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Two-agent single-machine scheduling with position-dependent processing times

Abstract

A new scheduling model in which both two-agent and position-dependent processing times exist simultaneously is considered in this paper. Two agents compete to perform their respective jobs on a common single machine, and each agent has his own criterion to optimize. The job position-dependent processing time is characterized by increasing or decreasing function dependent on the position of a job in the sequence. We introduce an aging effect and a learning effect into the two-agent single-machine scheduling, where the objective is to minimize the total completion time of the first agent with the restriction that the maximum cost of the second agent cannot exceed a given upper bound. We propose the optimal properties for the considered scheduling problems and then present the optimal polynomial time algorithms to solve the two scheduling problems, respectively.

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Correspondence to Peng Liu.

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Liu, P., Zhou, X. & Tang, L. Two-agent single-machine scheduling with position-dependent processing times. Int J Adv Manuf Technol 48, 325–331 (2010). https://doi.org/10.1007/s00170-009-2259-5

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Keywords

  • Scheduling
  • Two-agent
  • Position-dependent processing times
  • Aging effect
  • Learning effect
  • Single machine