Optimization techniques in coal markets: a global cost minimization and a multi-stage procurement strategy

Abstract

Thermal coal is a prominent resource from which electricity is produced. In recent years, the price of this widely used commodity has declined, largely due to increases in environmental regulations, incentives for renewable resources, and technological advances in the production of natural gas, which is a cleaner-burning alternative fuel. As such, coal markets have drastically changed. We develop optimization models to help understand the current climate on a global scale and to help a domestic utility reevaluate its forward purchase strategy given depressed coal prices. We first develop a global thermal coal optimization model that minimize the cost to ship coal from countries that are net exporters to those that are net importers, taking into account coal quality specifications and shipping constraints, such as port and vessel capacity. Using this model, we explore the global effects of price variability, changes in operation from large market players such as China and India, and the impact of the Panama Canal expansion. We next develop a methodology for determining an optimal purchase strategy for a U.S. utility; using historical observations, we build a regression model to forecast prices, then select representative scenarios to include in a multi-stage stochastic program that minimizes the expected value and conditional value-at-risk (CVaR) of coal procurement. We formulate a time-consistent nested CVaR minimization model, compare its performance to an expected CVaR model, and show that the expected CVaR model may be better suited to minimizing risk in a multi-stage setting. We conduct out-of-sample testing to assess our solution performance under new price realizations. Finally, we apply an expected CVaR model to determine a utility's procurement strategy and recommend a purchase plan for implementation that is expected to save the company $151 million over a five-year horizon.