Some single-machine scheduling with sum-of-processing-time-based and job-position-based processing times

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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Robust Single Machine Scheduling with Stochastic Processing Times Based on Event Point

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.668-669.1641 ◽

2014 ◽

Vol 668-669 ◽

pp. 1641-1645

Author(s):

Xiao Xia He ◽

Chun Yao ◽

Qiu Hua Tang

Keyword(s):

Single Machine ◽

Processing Time ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problems ◽

Model Base ◽

Processing Times ◽

Robust Model ◽

Stochastic Processing ◽

Stochastic Processing Times

The scheduling of the single machine is of major importance in applications. The focus of this work is to analyze the scheduling problems in single-machine scheduling in the presence of uncertain parameters. By assuming that the processing time is represented by the nominal value plus a perturbation, we propose a robust model base on event point, and we obtain the feasible job sequence with some probability confidence level.

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Single Machine Scheduling with Discretely Compressible Processing Times

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.787.1020 ◽

2013 ◽

Vol 787 ◽

pp. 1020-1024

Author(s):

Shu Xia Zhang ◽

Yu Zhong Zhang

Keyword(s):

Dynamic Programming ◽

Single Machine ◽

Processing Time ◽

Machine Scheduling ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Single Machine Scheduling ◽

Scheduling Problem ◽

Processing Times ◽

Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

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An Optimal Algorithm for Scheduling with Variable Job Processing Times and Rejection

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.775.449 ◽

2015 ◽

Vol 775 ◽

pp. 449-452

Author(s):

Ji Bo Wang ◽

Chou Jung Hsu

Keyword(s):

Objective Function ◽

Polynomial Time ◽

Single Machine ◽

Processing Time ◽

Optimal Algorithm ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problem ◽

Processing Times ◽

Rejection Penalty

This paper studies a single machine scheduling problem with rejection. Each job has a variable processing time and a rejection penalty. The objective function is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem can be solved in polynomial time.

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