Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

We study distributionally robust chance constrained programs (DRCCPs)  with individual chance constraints and random right-hand sides. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. We consider … Read more

Decision Rule Approaches for Pessimistic Bilevel Linear Programs under Moment Ambiguity with Facility Location Applications

We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds a continuous wait-and-see decision after observing the leader’s action and revelation of uncertainty. Only the information of the mean, covariance, and support is known. We formulate the problem as … Read more

Building Load Control using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. However, the time-varying PV generation is not perfectly known when the system operator decides the HVAC control schedules. To consider the unknown uncertain PV generation, in this paper, we formulate a distributionally robust … Read more

Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satis ed probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. … Read more

Integer Programming Approaches for Appointment Scheduling with Random No-shows and Service Durations

We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional … Read more