Re-planning with Minimal Perturbation

Mixed Integer Programming (MIP) models are known to be sensitive to slight changes. In this study, we measure the perturbation to a production plan that occurs when re-planning is carried-on due to new orders arrival. Perturbation level is measured using well known metrics: (1) the Hamming distance, (2) the edit distance, and (3) the Damerau-Levenshtein distance. We propose three alternative formulations of the MIP model that allows for the integration of these metrics directly into the objective function. By simulating arrival of new orders for a lumber finishing mill, we show how these new re-planning models reduce the perturbation and outperforms the approach of using the original planning model.