Modeling Single Machine Preemptive Scheduling to Minimize the Cost of Tardiness and Overtime

Abstract

We propose two alternative mathematical modeling approaches for the problem of finding a preemptive schedule that minimizes the total cost of tardiness for a set of jobs on a single processor under variable workload requirements. The first model follows from the conventional scheduling approach and the second borrows from the aggregate planning paradigm. We demonstrate with numerical experimentation and analytical methods that the latter modeling approach is more efficient and computes better lower bounds than the conventional model. We expand the study by analyzing special cases where overtime capacity is allowed and cases with equal work requirements where the advantages of the proposed aggregate model are fully exploded; finally, we validate the experimental results by applying the aggregate modeling paradigm to a real industry case where we compute well under four seconds the optimal overhaul schedule for 82 jobs under four different customers. Overall findings show that the proposed aggregate model is an effective tool for generating optimal or near-optimal schedules reasonably quick for real life applications.