TY - JOUR
T1 - Minimizing a General Penalty Function on a Single Machine via Developing Approximation Algorithms and FPTASs
JF - IUST
JO - IUST
VL - 28
IS - 3
UR - http://ijiepr.iust.ac.ir/article-1-710-en.html
Y1 - 2017
SP - 0
EP - 0
KW Single machine scheduling
KW Tardy/Lost penalty
KW Dynamic programming
KW Approximation algorithm
KW FPTAS
N2 - 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.
M3
ER -