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

Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

“…Let p A jr be the actual processing time of job J j if it is scheduled in position r in a sequence. As in Yin et al [23], we consider the following general positiondependent and time-dependent learning effects model, i.e.,…”

“…, n, represent the makespan, the total completion time, the sum of the hth (h P 0) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs of a given permutation, respectively. As in Yin et al [23], we denote the learning effect given in (1) by LE gtp and as in Koulamas and Kyparisis [30], the p-s-d setup time given in (2) by s psd . In the remaining part of the paper, all the problems considered will be denoted using the three-field notation scheme ajbjc introduced by Graham et al [34].…”

“…In addition, they presented polynomial optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time. Yin et al [23] considered some scheduling problems with general position-dependent and time-dependent learning effect model. They showed that the single machine makespan and the sum of the hth power of completion times problems remain polynomially solvable under the proposed model.…”

Two-Agent Scheduling to Minimize the Maximum Cost with Position-Dependent Jobs

“…Wang and Xia [7] and Wang [8] considered position-dependent processing times in some flow shop scheduling problems. Yin et al [9] generalized the position-dependent functions 2 Discrete Dynamics in Nature and Society of processing times and some theoretical results appearing in [4,5]. Yang [10] simultaneously considered the jobs deterioration and the position-dependent learning effect under deteriorating maintenance environment and analyzed some results of single-machine scheduling models.…”

Multiple-Machine Scheduling with Learning Effects and Cooperative Games

“…Since then, several classes of learning effects in scheduling problems have been studied, namely, time-dependent learning effects [2][3][4][5][6], position-based learning effects [7][8][9][10][11][12][13], combined effects of position-based effects and timedependent effects [14][15][16][17]. In a scheduling problem with timedependent learning effects, the actual processing time of a job depends on the total processing times of jobs already processed, while, in a scheduling problem with positionbased learning effects, the actual processing time of a job is a function of its position.…”