Analysis of single-machine scheduling problems with common due date

Abstract

This thesis considers four different cases of single machine deterministic scheduling problems with common due date. First, a non-preemptive scheduling problem is considered for dynamically arriving jobs with a given common due date to find the optimal schedule which minimizes the sum of earliness/tardiness and starting-time penalties. Second, a scheduling problem is considered for all jobs available at time zero with a given common due date to find the optimal schedule which minimizes the sum of earliness/tardiness and flow times (instead of starting-time penalty). Third, a scheduling problem is considered for all jobs available at time zero to find the optimal schedule (batching and sequencing) which minimizes mean flow time subject to no tardy jobs and restrictions on batch size. Finally, a scheduling problem is considered for all jobs available at time zero to find the optimal batching and sequencing which minimizes weighted mean flow time under restrictions on batch size. In each of the above cases, the optimal solution properties are characterized and then used in developing solution algorithms. In the first and second cases, it is assumed that any job splitting is not allowed and hence batching decision is not necessary. For those problems, the optimal schedule is characterized to form a V-shape type of sequencing, based upon which effective heuristic algorithms are suggested. In both the third and fourth cases, batching decision is additionally considered under the assumptions that the job splittings into smaller batches are allowed and each batch is restricted to have an integral size allowed within the given lower and upper bounds and also to have some batch setup time for process initiation. The optimal batching and sequencing are characterized to give the rule of processing the lager batch the earlier. This solution property is used to develop dynamic programming solution algorithms.