Invited Session Mon.1.MA 313

Monday, 10:30 - 12:00 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Optimization and equilibrium models in energy systems


Chair: Jong-Shi Pang



Monday, 10:30 - 10:55 h, Room: MA 313, Talk 1

Steven Adam Gabriel
A new method for MPECs with a natural gas application

Coauthor: Sauleh Siddiqui


We present a new method for solving MPECs based on SOS1 variables and a reformulation of the complementarity terms. We show two forms of the transformed problem: one using SOS1 variables and the other a penalty term. We present some theoretical results as well as numerical tests on a small energy production problem and a large-scale one for natural gas.



Monday, 11:00 - 11:25 h, Room: MA 313, Talk 2

Yueyue Fan
A stochastic variational inequality model for estimating traffic demand based on random link flow observations

Coauthor: Roger Wets


In this talk, we will discuss a problem of estimating travel demand of a network based on observations of link flow. First, we will show how the estimation problem can be formulated as a stochastic programming problem. The objective is to minimize the expected estimation error, subjected to physical and behavior assumptions of network flow. Next, we will extend the estimation problem to a sensor resource allocation problem, in which the goal is to identify the best sensor deployment strategy to maximize the benefit of information gained from the sensors. The design of numerical solution algorithms will be also discussed. The proposed modeling framework demonstrates a clear linkage between statistical estimation and optimization. From the engineering perspective, this work has the potential to improve the utilization of information technologies.



Monday, 11:30 - 11:55 h, Room: MA 313, Talk 3

Yun Bai
Biofuel supply chain design under competitive agricultural land use and feedstock market equilibrium

Coauthors: Yanfeng Ouyang, Jong-Shi Pang


The rapid expansion of the U.S. biofuel industry diverts a large amount of agricultural crops as energy feedstocks, and in turn affects farm land allocation, food market equilibrium, and agricultural economy. We present game-theoretic models that incorporate farmers' decisions on land use and market choice into the biofuel manufacturers' supply chain design problem (i.e., number and locations of biorefineries, resource procurement prices). A noncooperative bi-level Stackelberg game model and a cooperative game model are developed respectively to address possible business partnership scenarios between feedstock suppliers and biofuel manufacturers. Spatial market equilibrium is utilized to model crop supply and demand and the associated market price variations. We transform the bilevel model into a mixed integer quadratic program, and explore adaptive implementation of linear program relaxation and Lagrangian relaxation. The proposed methodology is illustrated using an empirical case study of the Illinois State, and the computation results reveal interesting insights into optimal land use strategies and supply chain design for the emerging "biofuel economy.''


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