Single Machine Scheduling with Outsourcing Under Different Fill Rates or Quantity Discount Rates

Lingfa Lu, Liqi Zhang (), Jie Zhang () and Lili Zuo ()
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Lingfa Lu: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China
Liqi Zhang: College of Information and Management Science, Henan Agricultural University, Zhengzhou, Henan 450003, P. R. China
Jie Zhang: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China
Lili Zuo: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 01, 1-15

Abstract: In this paper, we consider two single machine scheduling problems with outsourcing under different fill rates or quantity discount rates. From the manufacturer point of view, to maintain a predefined high service level under limited production capacity, it is required that the number of outsourced jobs must belong to a given interval [a,b]. We call this model “scheduling with outsourcing under different fill rates”. Meanwhile, from the outsourcers point of view, in order to encourage more outsourcing actions from the manufacturer, the outsourcers might provide an attractive discount scheme. Here, we assume that all discount rates depend only on the quantity (number) of the outsourced jobs. That is, the actual outsourcing cost equals to the original outsourcing cost multiplied by the corresponding discount rate. This model is called “scheduling with outsourcing under different quantity discount rates”. The objective is to minimize the sum of the makespan of the processed jobs and the (actual) outsourcing costs of the outsourced jobs. For the above two problems, some optimal algorithms, approximation algorithms and approximation schemes are proposed.

Keywords: Scheduling with outsourcing; fill rates; discount rates; approximation algorithm; FPTAS (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0217595919500337

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