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**1 - 7**of**7**### An FPTAS for parallel machine scheduling under a grade of service provision to minimize makespan

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, 2008

"... service provision to minimize makespan ..."

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### An FPTAS for Uniform Parallel-Machine Scheduling Problem with Deteriorating Jobs and Rejection

"... Abstract. This paper studies uniform parallel-machine scheduling problem with deteriorating jobs and rejection. The processing time of each job is a linear nondecreasing function of its starting time. A job can be rejected by paying a penalty cost. The objective is to minimize the sum of the total l ..."

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Abstract. This paper studies uniform parallel-machine scheduling problem with deteriorating jobs and rejection. The processing time of each job is a linear nondecreasing function of its starting time. A job can be rejected by paying a penalty cost. The objective is to minimize the sum of the total load of the accepted jobs on all machines and the total rejection penalties of the rejected jobs. We propose a fully polynomial-time approximation scheme (FPTAS) for this problem.

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"... parallel-machine scheduling with deteriorating jobs and rejection ..."

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"... Contents lists available at GrowingScience International Journal of Industrial Engineering Computations ..."

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Contents lists available at GrowingScience International Journal of Industrial Engineering Computations

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"... Abstract This paper considers the single machine scheduling problem with precedence constraints and deteriorating jobs and a mathematical model based on binary integer programming (BIP) is developed. Since the precedence constraints exist, a job cannot start before completion of its all predecessors ..."

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Abstract This paper considers the single machine scheduling problem with precedence constraints and deteriorating jobs and a mathematical model based on binary integer programming (BIP) is developed. Since the precedence constraints exist, a job cannot start before completion of its all predecessors. The proposed model consists of two steps: in the first step, the earliest starting time of each job is computed; then the results are used in the second step in which an optimal sequence between jobs is determined with the aim of minimizing the total completion time. Finally, a numerical example is presented and solved using optimization software LINGO 8.0.

### An FPTAS for Uniform Machine Scheduling to Minimize The Total Completion Time and The Total Rejection Penalty

"... Abstract. In this paper, we study the NP-hard problem of scheduling n jobs on m uniform machines to minimize the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. Each job's processing time is a simple linear increasing function of its starting tim ..."

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Abstract. In this paper, we study the NP-hard problem of scheduling n jobs on m uniform machines to minimize the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. Each job's processing time is a simple linear increasing function of its starting time. A job can be rejected by paying a penalty cost. We propose a fully polynomial-time approximation scheme (FPTAS) to show the problem is NP-hard in the ordinary sense.