Improving consistency in hierarchical tactical and operational planning using Robust Optimization

Many companies use optimization models to support their tactical planning production decisions. These tactical plans typically cover a horizon of several months. However, later on, when making daily or weekly operational decisions, inconsistencies may appear between the tactical and operational plans, due to various uncertainties and data aggregation. At the tactical level, planners attempt to take into account the potential cost of those inconsistencies, but that is not always easy. A 2-stage model under uncertainty might provide a solution, through the recourse, but this leads to harder problems and requires distributional information that is not always available. Hence, in our work we propose to use the methodology of Robust Optimization, based on uncertainty sets, at the tactical level to improve the consistency between the two planning problems. We illustrate our approach on a specific problem for sawmill operations in the forest industry, where at the tactical level the supply of logs is decided. At the operational level, the sawmill must plan the detailed operations, including which cutting patterns to use, based on the actual supply of logs, which might differ from what was initially planned. We show computational results on data from an actual company and provide some specific estimates of probabilities of consistency, for two approaches: ellipsoidal and polyhedral, or budgeted, uncertainty. Our results indicate that Robust Optimization is a viable methodology to improve consistency and it could be relevant in other problems where consistency between the tactical plan and the subsequent operational decisions is desirable.