Staged alert systems have been successfully implemented to minimize the socioeconomic loss while avoiding overwhelming the healthcare system. Optimizing the staged alert system parameters can be considered a challenging two-stage stochastic mixed-integer programming with a discontinuous recourse function. Traditional simulation-based optimization techniques assume continuity and smoothness within objective functions, while other metaheuristics often lack any optimality guarantee. We propose to develop a novel approach that combines Gaussian process-based optimization via simulation techniques with a methodology specifically designed to handle the discontinuity. We prove local optimality results with a convergence guarantee and demonstrate the efficacy of our proposed method by optimizing the stage thresholds in a pandemic staged alert system.

We consider an important type of production planning problems where firms need to decide the production and inventory level for each item, and the transportation between plants during a planning horizon. The objective is to minimize the total costs including the transportation, inventory holding cost, and a penalty cost for unmet demand, under constraints of limited resource and flow balance. In practice, the scale of such problems can be huge for large enterprises with a complex network structure and millions of decision variables and constraints, potentially including integer variables, which is hard for commercial solvers such as Gurobi and CPLEX to directly solve. In this work, we present a solution method for a mixed-integer large-scale production planning problem. The method involves decomposition in terms of items, where the item-based planning subproblems can be solved in parallel. Moreover, we put the integer requirements into the production decision-making subproblem with only simple capacity constraints, which can be efficiently solved through dynamic programming. To measure the quality of the solutions generated in the process, we compute an upper bound feasible solution and a lower bound estimate based on the current solution at each iteration. Numerical experiments suggest that the algorithm can converge to a good solution with properly chosen starting point and penalty parameter. We also evaluate our method on the basis of real-world data provided by a leading global corporation in China providing information and communications technology (ICT) solutions.

To better handle real-time load and wind generation volatility in unit commitment, we present an enhancement to the computation of security-constrained unit commitment (SCUC) problem. More specifically, we propose a two-stage optimization model for SCUC, which aims to provide a risk-aware schedule for power generation. Our model features a data-driven uncertainty set based on principal component analysis, which accommodates both load and wind production volatility and captures locational correlation of uncertain data. To solve the model more efficiently, we develop a decomposition algorithm that can handle nonconvex subproblems. Our extensive experiments on NYISO dataset show that the risk-aware model protects the public from potential high costs caused by adverse circumstances.

The modern theory of risk measures copes with uncertainty by considering multiple probability measures. While it is often assumed that a reference probability measure exists, under which all relevant probability measures are absolutely continuous, there are examples where this assumption does not hold, such as certain distributional robust functionals. In this talk, we introduce a novel class of dynamic risk measures that do not rely on this assumption. We will discuss its convexity, coherence, and time consistency properties.