Volume 28, Issue 3 (IJIEPR 2017)                   IJIEPR 2017, 28(3): 221-240 | Back to browse issues page

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Kianfar K, Moslehi G. Minimizing a General Penalty Function on a Single Machine via Developing Approximation Algorithms and FPTASs. IJIEPR. 2017; 28 (3) :221-240
URL: http://ijiepr.iust.ac.ir/article-1-710-en.html
1- Faculty of Engineering, University of Isfahan, 81746-73441, Isfahan, Iran , k.kianfar@eng.ui.ac.ir
2- Department of Industrial and Systems Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran
Abstract:   (2452 Views)

This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with rejection and hence, the results of this study are applicable for them. Initially, we present two approximation algorithms. Then, two special cases of the main problem are considered. In the first case, all jobs have the same tardiness weights where an FPTAS is developed using the technique of “structuring the execution of an algorithm". The second special case occurs when none of the jobs can be early. For this case, a 2-approximation algorithm is developed as well as a dynamic programming algorithm which is converted to an FPTAS.

Full-Text [PDF 655 kb]   (630 Downloads)    
Type of Study: Research | Subject: Operations Research
Received: 2017/01/18 | Accepted: 2017/07/16 | Published: 2017/07/16

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