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Related Experiment Videos

Cyclic scheduling via integer programs with circular ones.

J J Bartholdi, J B Orlin, H D Ratliff

    Operations Research
    |August 9, 1980
    PubMed
    Summary

    This study presents an efficient method for workforce scheduling to minimize costs. It uses network flow problems to solve cyclic staffing integer linear programs optimally.

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    Area of Science:

    • Operations Research
    • Applied Mathematics

    Background:

    • Cyclic staffing problems involve optimizing workforce size and schedules for cost-efficiency.
    • These problems are often modeled as integer linear programs (ILPs) with complex constraint matrices.

    Purpose of the Study:

    • To develop efficient algorithms for solving cyclic staffing ILPs.
    • To identify problem structures that allow for parametric solutions.

    Main Methods:

    • Modeling cyclic staffing as an integer linear program (ILP) with a cyclically structured 0-1 constraint matrix.
    • Identifying a class of problems solvable via a series of network flow problems.
    • Developing an alternative method involving solving the linear program (LP) and rounding the continuous solution.

    Main Results:

    • A large class of cyclic staffing ILPs can be solved parametrically using network flow problems.
    • An alternative method provides an optimal ILP solution by rounding the continuous LP solution.

    Conclusions:

    • The identified special structure enables efficient, parametric solutions for cyclic staffing problems.
    • Rounding techniques offer an alternative optimal approach to solving these workforce scheduling problems.

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