A flexible system design approach for multi-facility capacity expansion problems with risk aversion

Abstract

This article studies a model for risk aversion when designing a flexible capacity expansion plan for a multi-facility system. In this setting, the decision maker can dynamically expand the capacity of each facility given observations of uncertain demand. We model this situation as a multi-stage stochastic programming problem, and we express risk aversion through the Conditional Value-at-Risk (CVaR) and a mean-CVaR objective. We optimize the multi-stage problem over a tractable family of if–then decision rules using a decomposition algorithm. This algorithm decomposes the stochastic program over scenarios and updates the solutions via the subgradients of the function of cumulative future costs. To illustrate the practical effectiveness of this method, we present a numerical study of a decentralized waste-to-energy system in Singapore. The simulation results show that the risk-averse model can improve the tail risk of investment losses by adjusting the weight factors of the mean-CVaR objective. The simulations also demonstrate that the proposed algorithm can converge to high-performance policies within a reasonable time, and that it is also more scalable than existing flexible design approaches.

Keywords:

• Capacity expansion problem
• system design
• real options
• risk aversion
• multi-stage stochastic programming
• decision rules

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 72001141, 71931007, 72031007], by the Shanghai Sailing Program [grant number 20YF1420200], and by the National Research Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program.

Notes on contributors

Sixiang Zhao

Dr. Sixiang Zhao is an assistant professor in the Sino-US Global Logistics Institute, Shanghai Jiao Tong University. He received his B.Eng. degree in industrial engineering from Hunan University, his M.Eng. degree in industrial engineering from Shanghai Jiao Tong University, and his Ph.D. degree in industrial systems engineering & management from the National University of Singapore. Prior to joining Shanghai Jiao Tong University, Dr. Zhao worked as a Senior Data Scientist at GrabTaxi Holdings Pte. Ltd. His research interests include optimization under uncertainty, real options analysis, and dynamic decision-making problems.

William B. Haskell

Dr. William B. Haskell received his B.S. mathematics and M.S. econometrics degrees from the University of Massachusetts Amherst in 2005 and 2006, respectively. He then obtained his M.S. operations research, M.A. mathematics, and Ph.D. operations research degrees from the University of California Berkeley in 2007, 2010, and 2011, respectively. He is currently an assistant professor in the supply chain and operations Management Area in the Krannert School of Management at Purdue University. Dr. Haskell’s research focus is on algorithms for convex optimization and dynamic programming, with an emphasis on risk-aware decision-making.

Michel-Alexandre Cardin

Dr. Michel-Alexandre Cardin is a senior lecturer (eq. associate professor) in computational aided engineering at the Dyson School of Design Engineering, Imperial College London, where he leads the Strategic Engineering Laboratory. His work focuses on the development and evaluation of new computational aided methodologies, digital processes, and algorithms to support the design of engineering systems, with applications in infrastructure and financial systems. Before joining Imperial College, Dr. Cardin worked as a Quantitative Researcher in the hedge fund industry, developing strategies for derivatives trading using machine learning. He also worked as an assistant professor at the National University of Singapore, where he served as principal investigator on international collaborations like Future Resilient Systems with ETH Zürich, and Singapore-MIT Alliance for Research and Technology. Dr. Cardin holds a PhD in engineering systems and a master of science in technology and policy from MIT, a master of applied science in aerospace engineering from the University of Toronto, Honors BSc in physics from McGill University in Canada, and graduate of the Space Science Program at the International Space University. He is currently serving as associate editor for the ASME Journal of Mechanical Design, and served on the editorial boards of the INCOSE Journal Systems Engineering and IEEE Transactions on Engineering Management.