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.     

The single-machine total weighted tardiness scheduling problem with position-based learning effects

This study addresses the problem of minimizing the total weighted tardiness on a single-machine with a position-based learning effect. Several dominance properties are established to develop branch and bound algorithm and a lower bound is provided to derive the optimal solution. In addition, three heuristic procedures are developed for near-optimal solutions. Computational results are also presented to evaluate the performance of the proposed algorithms.     

Uniform parallel-machine scheduling to minimize makespan with position-based learning curves

Scheduling with learning effects has become a popular topic in the past decade; however, most of the research focuses on single-machine problems. In many situations, there are machines in parallel and the skills of workers might be different due to their individual experience. In this paper, we study a uniform parallel machine problem in which the objective is to jointly find an optimal assignment of operators to machines and an optimal schedule to minimize the makespan. Two heuristic algorithms are proposed and computational experiments are conducted to evaluate their performance.     

A note on “Single machine scheduling with time-dependent deterioration and exponential learning effect”

result in a recent paper Huang, Wang, Wang, Gao, and Wang (2010) (Computers & Industrial Engineering 58 (2010) 58–63) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect.     

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 with past-sequence-dependent setup times and learning effects

This paper studies a single machine scheduling problem with setup times and learning considerations. The setup times are proportional to the length of the already scheduled jobs. That is, the setup times are past-sequence-dependent. It is assumed that the learning process reflects a decrease in the process time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. The following objectives are considered: the makespan, the total completion time, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalty. Polynomial time algorithms are proposed to optimally solve the above objective functions.     

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.     

Resource-dependent scheduling with deteriorating jobs and learning effects on unrelated parallel machine

The focus of this paper is to analyze unrelated parallel-machine resource allocation scheduling problem with learning effect and deteriorating jobs. The goal is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing the cost function including the total load, the total completion time, the total absolute deviation of completion time and the total resource cost. We show that the problem is polynomial time solvable if the number of machines is a given constant.     

A note on scheduling problems with learning effect and deteriorating jobs

In this note, we consider the machine scheduling problems with the effects of deterioration and learning. In this model, job processing times are defined by functions of their starting times and positions in the sequence. The scheduling objectives are makespan (weighted) sum of completion times and maximum lateness. It is shown that even with the introduction of deterioration and learning effect to job processing times, several single machine problems and several flow shop problems remain polynomially solvable, respectively.     

Single machine scheduling with autonomous learning and induced learning

As an important management tool of winning competitive advantage, induced learning effect has been widely studied in empirical research area. But it is hardly considered in scheduling problems. In this paper, autonomous and induced learning are both taken into consideration. The investment of induced learning is interpreted as specialized time intervals to implement training, knowledge sharing and transferring etc. We present algorithms to determine jointly the optimal job sequence and the optimal position of induced learning intervals, with the objective of minimizing makespan.     

A note on evidence and confirmation in machine learning

This paper addresses the problem in inductive generalization of determining when a general hypothesis is supported by a particular instance. If we accept that, first, some facts do indeed support a general hypothesis and, second, that an instance that supports a hypothesis also supports all logical consequences of the hypothesis, then unintuitive and problematic results are immediately forthcoming. These assumptions lead, for example, to the conclusion that a blue Honda is confirming evidence for the hypothesis that ravens are black. This problem is variously known as the paradoxes of confirmation or Hempel's paradox . In this paper I develop a formal characterization of the problem. The assumption that whatever supports all classical consequences of the hypothesis is rejected. Rather, I argue that a weaker notion of consequence should be adopted for determining what consequences of a hypothesis are supported by the same evidence. An extant formal system for learning from examples is used to address these problems of evidential support, and it is shown that in this framework the problems do not arise.     

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.     

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.     

Scheduling with general position-based learning curves

Learning effect in scheduling problems has received growing attention since Biskup [3] introduced the position-based model, where the learning curve is expressed as a power function of a job position. Hurley [11] pointed out that the actual processing time of a given job drops to zero precipitously as the number of jobs increases in the standard power model. Moreover, the learning rates show considerable variation within industries or firms. The variation extends not only across firms at a given time, but also within firms over time. For instance, the learning curves usually have an initial downward concavity, and no further improvements are made after some amount of production. Beside the standard power model, learning curve is seldom discussed in scheduling. In this paper, we offer a surprising simple yet realistic learning effect model which has the flexibility to describe different learning curves easily. For instance, the standard power model, the well-known S-shaped and the plateau functions are special cases of the proposed model. We then present the optimal solution for some scheduling problems.     

A note on a single machine scheduling problem with generalized total tardiness objective function

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered.     

An approach for modeling a new single machine scheduling problem with deteriorating and learning effects

This paper presents a new approach to model a mixed-integer mathematical programming for a single machine scheduling problem with deteriorating and learning effects. Neglecting the effect of performing a job on its own processing time is mentioned as a deficiency in the literature of industrial scheduling. At first, self-influential factors are defined and then equations are presented to utilize these new factors. GAMS IDE/CPLEX software is used to validate the represented model by solving small to medium-sized sample problems, in which the associate results are compared with a hybrid meta-heuristic algorithm based on Ant Colony Optimization (ACO), Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). The vitality of considering and modeling the effect of learning and deteriorating made by a job, on its own processing time is tested for several sample problems. Then a significant improvement is observed by comparing the results acquired by neglecting the self-influential factors with the results based on considering them. Finally, the computational results are analyzed and the conclusion is given.     

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.     

A note on on-line broadcast scheduling with deadlines

In this paper, we study an on-line broadcast scheduling problem with deadlines, in which the requests asking for the same page can be satisfied simultaneously by broadcasting this page, and every request is associated with a release time, deadline and a required page with a unit size. The objective is to maximize the number of requests satisfied by the schedule. In this paper, we focus on an important special case where all the requests have their spans (the difference between release time and deadline) less than 2. We give an optimal online algorithm, i.e., its competitive ratio matches the lower bound of the problem.