Minimizing a weighted quadratic function of job lateness in the single machine system

In many real world environments, early completion of a job is as undesirable as is late completion of the job. In such cases, minimizing the sum of squares of lateness of all the jobs may be an appropriate decision. Also, lateness (or earliness) of one job may be more or less expensive then lateness (or earliness) of another job. In those situations, different weights may be assigned to different jobs. Hence, the objective function to be minimized is the sum of weighted quadratic functions of mob lateness. A similar problem has been attempted earlier where machine idle times are not acceptable. This paper relaxes this restriction and allows for idle time immediately prior to starting the first job on the machine. It presents a branch-and-bound methodology for the problem.