A Robust Optimization Approach for the Multi-Period Strip Cutting Problem with Multi-Cutter Slitting Machines

Abstract

This paper studies a multi-period strip cutting problem motivated by the paper industry. The focus is on multi-cutter slitting machines, which allow the simultaneous production of items with different lengths and provide higher cutting flexibility compared to conventional single-cutter machines. We propose a pattern-based mixed-integer programming formulation to evaluate the benefits of multi-cutter machines and compare it with heuristic strategies and a single-cutter benchmark. To address demand uncertainty, we extend the model using robust optimization with budgeted uncertainty sets and derive a tractable reformulation. Computational experiments with real-world data show that multi-cutter machines can substantially reduce raw material usage costs compared to the single-cutter setting. Under demand uncertainty, the budgeted robust model provides lower realized costs and smaller variability than both deterministic and box-type robust models.