Optimization of multi-scale decision-oriented dynamic systems and distributed computing

Abstract

In this dissertation, a stochastic programming model is presented for multi-scale decision-oriented dynamic systems (DODS) which are discrete-time systems in which decisions are made according to alternative discrete-time sequences which depend upon the organizational layer within a hierarchical system. A multi-scale DODS consists of multiple modules, each of which makes decisions on a time-scale that matches their specific task. For instance, in a large production planning system, the aggregate planning module may make decisions on a quarterly basis, whereas, weekly, and daily planning may use short-term scheduling models. In order to avoid mismatches between these schedules, it is important to integrate the short-term and long-term models. In studying models that accommodate multiple time-scales, one of the challenges that must be overcome is the incorporation of uncertainty. For instance, aggregate production planning is carried out several months prior to obtaining accurate demand estimates. In order to make decisions that are cognizant of uncertainty, we propose a stochastic programming model for the multi-scale DODS. Furthermore, we propose a modular algorithm motivated by the column generation decomposition strategy. The convergence of this modular algorithm is also demonstrated. Our experimental results demonstrate that the modular algorithm is robust in solving large-scale multi-scale DODS problems under uncertainty. Another main issue addressed in this dissertation is the application of the above modeling method and solution technique to decision aids for scheduling and hedging in a deregulated electricity market (DASH). The DASH model for power portfolio optimization provides a tool which helps decision-makers coordinate production decisions with opportunities in the wholesale power market. The methodology is based on a multi-scale DODS. This model selects portfolio positions for electricity and fuel forwards, while remaining cognizant of spot market prices, and generation costs. When compared with a commonly used fixed-mix policy, our experiments demonstrate that the DASH model provides significant advantages over fixed-mix policies. Finally, a multi-level distributed computing system is designed in a manner that implements the nested column generation decomposition approach for multi-scale decision-oriented dynamic systems based on a nested column generation decomposition approach. The implementation of a three-level distributed computing system is discussed in detail. The computational experiments are based on a large-scale real-world problem arising in power portfolio optimization. The deterministic equivalent LP for this instance with 200 scenarios has over one million constraints. Our computational results illustrate the effectiveness of this distributed computing approach.