Protecting a Sensitive Queue from Arrival Variability

Minimizing item waiting time between stages is a general focus of operations research, and of particular concern for certain industries. We propose a two-stage production system where, to minimize the waiting time before stage 2, we focus on spreading the completion times of the stage 1 machines across the available interval. We contrast this objective with a similar problem defined in a healthcare context, but that has an assumption of fixed assignment. We obtain insights in the added value that free assignment can provide, by comparing the solutions of a local search method for assignment, with those of a reference case where assignment is fixed. Computational results show that this added value is highest in cases where task means differ insufficiently to be ordered effectively, and where task distributions have low variance. For the discussed instances, significant reductions in item waiting times can be achieved while making minimal concessions on expected makespan.