Decision rule-based method for flexible multi-facility capacity expansion problem

ABSTRACT

Strategic capacity planning for multiple-facility systems with flexible designs is an important topic in the area of capacity expansion problems with random demands. The difficulties of this problem lie in the multidimensional nature of its random variables and action space. For a single-facility problem, the decision rule method has been shown to be efficient in deriving desirable solutions, but for a Multiple-facility Capacity Expansion Problem (MCEP), it has not been well studied. This article designs a novel decision rule–based method for the solution of an MCEP with multiple options, discrete capacity, and a concave capacity expansion cost. An if–then decision rule is designed and the original multi-stage problem is thus transformed into a master problem and a multi-period sub-problem. As the sub-problem contains non-binding constraints, we combine a stochastic approximation algorithm with a branch-and-cut technique so that the sub-problem can be further decomposed across scenarios and be solved efficiently. The proposed decision rule–based method is also extended to solving the MCEP with fixed costs. Numerical studies in this article illustrate that the proposed method affords not only improved performance relative to an inflexible design taken as benchmark but also time savings relative to approximate dynamic programming analysis.

KEYWORDS:

• Capacity expansion problem
• multi-facility system
• flexibility, real options
• stochastic programming, decision rule

Notes

1 Throughout this article, when referring to uncertainty, we mean that the exogenous/endogenous variables of the system can be modeled as random variables.

2 Non-anticipativity means that the decisions made at stage t depend on the information available up to time t but not on the results of future observations (Shapiro et al., 2009).

3 Because of the capacity limits, the expanded amount should be piecewise linear with respect to the uncertainties and control parameters.

Additional information

Funding

This research/project is supported by the National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme.

Notes on contributors

Sixiang Zhao

Sixiang Zhao is a Ph.D. candidate in the Department of Industrial Systems Engineering and Management at the National University of Singapore. He received his B.Eng. degree in industrial engineering (2012) from Hunan University and his M.Eng. degree in industrial engineering (2015) from Shanghai Jiao Tong University. His current research interests include optimization under uncertainty, flexibility, and real options analysis.

William Benjamin Haskell

William B. Haskell received his B.S. degree in mathematics and M.S. degree in econometrics from the University of Massachusetts Amherst in 2006 and his Ph.D. degree in operations research from the University of California Berkeley in 2011. Currently, he is an assistant professor in the Department of Industrial Systems Engineering and Management at the National University of Singapore. His research interests include convex optimization, risk-aware decision making, and dynamic programming.

Michel-Alexandre Cardin

Michel-Alexandre Cardin is an assistant professor in the Department of Industrial Systems Engineering and Management at the National University of Singapore and Lead of the Strategic Engineering Laboratory. He is a research affiliate at the Massachusetts Institute of Technology and principal investigator at the Singapore-ETH Centre Future Resilient Systems project and has led several projects at the Singapore-MIT Alliance for Research and Technology. His research interests include development, empirical evaluation, and applications of novel methodologies to design and architect engineering systems for uncertainty and flexibility, also known as real options. Applications focus on infrastructure systems in domains such as aerospace, defense, energy, real estate, oil and gas, transportation, and water management. He is an associate editor of the INCOSE Journal Systems Engineering, a member of the Editorial Review Board for IEEE Transactions on Engineering Management, and founding chairman of the organizing committee for the conference on Complex Systems Design and Management Asia. He received a bachelor's (Hons.) degree in physics from McGill University, a master of applied science degree in aerospace science and engineering from the University of Toronto, a master's degree in technology and policy, as well as a Ph.D. in engineering systems from MIT. He is also a graduate from the space science program at the International Space University.