Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration

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.…”

Minimizing Makespan with Start Time-Dependent Jobs in a Two-Machine Flow Shop

“…The job size [9] was fixed at n=11 and the value of deterioration rate b was segmented to ten groups (small to large) and have been generated randomly from continuous uniform distributions over (0 Evaluating the efficiency of the B&B algorithm and the performance of the best heuristic algorithm are as the goals of the second experiment; the results are given in Table 2. In this experiment, the algorithms are tested with nine different job sizes 8,10,12,14,16,18,20,22 24 n and  and the deterioration rates are generated [11] from a continuous uniform distribution from interval (0, 1). For any condition, 20 replications were randomly generated; since, 10 experimental conditions were examined in the first experiment and 9 conditions in the second one; therefore, 380 problems (i.e., 19×20) are generated, totally.…”

“…Wang et al [15] showed that two machine flow shop scheduling problem under simple linear deteriorating jobs to minimize total completion time is NP-hard; they proposed a B&B algorithm able to handle 14 jobs. Yang and Wang [16] continued this problem to minimize total weighted completion time and developed a B&B and heuristic algorithm to solve the problem.…”

“…There is a growing interest in the literature to study the Scheduling problems on flow shop environment. Researchers considered this problem with various assumptions, e.g., flow shop scheduling problem with modified learning effect [20], two-stage hybrid flow shop scheduling problem with serial batching [21], nowait reentrant flow shop scheduling problem [22], and deteriorating jobs [6][7][8][9][14][15][16].…”

Joint reply to the erratum and the note on “Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning” [Math. Comput. Modelling 50 (2009) 401–406]

“…As an illustration, this is the case for twenty papers [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]3] published in the last five years. It is unfortunate that Wang et al [2] and Yin and Xu [3] set the deterioration rate as 100.…”