Single-machine scheduling with nonlinear deterioration

Abstract

In this paper, we consider the single-machine scheduling problems with nonlinear deterioration. By the nonlinear deterioration effect, we mean that the processing times of jobs are nonlinear functions of their starting times. We show that even with the introduction of nonlinear deterioration to job processing times, single machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm utilizing the V-shaped property is proposed, and computational experiments show that it performs effectively and efficiently in obtaining near-optimal solutions.

Variable Neighborhood Search for Parallel Machines Scheduling Problem with Step Deteriorating Jobs

“…In these cases, the corresponding scheduling problem was first studied by Browne and Yechiali 1 and J. N. D. Gupta and S. K. Gupta 2 . They assumed that the processing time of all jobs is a function of their starting point p i a i α i × s i , where a i is the normal processing time, α i is a deterioration rate, and s i is the starting time of job i. From then onwards, more papers considering scheduling jobs with deterioration effects have been published recently [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . Comprehensive reviews and discussions of different models and problems with timedependent processing times were given by 20, 21 . Most of the current researches in deteriorating jobs scheduling problems assume that the job processing times are linear functions of their starting times.…”

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

“…More recently, Wang and Wang [27] considered single-machine scheduling problems with nonlinear deterioration. They showed that the makespan minimization problem remains polynomially solvable.…”

Machine scheduling problems with a position-dependent deterioration

“…Extensive surveys of research related to scheduling deteriorating jobs and/or learning effects can be found in Alidaee and Womer [1], Cheng et al [2], Gawiejnowicz [3], and Biskup [4], Janiak et al [5]. More literature which has considered scheduling jobs with deteriorating jobs and/or learning effects includes Cheng et al [6], Wang [7][8][9], Lee and Wu [10], Lee et al [11], Wu and Lee [12], Wang et al [13], Yin et al [14], Zhang and Yan [15], Huang et al [16], Liu et al [17], Rudek [18,19], Wang and Wang [20], Lai et al [21], Shen et al [22], Wang and Wang [23], Wang et al [24], Ji et al [25], Lu et al [26], Wang and Wang [27,28], Wang and Liu [29], Yin et al [30], Yin et al [31], Yin et al [32], Yin et al [33], Niu et al [34], and Bai et al [35].…”