Single-machine scheduling with trade-off between number of tardy jobs and compression cost

We consider a single-machine scheduling problem in which the job processing times are controllable or compressible. The performance criteria are the compression cost and the number of tardy jobs. For the problem where no tardy jobs are allowed and the objective is to minimize the total compression cost, we present a strongly polynomial time algorithm. For the problem to construct the trade-off curve between the number of tardy jobs and the maximum compression cost, we present a polynomial time algorithm. Furthermore, we extend the problem to the case of discrete controllable processing times where the processing ∗This research was supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the MOE, China, and the National Natural Science Foundation of China (10271110). The third author was supported in part by The Hong Kong Polytechnic University under a grant from the ASD in China Business Services. †Email: [email protected] ‡Email: [email protected] §Corresponding author; email: [email protected] 1 This is the Pre-Published Version.