A common due-date assignment problem with job rejection on parallel uniform machines

We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent asymmetric earliness tardiness unit costs. scheduler may process only subset of the jobs, i.e. option job-rejection is allowed. objective function consists three cost components: total earliness-tardiness all scheduled due-date, rejection cost. For given number rejected reduced non-standard linear problem. Consequently, optimal solution shown be obtained in polynomial time jobs. case (possibly restrictive) extension setting more than machines, special cases, also discussed.