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<p>This article addresses single-machine scheduling with variable processing times, where the variable processing times mean that the actual processing times of tasks have resource allocations, learning and deteriorating effects. Under three variable processing time models, the aim is to find the optimal task sequence, the optimal compression such that the weighted sum of scheduling cost and resource compression cost is minimized, where the scheduling cost is denoted by the product of two vectors. Some optimal solution properties are presented, and it is showed that the problem under three variable processing time models is solved optimally in polynomial time <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(n^3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, where <i>n</i> is the number of tasks. In addition, two extensions are given for the general earliness-tardiness costs.</p>

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A unified analysis for single-machine scheduling with resource allocations, learning and deteriorating effects simultaneously

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Yuan-Yuan Lu,
  • Mei-Hang Li

摘要

This article addresses single-machine scheduling with variable processing times, where the variable processing times mean that the actual processing times of tasks have resource allocations, learning and deteriorating effects. Under three variable processing time models, the aim is to find the optimal task sequence, the optimal compression such that the weighted sum of scheduling cost and resource compression cost is minimized, where the scheduling cost is denoted by the product of two vectors. Some optimal solution properties are presented, and it is showed that the problem under three variable processing time models is solved optimally in polynomial time \(O(n^3)\) O ( n 3 ) , where n is the number of tasks. In addition, two extensions are given for the general earliness-tardiness costs.