Some Properties of Optimal Schedule of Jobs with a Common Due Date

Kanet (Naval Research Logistics Quarters, 1981) considered the problem of minimizing the average deviation of job completion times above a common due date. Under the condition that the common due date exceeds the makespan of the job set, he obtained a procedure SCHED which yields optimal sequence for the problem. In this paper, we consider the general problem without any condition and some general properties and in particular the V – shape of optimal schedule is proved. It is also shown that the SCHED algorithm of Kanet gives optimal sequence under less restrictive and a more practical condition on d. A few special cases including the complete solution for n=3 jobs are also given.