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• W4310157292 abstract "We consider two two-agent scheduling problems with deteriorating jobs and rejection. Two agents <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>A</mi> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>B</mi> </math> compete for the usage of a single machine. The actual processing time of job <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <msubsup> <mi>J</mi> <mi>j</mi> <mi>X</mi> </msubsup> </math> is <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <msubsup> <mi>p</mi> <mi>j</mi> <mi>X</mi> </msubsup> <mo>=</mo> <msubsup> <mi>b</mi> <mi>j</mi> <mi>X</mi> </msubsup> <mfenced open=( close=) separators=|> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>t</mi> </mrow> </mfenced> </math> , <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>X</mi> <mo>∈</mo> <mfenced open={ close=} separators=|> <mrow> <mi>A</mi> <mo>,</mo> <mi>B</mi> </mrow> </mfenced> </math> , where <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <msubsup> <mi>b</mi> <mi>j</mi> <mi>X</mi> </msubsup> </math> is the normal processing time of <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <msubsup> <mi>J</mi> <mi>j</mi> <mi>X</mi> </msubsup> </math> , <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mi>a</mi> <mo>≥</mo> <mn>0</mn> </math> , <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <mi>b</mi> <mo>≥</mo> <mn>0</mn> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mi>t</mi> </math> denotes the starting time of <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <msubsup> <mi>J</mi> <mi>j</mi> <mi>X</mi> </msubsup> </math> . A job is either rejected by paying a rejection penalty, or accepted and processed on the machine. The objective is to minimize the sum of the completion time of the accepted <math xmlns=http://www.w3.org/1998/Math/MathML id=M12> <mi>A</mi> </math> -jobs and total rejection penalty of the rejected <math xmlns=http://www.w3.org/1998/Math/MathML id=M13> <mi>A</mi> </math> -jobs subject to an upper bound on the sum of the given objective function <math xmlns=http://www.w3.org/1998/Math/MathML id=M14> <msup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msup> </math> of the accepted <math xmlns=http://www.w3.org/1998/Math/MathML id=M15> <mi>B</mi> </math> -jobs and total rejection penalty of the rejected <math xmlns=http://www.w3.org/1998/Math/MathML id=M16> <mi>B</mi> </math> -jobs, where <math xmlns=http://www.w3.org/1998/Math/MathML id=M17> <msup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msup> <mo>∈</mo> <mfenced open={ close=} separators=|> <mrow> <msubsup> <mrow> <mi>C</mi> </mrow> <mrow> <mi mathvariant=normal>max</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mo stretchy=false>∑</mo> <msubsup> <mi>C</mi> <mi>j</mi> <mi>B</mi> </msubsup> </mrow> </mfenced> </math> . We give dynamic programming algorithms for them, respectively. When <math xmlns=http://www.w3.org/1998/Math/MathML id=M18> <msup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msup> <mo>=</mo> <msubsup> <mrow> <mi>C</mi> </mrow> <mrow> <mi mathvariant=normal>max</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msubsup> </math> , we present a fully polynomial-time approximation scheme (FPTAS) for the case <math xmlns=http://www.w3.org/1998/Math/MathML id=M19> <mi>a</mi> <mo>=</mo> <mn>0</mn> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M20> <mi>b</mi> <mo>=</mo> <mn>1</mn> </math> . When <math xmlns=http://www.w3.org/1998/Math/MathML id=M21> <msup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msup> <mo>=</mo> <mo stretchy=false>∑</mo> <msubsup> <mi>C</mi> <mi>j</mi> <mi>B</mi> </msubsup> </math> , a fully polynomial-time approximation scheme is also presented." @default.
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• W4310157292 date "2022-11-28" @default.
• W4310157292 modified "2023-10-16" @default.
• W4310157292 title "Two-Agent Single Machine Scheduling with Deteriorating Jobs and Rejection" @default.
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