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Positive reinforcement is a powerful method for teaching new behaviors to both animals and humans. B.F. Skinner demonstrated this with his experiments using rats in a Skinner box. When a rat pressed a lever, it received a food pellet. This immediate reward encouraged the rat to repeat the behavior. This method, where a reward follows every instance of the behavior, is known as continuous reinforcement. It is highly effective for establishing new behaviors quickly.
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Resource dependent scheduling with truncated learning effects.

Xuyin Wang1, Weiguo Liu1, Lu Li1

  • 1Business School, Northwest Normal University, Lanzhou 730070, China.

Mathematical Biosciences and Engineering : MBE
|May 23, 2022
PubMed
Summary
This summary is machine-generated.

This study addresses single-machine scheduling with a learning effect and resource allocation. An efficient assignment formulation solves the problem in O(n^3) time, minimizing costs.

Keywords:
learning effectresource allocationschedulingsingle-machine

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Area of Science:

  • Operations Research
  • Computer Science
  • Industrial Engineering

Background:

  • The single-machine scheduling problem is a fundamental challenge in operations management.
  • Incorporating learning effects and resource allocation adds complexity to traditional scheduling models.
  • Minimizing combined scheduling and resource costs is crucial for operational efficiency.

Purpose of the Study:

  • To investigate a single-machine scheduling problem featuring a truncated learning effect and dynamic resource allocation.
  • To develop an efficient method for determining optimal job sequencing and resource assignment.
  • To minimize a weighted objective function encompassing both scheduling costs and resource consumption costs.

Main Methods:

  • The problem is modeled as a single-machine scheduling scenario.
  • A general function describes job processing times based on allocated resources and sequence position.
  • An assignment formulation is employed to find the optimal solution.

Main Results:

  • The proposed method effectively determines the optimal resource allocation and job sequence.
  • The problem is demonstrably solvable within a cubic time complexity, specifically O(n^3).
  • This provides an efficient computational approach for complex scheduling scenarios.

Conclusions:

  • The developed assignment formulation offers an efficient solution for single-machine scheduling with learning and resource allocation.
  • The O(n^3) time complexity makes this approach practical for a considerable number of jobs.
  • This research contributes to optimizing production and service systems by balancing scheduling efficiency and resource utilization.