Effective robust formulation of right-hand-side budget of uncertainty with application to power dispatch optimization Milad Dehghani Filabadi a,∗ , Houra Mahmoudzadeh a a Department of Management Sciences, University of Waterloo, Waterloo, ON, Canada Abstract Robust optimization (RO) tackles data uncertainty by finding an optimal solution that is protected against any realization of the uncertain parameter(s). To control the level of conservatism in RO, one can use set a budget of uncertainty that limits the amount of uncertainty to be considered in the model. However, in specific problems where the uncertain parameter appears in the right-hand side of a constraint, this approach may produce non- intuitive results. In this paper, we present cases where robust optimal solutions may be insensitive to an increase in the budget of uncertainty by more than a certain threshold. We refer to this phenomenon as “ineffective budgets” and propose a new tractable two-stage robust optimization approach that reformulates the conventional setting in order to account for the budget of uncertainty in problems with RHS uncertainty. In the first stage, we identify the subset of the uncertainty set which would result in an ineffective budget. In the second stage, we provide a reformulation that eliminates the ineffective part of the budget of uncertainty, and hence, provides meaningful insights on the trade-off between robustness and economy in such problems. We motivate the proposed model and demonstrate its applicability using a power dispatch optimization problem with wind power uncertainty. The numerical results confirm the merits of the proposed approach from various aspects such as the effectiveness of the budget of uncertainty, robustness, and cost efficiency and reliability against randomly-simulated scenarios. Keywords: Robust optimization, Budget of uncertainty, Right-hand-side uncertainty, Effective budget, Wind uncertainty, Power dispatch optimization * Corresponding author Email addresses: m23dehgh@uwaterloo.ca (Milad Dehghani Filabadi), houra.mahmoudzadeh@uwaterloo.ca (Houra Mahmoudzadeh) arXiv:1907.02917v3 [math.OC] 27 Dec 2019