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 undes irable 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 deci sion, Also, lateness (or earliness) of one job may be more or less exp ensive than lateness (or earliness) of another job. In those situation s, different weights may be assigned to different jobs. Hence, the obj ective function to be minimized is the sum of weighted quadratic funct ions of job lateness. A similar problem has been attempted earlier whe re machine idle times are not acceptable. This paper relaxes this rest riction and allows for idle time immediately prior to starting the fir st job on the machine. It presents a branch-and-bound methodology for the problem.