Minimizing the Sum of Makespan and Maximum Tardiness on Single Machine with Release Dates

This paper considers the bicriteria scheduling problem of simultaneously minimizing makespan (Cmax) and maximum tardiness (Tmax) on a single machine with release dates. The problem is, by nature, NP-Hard. Therefore, one approximation algorithm (labeled as CTA1) was proposed for solving this problem. The CTA1 algorithm was compared with the Branch and Bounds (BB) procedure specifically implemented for this problem. The two criteria (makespan and maximum tardiness) were aggregated together into a linear composite objective function (LCOF). The performances of CTA1 and BB methods were evaluated based on effectiveness and efficiency. The two solution methods were tested on a set of 900 randomly generated single machine scheduling problems (problem sizes ranges from 10 to 500). Due to prohibitive long time, the BB procedure could not be applied to problems involving more than 100 jobs. Experimental results show that the CTA1 algorithm performed competitively (with respect to effectiveness) compared with the BB procedure when the number of jobs is less than 60. When the number of jobs exceeds 50, the BB outperformed (with respect to effectiveness) the CTA1 algorithm. However, the CTA1 outperformed (with respect to efficiency) the BB procedure for all the problem sizes considered.