This paper compares risk-averse optimization methods to address the self-scheduling and market involvement of a virtual power plant (VPP). The decision-making problem of the VPP involves uncertainty in the wind speed and electricity price forecast. We focus on two methods: risk-averse two-stage stochastic programming (SP) and two-stage adaptive robust optimization (ARO). We investigate both methods concerning formulations, uncertainty and risk, decomposition algorithms, and their computational performance. To quantify the risk in SP, we use the conditional value at risk (CVaR) because it can resemble a worst-case measure, which naturally links to ARO. We use two efficient implementations of the decomposition algorithms for SP and ARO; we assess (1) the operational results regarding first-stage decision variables, estimate of expected profit, and estimate of the CVaR of the profit and (2) their performance taking into consideration different sample sizes and risk management parameters. The results show that similar first-stage solutions are obtained depending on the risk parameterizations used in each formulation. Computationally, we identified three cases: (1) SP with a sample of 500 elements is competitive with ARO; (2) SP performance degrades comparing to the first case and ARO fails to converge in four out of five risk parameters; (3) SP fails to converge, whereas ARO converges in three out of five risk parameters. Overall, these performance cases depend on the combined effect of deterministic and uncertain data and risk parameters. Summary of Contribution: The work presented in this manuscript is at the intersection of operations research and computer science, which are intrinsically related with the scope and mission of IJOC. From the operations research perspective, two methodologies for optimization under uncertainty are studied: risk-averse stochastic programming and adaptive robust optimization. These methodologies are illustrated using an energy scheduling problem. The study includes a comparison from the point of view of uncertainty modeling, formulations, decomposition methods, and analysis of solutions. From the computer science perspective, a careful implementation of decomposition methods using parallelization techniques and a sample average approximation methodology was done . A detailed comparison of the computational performance of both methods is performed. Finally, the conclusions allow establishing links between two alternative methodologies in operations research: stochastic programming and robust optimization.

We consider a significant problem that arises in the planning of many projects. Project companies often use outsourced providers that require capacity reservations that must be contracted before task durations are realized. We model these decisions for a company that, given partially characterized distributional information, assumes the worst-case distribution for task durations. Once task durations are realized, the project company makes decisions about fast tracking and outsourced crashing, to minimize the total capacity reservation, fast tracking, crashing, and makespan penalty costs. We model the company’s objective using the target-based measure of minimizing an underperformance riskiness index. We allow for correlation in task performance, and for piecewise linear costs of crashing and makespan penalties. An optimal solution of the discrete, nonlinear model is possible for small to medium size projects. We compare the performance of our model against the best available benchmarks from the robust optimization literature, and show that it provides lower risk and greater robustness to distributional information. Our work thus enables more effective risk minimization in projects, and provides insights about how to make more robust capacity reservation decisions. Summary of Contribution: This work studies a financially significant planning problem that arises in project management. Companies that face uncertainties in project execution may need to reserve capacity with outsourced providers. Given that decision, they further need to plan their operational decisions to protect against a bad outcome. We model and solve this problem via adjustable distributionally robust optimization. While this problem involves two-stage decision making, which is computationally challenging in general, we develop a computationally efficient algorithm to find the exact optimal solution for instances of practical size.

Natural-gas and power systems are increasingly interdependent due to the integration of an increasing number of combined cycle gas turbines in the power generation mix. However, natural gas and power systems are generally independently operated. This is the result of history and the fact that natural gas has not been important for electricity production until recently. Adopting a power system perspective, this article reviews in a tutorial manner models for the operations and long-term expansion planning of interdependent but independently operated natural-gas and power systems.

This paper deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of the origin-destination (OD)-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows, and related problems. A modified topological version of an existing algebraic method for solving observability problems is given. The method is based on a step-by-step procedure, allowing us to update the information once each item of information (OD-pair or link flow) becomes available. In particular, three different observability problems are stated and solved using the proposed methodology, which is illustrated by its application to the Nguyen-Dupuis network and compared with the algebraic version. The topological version is much faster, uses much less memory, and presents no rounding errors or zero test problems but identifies fewer observable flows.