Invited Session Mon.1.MA 144

Monday, 10:30 - 12:00 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

Optimization of physical systems under uncertainty


Chair: Mihai Anitescu



Monday, 10:30 - 10:55 h, Room: MA 144, Talk 1

Victor M. Zavala
Stochastic optimization: Impacts on electricity markets and operations

Coauthors: Mihai Anitescu, John Birge


In this talk, we discuss impacts of stochastic optimization on market clearing procedures and power plant operations. In particular, we demonstrate that stochastic optimization leads to more consistent prices that maximize social welfare, reduce variance of spot prices, and diversify generation. In addition, we demonstrate how stochastic optimization leads to large amounts of power can be saved in large base-load plants in the present of water constraints.



Monday, 11:00 - 11:25 h, Room: MA 144, Talk 2

Jim Luedtke
Branch-and-cut approaches for chance-constrained formulations of reliable network design problems

Coauthor: Yongjia Song


We study the design of reliably connected networks. Given a graph with arcs that may fail at random, the goal is to select a minimum cost set of arcs such that a path between nodes s and t exists with high probability. We model this problem as a chance-constrained stochastic integer program, and present two solution approaches. The first approach is based on a formulation that uses binary variables to determine if an s-t path exists in each arc failure scenario. We present a branch-and-cut decomposition algorithm to solve this formulation, based on inequalities derived from individual scenario graph cuts. The second approach uses an alternative formulation based on probabilistic s-t cuts, which is an extension of s-t cuts to graphs with random arc failures. Probabilistic s-t cut inequalities define the feasible region and can be separated efficiently at integer solutions, allowing this formulation to be solved by a branch-and-cut algorithm. Computational results will be presented that demonstrate that the approaches can solve large instances. We also show how our results can be applied to more general connectivity requirements.



Monday, 11:30 - 11:55 h, Room: MA 144, Talk 3

Bernardo K. Pagnoncelli
The optimal harvesting problem under risk aversion

Coauthor: Adriana Piazza


I will present a model for the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The problem is stated as a risk averse stochastic dynamic programming, with the conditional value-at-risk (CVaR) as a risk measure. Timber price is uncertain and two important cases are considered: geometric Brownian motion and a mean-reverting (Ornstein-Uhlenbeck) process. In both cases the problem is solved for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state. I will compare the results with the risk neutral framework and discuss the differences between the two cases. Finally I will show how to generalize the results to any coherent risk measure that is affine on the current price.


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