Application of The Overlapping Method to The Flow Shop Scheduling Problem to Minimize The Makespan

Abstract

This paper investigates a flow-shop scheduling policy that combines controlled overlapping (lot streaming) with setup-time reduction to minimize makespan. The approach is parameterized by an overlap factor () and the number of lots () and synchronizes the bottleneck and critical stages to prevent starvation and blocking. Using a 12-machine case with a daily demand of 1,200 units, we evaluate four scenarios: (i) baseline (no overlap), (ii) overlap only, (iii) overlap with lot streaming, and (iv) overlap with lot streaming plus setup reduction. Results show that the best configuration ( = 6 lots and  = 0.6) compresses the makespan from 1,304 min (baseline) to approximately 680 min; with setup-time reduction (Machine 2 standardized at 12 min), the makespan further decreases to about 420 min, enabling completion within a single working shift. Within the tested range  at , the best configuration is . Overlap alone yields 1,216.8 min (−6.7% vs. baseline). The procedure is implemented via deterministic Python simulation to ensure reproducibility. The findings provide a practical recipe for tuning () and setup policies in flow shops to achieve significant time compression under realistic operating constraints.