Abstract
This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.
Highlights
Recent years, position-effect and processing-time-dependent scheduling problems have been paid more attention
Cheng et al [5] considered deteriorated-effect scheduling problems, where the actual processing time of a job means a function of the logarithm of the sum of the normal processing time of the jobs processed and the setup times are proportional to the actual processing times of the jobs processed
Yin et al [6] addressed another deterioration model to minimize the makespan and the total completion time, where the actual processing time of a job depends on its starting time and its position. ey showed that there exists optimal sequence based on the relationships between problem parameters, including the shortest processing time, longest processing time, or V-shaped with respect to the normal processing times
Summary
Position-effect and processing-time-dependent scheduling problems have been paid more attention. Rudek [7, 8] considered the general sum-of-processing time-based learning or aging effects and showed that the total weighted completion times’. Luo [19] presented more general sum-of-processing-timebased scheduling models, which cover the normal processing time or the actual processing times. (iii) e total weighted completion times’ problem and the lateness problem can be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the sum of the completion time problem with 0 < a1 ≤ 1, a V-shaped property based on the normal processing times is obtained in an optimal sequence which satisfies some agreeable relations.
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