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The paper deals with resource allocation scheduling problems in which the processing time of a job is defined by a function of its starting times and its position in a sequence. We also assume that the resource-dependent ready times of jobs are continuous functions of their consumed resource. Our objective is to minimize the resource consumption (the makespan) subject to the makespan constraint (limited resource availability). We prove that these two single-machine scheduling problems can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

In this paper, we study the issue of single-machine rescheduling with linear deteriorating jobs and position-based learning effects simultaneously in response to an unexpected arrival of new jobs. The scheduling efficiency is measured in terms of the makespan, while the cost of disruption is measured in terms of the maximum difference in processing orders of the original jobs before and after disruption. By introducing the effects of deterioration and learning, the job actual processing time is defined by an increasing function of its starting time, meanwhile a decreasing function of its position. Two types of problems are considered. For the first one, the makespan is minimised subject to a limit on the maximum sequence disruption; while in the second one, a linear combination of the makespan and the maximum sequence disruption is minimised. For each problem, the polynomial solvability is demonstrated, and an efficient algorithm is then developed. Finally, extensive computational experiments are conducted to show the efficiency and running behaviours of the proposed algorithms. [ABSTRACT FROM PUBLISHER]

In scheduling problems with learning effects, most research assumes that processing times are deterministic. This paper studies a single-machine scheduling problem with a position-based learning effect and fuzzy processing times where the objective is to minimize the makespan. The position-based learning effect of a job is assumed to be a function of its position. The processing times are considered to be triangular fuzzy numbers. Two different polynomial-time algorithms are developed for the problem. The first solution methodology is based on the fuzzy chance-constrained programming, whereas the second is based on a method to rank fuzzy numbers. Computational experiments are then conducted in order to evaluate the performance of the algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this study is to explore the single-machine scheduling with the effects of exponential learning and general deterioration. By the effects of exponential learning and general deterioration, we meant that job processing time is decided by the functions of their starting time and positions in the sequence. Results showed that with the introduction of learning effect and deteriorating jobs to job processing time, single-machine makespan, and sum of completion time (square) minimization problems remained polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion time and the maximum lateness, this paper proved that the weighted smallest basic processing time first (WSPT) rule and the earliest due date first (EDD) rule constructed the optimal sequence under some special cases, respectively. [Copyright &y& Elsevier]

Abstract: This paper deals with a bi-criteria single machine scheduling problem with a time-dependent learning effect and release times. The objective is to minimize the weighted sum of the makespan and the total completion time. The problem is NP-hard, thus a mixed integer non-linear programming formulation is presented, and a set of dominance properties are developed. To solve the problem efficiently, a procedure is then proposed by incorporating the dominance properties with an ant colony optimization algorithm. In the proposed algorithm, artificial ants construct solutions as orders of jobs based on the heuristic information as well as pheromone trails. Then, the dominance properties are added to obtain better solutions. To evaluate the algorithm performance, computational experiments are conducted. [Copyright &y& Elsevier]

Abstract: In this paper we consider several single-machine scheduling problems with general learning effects. By general learning effects, we mean that the processing time of a job depends not only on its scheduled position, but also on the total normal processing time of the jobs already processed. We show that the scheduling problems of minimization of the makespan, the total completion time and the sum of the θth () power of job completion times can be solved in polynomial time under the proposed models. We also prove that some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time. [Copyright &y& Elsevier]

In most studies, the learning effect model applied in a scheduling problem assumes that the actual processing time of a job is a function of its scheduled position or the sum of the normal processing times of the jobs already scheduled. In this article, we introduce a learning effect model and a past-sequence-dependent (psd) setup time into a single machine group scheduling problem. The actual processing time of a job in each group is a function of the sum of the normal processing times of the jobs already scheduled and the position of the corresponding job group in the sequence. It shows that the addressed problem remains polynomially solvable for the objectives: minimisation of the makespan and the total completion time. It also shows that the smallest processing time rule provides the optimal jobs sequence in each group and the optimal group sequence for the addressed problem, respectively. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the single-machine scheduling problems with both learning and deterioration effects. 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 minimization problem and the sum of the θth power of job completion times minimization problem 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. [Copyright &y& Elsevier]

Abstract: Learning and job deterioration co-exist in many realistic scheduling situations. This paper introduces a general scheduling model with the effects of learning and deterioration simultaneously which is a significant generalization of some existing models in the literature. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their start times and positions in the sequence. This paper shows that the single-machine scheduling problems to minimize the makespan, sum of the th power of completion times, total lateness and sum of earliness penalties (with a common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time, discounted total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with a common due date) are polynomially solvable under certain conditions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we bring into the scheduling field a general learning effect model where the actual processing time of a job is not only a general function of the total actual processing times of the jobs already processed, but also a general function of the job’s scheduled position. We show that the makespan minimization problem and the sum of the kth power of completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions. [Copyright &y& Elsevier]

The learning effect in scheduling has received considerable attention recently. However, most researchers consider a single criterion with the assumption that jobs are all ready to be processed. The research of bi-criterion problems with learning effect is relatively limited. This paper studies a single-machine learning effect scheduling problem with release times where the objective is to minimize the sum of makespan and total completion time. First, we develop a branch-and-bound algorithm incorporating with several dominance properties and a lower bound to derive the optimal solution. Secondly, we propose a genetic algorithm to obtain near-optimal solutions. Finally, a computational experiment is conducted to evaluate the performance of the branch-and-bound and the genetic algorithms. [Copyright &y& Elsevier]

Abstract: In a recent paper, Lee and Wu [W.-C. Lee, C.-C. Wu, A note on single-machine group scheduling problems with position-based learning effect, Appl. Math. Model. 33 (2009) 2159–2163] proposed a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. They investigate the makespan and the total completion time minimization problems on a single-machine. As for the total completion time minimization problem, they assumed that the numbers of jobs in each group are the same and the group normal setup and the job normal processing times are agreeable. Under the assumption conditions, they showed that the total completion time minimization problem can be optimally solved in polynomial time solution. However, the assumption conditions for the total completion time minimization problem do not reflect actual practice in many manufacturing processes. Hence, in this note, we propose other agreeable conditions and show that the total completion time minimization problem remains polynomially solvable under the agreeable conditions. [Copyright &y& Elsevier]