with deteriorating jobs. However, research on scheduling problems with deteriorating jobs has rarely considered explicit (separable) setup time (cost). In this paper, we consider a single-machine scheduling problem with deteriorating jobs and setup times to minimize the maximum tardiness. We provide a branch-and-bound algorithm to solve this problem. Computational experiments show that the algorithm can solve instances up to 1000 jobs in reasonable time.     

The solution algorithms for the multiprocessor scheduling with workspan criterion

In this paper, we consider multiprocessor scheduling problems, where each job (task) must be executed simultaneously by the specified number of processors, but the indices of the processors allotted to each job do not have to be contiguous (i.e., jobs can be fragmentable). Unlike other research in this domain, we analyse the problem under the workspan criterion, which is defined as the product of the maximum job completion time (makespan) and the number of used processors. Moreover, the job processing times can be described by non-increasing or non-decreasing functions dependent on the start times of jobs that model improvement (learning) or degradation (deteriorating), respectively. To solve the problems, we construct some polynomial time algorithms and analyse numerically their efficiency.     

Three scheduling problems with deteriorating jobs to minimize the total completion time

In this paper, three scheduling problems with deteriorating jobs to minimize the total completion time on a single machine are investigated. By a deteriorating job, we mean that the processing time of the job is a function of its execution start time. The three problems correspond to three different decreasing linear functions, whose increasing counterparts have been studied in the literature. Some basic properties of the three problems are proved. Based on these properties, two of the problems are solved in O(nlogn) time, where n is the number of jobs. A pseudopolynomial time algorithm is constructed to solve the third problem using dynamic programming. Finally, a comparison between the problems with job processing times being decreasing and increasing linear functions of their start times is presented, which shows that the decreasing and increasing linear models of job processing times seem to be closely related to each other.     

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of ?1?a?a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.