Single machine scheduling with early and quadratic tardy penalties

This paper considers the problem of scheduling a single machine when the objective uses a penalty for each job that is equal to the earliness of the job plus the squared tardiness of the job. A timetabling algorithm is presented that inserts idle time into a sequence in order to minimize the objective considered. Optimal branch and bound algorithms are presented as well as efficient heuristic algorithms. The procedures are tested on randomly generated problems of varying numbers of jobs and due date tightness parameters. The results show that a branch and bound procedure can solve small and medium sized problems in a reasonable amount of time and that a simple descent procedure can quickly generate solutions that are close to optimal.