Making decisions when buffeted by uncertainty
“Uncertainty is the only certainty there is, and learning how to live with insecurity is the only security,” American mathematician John Allen Paulos wrote in his book A Mathematician Plays the Stock Market. Uncertainties abound everywhere, and come from myriad sources. We think data-driven tools can help professionals in any sector reach high-stakes decisions under the uncertainty that is rife throughout their domain.
Everyone knows how hard it is to make long-term forecasts due to lack of information; look at how natural gas prices can change dramatically. Short-term fluctuations also pose challenges; weather can shift at the drop of a hat because of events like wildfires and snowstorms, bringing confusion and sometimes havoc to the best laid plans.
Managing uncertainty is crucial for successful business operations. Industries with complicated supply chains have to consider potential disruptions to various parts of the chain. The interruptions can come from any number of random events, such as weather; geopolitical upheaval; or even the spread of a pandemic, as we have witnessed over the past three years.
Energy systems planning in particular requires considering the uncertainty of weather. For example, in planning power systems, you have to factor in unknowns regarding wind and solar output. Failure to consider that unpredictability can lead to power blackouts during extreme weather, which can result in serious disruptions in human affairs and billions of dollars in losses.
Traditional approaches to factoring in uncertainty when making plans fall woefully short. In the conventional method, operators design things like supply chain and energy systems with a scenario, typically developing a “deterministic” forecast, which focuses on fixed values and takes insufficient account of randomness.
Our approach of data-driven optimization can consider all the scenarios that could take place and include all of them in the optimization framework. For example, in designing power systems, you would like to take into account different rainy days and sunny days. Our framework optimizes the design of both energy systems and supply chains, hedging against uncertainties.
The framework has three distinct elements, or steps:
- Collect historical data to develop a forecast model. The model will be able to predict all the scenarios that could occur in the future and, critically, the probability of the occurrence of each scenario.
- Use these scenarios to construct a “scenario tree” that represents the totality of uncertainties.
- Develop a “stochastic programming” model that incorporates the scenario tree. “Stochastic” derives from the Greek word stokhastikos, which the Oxford English Dictionary translates as “to aim at a mark.” Stochastic programming models the probabilities of events occurring, and takes into account the random behaviors that characterize the real world.
Because the stochastic programming model includes all the scenarios that could occur — the entire range of probabilities — it can hedge against multiple uncertainties. Instead of optimizing for a single scenario, the model optimizes the expected value of all the scenarios simultaneously, assigning each a value that represents the probability it may occur. All these potential realizations of uncertainties are considered at the same time.
We work with a specially designed algorithm called a “decomposition algorithm.” The idea is to break down a large-scale optimization problem — like a supply chain or energy system — into multiple small problems and solve them in parallel. The primary challenges we face in our research are to develop algorithms that are scalable to problems of industrial relevance and to convince users of the values of the algorithms. To do the latter, we plan to develop tools that can make our algorithms more explainable — a task with which many are wrestling today.
Our goal is to create tools that can help decision makers in industry and in government agencies make choices that achieve desirable outcomes under differing circumstances and uncertainties. A mathematical framework with explainable tools can significantly reduce human intervention required to consider the huge amounts of data that characterize multiple uncertainties in what often are constrained, pressure-packed pockets of time — helping users to make the best decisions based on the most probable conditions and outcomes.
Can Li, PhD
Assistant Professor of Chemical Engineering
Davidson School of Chemical Engineering
Faculty Contributor, Center for Innovative and Strategic Transformation of Alkane Resources (CISTAR)
College of Engineering
Purdue University
