Single-machine scheduling with a sum-of-actual-processing-time-based learning effect

Scheduling involving jobs with time-dependent processing times has recently attracted much research attention. However, multiagent scheduling with simultaneous considerations of jobs with time-dependent processing times and ready times is relatively unexplored. Inspired by this observation, we study a two-agent single-machine scheduling problem in which the jobs have both time-dependent processing times and ready times. We consider the model in which the actual processing time of a job of the first agent is a decreasing function of its scheduled position while the actual processing time of a job of the second agent is an increasing function of its scheduled position. In addition, each job has a different ready time. The objective is to minimize the total completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We propose a branch-and-bound and several genetic algorithms to obtain optimal and near-optimal solutions for the problem, respectively. We also conduct extensive computational results to test the proposed algorithms and examine the impacts of different problem parameters on their performance.

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SINGLE MACHINE SCHEDULING WITH A LEARNING EFFECT AND A RATE-MODIFYING ACTIVITY

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595911003211 ◽

2011 ◽

Vol 28 (04) ◽

pp. 511-521 ◽

Cited By ~ 5

Author(s):

CHUANLI ZHAO ◽

HENGYONG TANG

Keyword(s):

Single Machine ◽

Processing Time ◽

Learning Effect ◽

Window Size ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problems ◽

Polynomial Time Algorithms ◽

Due Window ◽

Machine Scheduling Problems

In the paper, single machine scheduling problems with a learning effect and a rate-modifying activity are considered. Under the learning effect, the processing time of a job is a decreasing function of its position in the sequence. The rate-modifying activity is an event that can change the speed of the machine, and hence the processing time of jobs after the activity. The following objective functions are considered: the makespan, the total earliness, tardiness and completion time penalty, and the total earliness, tardiness, due-window starting time and due-window size penalty. Polynomial time algorithms are proposed to optimally solve the problems.

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Single-machine scheduling with a sum-of-processing-time based learning effect and deteriorating jobs

The International Journal of Advanced Manufacturing Technology ◽

10.1007/s00170-009-1950-x ◽

2009 ◽

Vol 45 (3-4) ◽

pp. 336-340 ◽

Cited By ~ 7

Author(s):

Li-Yan Wang ◽

Ji-Bo Wang ◽

Dan Wang ◽

Na Yin ◽

Xue Huang ◽

...

Keyword(s):

Single Machine ◽

Processing Time ◽

Learning Effect ◽

Deteriorating Jobs ◽

Machine Scheduling ◽

Single Machine Scheduling

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Single-Machine Scheduling with Upper Bounded Maintenance Time under the Deteriorating Effect

Discrete Dynamics in Nature and Society ◽

10.1155/2013/756251 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Pengfei Xue ◽

Yulin Zhang

Keyword(s):

Single Machine ◽

Upper Bound ◽

Processing Time ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problem ◽

Maintenance Time ◽

Optimal Maintenance ◽

Special Case ◽

Actual Processing Time

We consider a single-machine scheduling problem with upper bounded actual processing time and upper bounded maintenance time under deteriorating effect. The actual processing time of a job is a position-dependent power function. If the actual processing time of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance should also be paid. The maintenance duration studied in the paper is a position-dependent exponential function. The objective is to find jointly the optimal maintenance frequency and the optimal job sequence to minimize the total cost, which is a linear function of the makespan and the total tardiness. We show that the studied scheduling problem can be transformed as a classic assignment problem to solve. There is also shown that a special case of the scheduling problem can be optimally solved by a lower order algorithm.

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