Xue Huang

Single machine scheduling with time-dependent deterioration and exponential learning effect

In this paper we consider the single machine scheduling problems with time-dependent deterioration and exponential learning effect, i.e., the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. We consider the following objective functions: the makespan, the sum of the @dth (@d>=0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the sum of the @dth power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, 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.

Single-machine group scheduling with both learning effects and deteriorating jobs

In the paper two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered. By learning effects, deteriorating jobs and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

A Note On "Scheduling Problems With The Effects Of Deterioration And Learning"

Two results in a recent paper by Wang and Cheng [Wang, J-B and TCE Cheng (2007). Asia-Pacific Journal of Operational Research, 24, 245–261] are incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published results are incorrect.

Scheduling with Proportional Linear Deteriorating and a Maintenance Activity

In this paper, we consider single machine scheduling with proportional linear deteriorating in which the processing time of a job depends on its starting time in a sequence. We assume that a maintenance activity is performed in a schedule. After a maintenance activity, machine will revert to its initial condition. The objective is to find simultaneously the optimal sequence for jobs and the position of a maintenance activity to minimize the makespan. A polynomial time algorithm is provided to solve the problem.