Approximation Algorithms for Minimizing Sum of Flow Time on a Single Machine with Release Dates

This paper considers the scheduling problem of minimizing the sum of flowtime on single machine with release dates. It is well known that the problem is NP-Hard, therefore in order to solve the problem, two approximation algorithms (KSA1 and KSA2) were proposed. KSA1 and KSA2 algorithms were compared with the MPSW (selected from the literature) and the Branch and Bound (BB) method. All the four solution methods were evaluated on a set of randomly generated problems. Twenty problem sizes ranging from 3 to 100 jobs and fifty problem instances under each problem size were generated. A total of 1000 (50x20) problem instances were solved. Experimental results based on effectiveness show that the MPSW algorithm performs closest to the BB method and outperformed both the KSA1 and KSA2 algorithms for all the problem sizes considered. On the other hand, based on efficiency, the KSA1 and KSA2 algorithms outperformed both MPSW and BB methods.