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This paper deals with the machine scheduling problems with the effects of deterioration and learning. In this model the processing times of jobs are defined as functions of their starting times and positions in a sequence. We introduce polynomial solutions for some single machine problems and flow shop problems. The performance measures include makespan, total completion time, total weighted completion time, and maximum lateness.

In this paper, we consider the rescheduling problem for jobs on a single machine with release dates to minimize total sequence disruption under a limit on the makespan. We show that the considered problem can be solved in polynomial time. Consequently, the rescheduling problem for jobs on a single machine with release dates to minimize makespan under a limit on the total sequence disruption can also be solved in polynomial time.

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a lower bounding procedure based on the relaxation of the jobs' completion times. Optimal branch-and-bound algorithms are then presented. These algorithms incorporate the proposed lower bound, as well as an insertion-based dominance test.

The branch-and-bound procedures are tested on a wide set of randomly generated problems. The computational results show that the branch-and-bound algorithms are capable of optimally solving, within reasonable computation times, instances with up to 20 jobs.

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, to analyze the effect of different rules on the effectiveness of the beam search algorithms.

The computational results show that using better rules improves the performance of the beam search heuristics. The detailed, filtered beam search (FBS) and recovering beam search (RBS) procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, the detailed beam search (DBS) algorithm requires excessive computation times, and the RBS procedure then becomes the heuristic of choice.

In this paper, we have proposed a hybrid permutation-coded steady-state genetic algorithm for a single machine scheduling problem with earliness and tardiness costs and no machine idle time. The steady-state genetic algorithm generates schedules, which are further improved by successive applications of an adjacent pairwise interchange procedure. We have compared our approach against the best approaches reported in the literature. Computational results show the effectiveness of our approach, since it obtained better quality solutions in shorter time.

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.

Two results in a recent paper by Wang and Cheng [Wang, J-B and TCE Cheng (2007). Asia-Pacific Journal of Operational Research, 24, 245–261] are 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 results are incorrect.

The note deals with machine scheduling problems with a more general learning effect model, i.e., the actual job processing time is a function of the sum of the function of the processing times of the jobs already processed and job position. We show that some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.

Job learning and deterioration coexist in many realistic machine-job scheduling situations. However, in literature, the constructed forms of the machine scheduling models with job learning and/or deteriorating effects were specific types of functions, which constrained their applicability in practice. This paper introduces a new single-machine scheduling model, where the actual processing time of a job is a general function of its starting time as well as scheduled position, which shows a broad generalization in contrast to that of certain existing models. For three objectives corresponding to the single-machine scheduling problem–total weighted completion time, discounted total weighted completion time, and maximum lateness — this paper presents their respective approximation result on the basis of the worst-case bound analysis from the optimal algorithm. The results demonstrate that under our proposed model, minimization of scheduling operations such as the makespan, sum of the kth power of completion times, and total lateness are polynomially solvable. Moreover, under some feasible conditions for the scheduling parameters, the minimum optimization problems of the total weighted completion time, discounted total weighted completion time, maximum lateness, and total tardiness are all recognized as polynomial forms and their solutions are provided.

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

We consider the problem of online scheduling a single machine with family setups under job availability. A setup must be scheduled when the next job comes from a different family from the last completed one, if any. The aim is to minimize the total completion time of all jobs. For the special case of identical processing times, we provide a lower bound for the competitive ratio and an online algorithm with its competitive analysis.

This paper deals with the single machine scheduling problem with deteriorating jobs in which there are two distinct families of jobs (i.e., two-agent) pursuing different objectives. In this model the processing time of a job is defined as a function that is proportional to a linear function of its stating time. For the following three scheduling criteria: minimizing the makespan, minimizing the total weighted completion time, and minimizing the maximum lateness, we show that some basic versions of the problem are polynomially solvable. We also establish the conditions under which the problem is computationally hard.

In this paper, a single-machine semi-online scheduling problem with rejection is addressed. In this model, “semi-online” implies that $\frac{p_{max}}{p_{min}}\le \gamma$, where $p_{max}$ and $p_{min}$ are the maximum processing time and the minimum one among all jobs, respectively, $\gamma \ge 1$. In this setting, each job arrives online over time, and rejection is allowable. Our goal is minimizing the total penalty cost of rejected jobs plus the total completion time of processed jobs. The seminal result of this study is that we offer an algorithm with competitive ratio $1+\frac{\sqrt{1+\gamma (\gamma -1)}-1}{\gamma }$, which matches the result of the problem without rejection.

We present a unified approach to single-machine scheduling with position-based processing times, an availability constraint, and job rejection. The approach uses two general position-based processing time functions to model both the learning and aging effects in scheduling. In addition, taking machine availability and job rejection into consideration, the models are more realistic, which seek to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. We present fully polynomial-time approximation schemes to address the two NP-hard problems.

In this paper a general formulation of a fuzzy single machine scheduling problem is proposed. Such notions as schedule, precedence relation and cost function in the fuzzy case are defined. The concept of f-regular function, being a generalization of a regular function, known from the classical theory of scheduling is introduced. A wide class of problems with f-regular cost functions is analyzed and some general properties of such problems are shown.

In this paper, the single machine total weighted completion time scheduling problem is studied. The jobs have nonzero release time and processing time increases during the production due to the effect of deterioration on the machine. An operator sets up the machine and manually loads the job in the machine and unloads it at the end of the working time. The setup time and the removal time are influenced by the ability of the worker due to his work experience and learning capacity. Heuristic algorithms are proposed to solve the scheduling problem, and their efficiency is evaluated on a wide benchmark.