Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects

In this paper we introduce a new scheduling model with learning effects in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the job’s scheduled position. We show that the single-machine problems to minimize makespan and total completion time are polynomially solvable. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. Finally, we present polynomial-time optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time.     

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.     

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 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.     

Notes on “some single-machine scheduling problems with general position-dependent and time-dependent learning effects”

This paper provides a continuation of the idea presented by Yin et al. [Yin et al., Some scheduling problems with general position-dependent and time-dependent learning effects, Inform. Sci. 179 (2009) 2416-2425]. For each of the following three objectives, total weighted completion time, maximum lateness and discounted total weighted completion time, this paper presents an approximation algorithm which is based on the optimal algorithm for the corresponding single-machine scheduling problem and analyzes its worst-case bound. It shows that the single-machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties. It also shows that the problems of minimizing the total tardiness, discounted total weighted completion time and total weighted earliness penalty are polynomially solvable under some agreeable conditions on the problem parameters.     

Several flow shop scheduling problems with truncated position-based learning effect

The concept of truncated position-based learning process plays a key role in production environments. However, it is relatively unexplored in the flow shop setting. In this paper, we consider the flow shop scheduling with truncated position-based learning effect, i.e., the actual processing time of a job is a function of its position and a control parameter in a processing permutation. The objective is to minimize one of the six regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the discounted total weighted completion time, the sum of the quadratic job completion times, and the maximum lateness. We present heuristic algorithms and analyze the worst-case bound of these heuristic algorithms. We also provide the computational results to evaluate the performance of the heuristics.     

Single machine scheduling problems with exponentially time-dependent learning effects

In this paper, we introduce a single-machine scheduling problem with an exponentially time-dependent learning effect. The processing time of a job is assumed to be an exponential function of the total normal processing time of jobs already processed before it. For such a scheduling problem, we first provide the upper bound for the maximum lateness and for the total weighted completion time. Next, we show that problems with the following criteria: makespan, the total completion time, the total weighted completion time, the total earliness/tardiness penalties and the maximum lateness under some agreeable conditions, are polynomially solvable.     

A note on single-machine scheduling with general learning effect and past-sequence-dependent setup time

In this paper, we study a scheduling model with the consideration of both the learning effect and the setup time. Under the proposed model, the learning effect is a general function of the processing time of jobs already processed and its scheduled position, and the setup time is past-sequence-dependent. We then derive the optimal sequences for two single-machine problems, which are the makespan and the total completion time. Moreover, we showed that the weighted completion time, the maximum lateness, the maximum tardiness, and the total tardiness problems remain polynomially solvable under agreeable conditions.     

Single machine scheduling problems under position-dependent fuzzy learning effect with fuzzy processing times

In this paper, we consider single machine scheduling problems under position-dependent fuzzy learning effect with fuzzy processing times. We study three objectives which are to minimize makespan, total completion time and total weighted completion time. Furthermore, we show that these three problems are polynomially solvable under position-dependent fuzzy learning effects with fuzzy processing times. In order to model the uncertainty of fuzzy model parameters such as processing time and learning effect, we use an approach called likelihood profile that depends on the possibility and necessity measures of fuzzy parameters. For three objective functions, we build Fuzzy Mixed Integer Nonlinear Programming (FMINP) models using dependent chance constrained programming techniques for the same predetermined confidence levels. Furthermore, we present polynomially solvable algorithms for different confidence levels for these problems.     

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.     

Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns

The focus of this study is to analyze position-based learning effects in single-machine stochastic scheduling problems. The optimal permutation policies for the stochastic scheduling problems with and without machine breakdowns are examined, where the performance measures are the expectation and variance of the makespan, the expected total completion time, the expected total weighted completion time, the expected weighted sum of the discounted completion times, the maximum lateness and the maximum tardiness.     

Note on a unified approach to the single-machine scheduling problem with a deterioration effect and convex resource allocation

In many resource allocation problems in physical or economic systems, a linear resource consumption function is commonly considered, and job processing times are assumed to be fixed parameters. However, the former assumption fails to reflect the law of diminishing returns, and the latter may be controlled by changing the allocation of resources to jobs. Motivated by these observations, we provide a unified model for solving single-machine scheduling problems in which each job's processing time is a function of its starting time and convex resource allocation. The objective is to find the optimal sequence of jobs subject to a limited resource consumption. We first show how this unified model can be useful in solving scheduling problems under due date assignment considerations. We analyze the problem with four different due date assignment methods, and our objective function includes costs for earliness, tardiness and due date assignments. We also consider scheduling problems without involving due date assignment decisions. The objective function is to minimize the makespan, total completion time, total absolute variation in completion times, and total absolute variation in waiting times. We show that several existing well-known problems can be reduced to a special case of our unified model and solved in O(nlogn) time.     

Single-machine group scheduling with a time-dependent learning effect

In many realistic situations, the more time you practice, the better learning effect you obtain. Thus, we propose a time-dependent learning effect and introduce it into the single-machine group scheduling problems. The two objectives of scheduling problems are to minimize the makespan and the total completion time, respectively. We also provide two polynomial time algorithms to solve these 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.     

Minimizing total weighted completion time under makespan constraint for two-agent scheduling with job-dependent aging effects

In this paper, we consider a two-agent single-machine scheduling problem with linear position-based aging effects and job-dependent aging ratios. The objective is to minimize the total weighted completion time of all jobs for two agents, where the makespan for one agent is constrained under an upper bound. After showing that this problem is at least NP-hard, we develop two solution algorithms: First, we devise a branch-and-bound algorithm to find an optimal solution through the establishment of several dominance and feasibility properties, and a lower bound. Second, we propose efficient simulated annealing algorithms, using three different methods to generate an initial solution. Through a numerical experiment, we demonstrate that the suggested algorithms can be applied to efficiently find near-optimal solutions within a reasonable amount of CPU time. In particular, we show that the initial solution method (arranging the jobs for one agent in non-increasing order of aging ratio, and scheduling the jobs for the other in the weighted shortest normal processing time order) is superior to others. Moreover, through scalability testing, we verify its consistent and relatively outstanding performance for larger systems with many processing jobs.     

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.     

The common due-date early/tardy scheduling problem on a parallelmachine under the effects of time-dependent learning and linear and nonlinear deterioration

This paper considers earliness/tardiness (ET) scheduling problem on a parallel machine environment with common due-date under the effects of time-dependent learning and linear and nonlinear deterioration. In this paper, the effects of learning and deterioration are considered 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. This study shows that optimal solution for ET scheduling problem under effects of learning and deterioration is V-shape schedule under certain agreeable conditions. Furthermore, we present a mathematical model for the problem under study and an algorithm for solving large test problems. The algorithm can solve problems of 1000 jobs and four machines within 3 s on average.     

Scheduling a variable maintenance and linear deteriorating jobs on a single machine

We investigate a single machine scheduling problem in which the processing time of a job is a linear function of its starting time and a variable maintenance on the machine must be performed prior to a given deadline. The goals are to minimize the makespan and the total completion time. We prove that both problems are NP-hard. Furthermore, we show that there exists a fully polynomial time approximation scheme for the makespan minimization problem. For the total completion time minimization problem we point out that there exists a fully polynomial time approximation scheme for a special case.     

Single-machine and flowshop scheduling with a general learning effect model

Learning effects in scheduling problems have received growing attention recently. Biskup [Biskup, D. (2008). A state-of-the-art review on scheduling with learning effect. European Journal of Operational Research, 188, 315–329] classified the learning effect scheduling models into two diverse approaches. The position-based learning model seems to be a realistic assumption for the case that the actual processing of the job is mainly machine driven, while the sum-of-processing-time-based learning model takes into account the experience the workers gain from producing the jobs. In this paper, we propose a learning model which considers both the machine and human learning effects simultaneously. We first show that the position-based learning and the sum-of-processing-time-based learning models in the literature are special cases of the proposed model. Moreover, we present the solution procedures for some single-machine and some flowshop problems.