Data‐driven distributionally robust optimization of shale gas supply chains under uncertainty

Abstract

This article aims to leverage the big data in shale gas industry for better decision making in optimal design and operations of shale gas supply chains under uncertainty. We propose a two‐stage distributionally robust optimization model, where uncertainties associated with both the upstream shale well estimated ultimate recovery and downstream market demand are simultaneously considered. In this model, decisions are classified into first‐stage design decisions, which are related to drilling schedule, pipeline installment, and processing plant construction, as well as second‐stage operational decisions associated with shale gas production, processing, transportation, and distribution. A data‐driven approach is applied to construct the ambiguity set based on principal component analysis and first‐order deviation functions. By taking advantage of affine decision rules, a tractable mixed‐integer linear programming formulation can be obtained. The applicability of the proposed modeling framework is demonstrated through a small‐scale illustrative example and a case study of Marcellus shale gas supply chain. Comparisons with alternative optimization models, including the deterministic and stochastic programming counterparts, are investigated as well. © 2018 American Institute of Chemical Engineers AIChE J, 65: 947–963, 2019

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

“…However, characterizing such unknown disturbances as stochastic processes (with known probability distributions) is not an easy task, leading to the conundrum of uncertainty about uncertainty. As an emerging and promising optimization approach, distributionally robust optimization (DRO) gives a way to resolve the ambiguity of the uncertainty distribution, 9,10 and is widely used in many fields, including production planning and scheduling, 11,12 supply chain, 13,14 energy systems, [15][16][17] and finance. 18 Stochastic programming (SP), as another popular mathematical optimization approach, optimizes the expected value of the cost function, 19,20 based on the exact distribution of the disturbance and thus does not incorporate distribution ambiguity into the calculation.…”

“…As a short explanation, note that by setting the φ-dependent coefficient matrix Y to be zeros in Equation 23, it would reduce to the classic linear feedback law of u = h + Mw, meaning that any feasible solution (h, M, ε u , ε x ) to Equation 48 can be attained in Equation 47 by letting (h, M, Y, ε u , ε x ) = (h,M, 0, ε u , ε x ). By adopting this richer presentation, problem (P) is parameterized as a relaxed program in (47) compared with(48), which parameterizes the control law only in terms of the disturbance, as any feasible solution to the latter problem is still feasible to the former one,13 achieving at least equally optimal values. Therefore, thanks to the introduction of an auxiliary random vector φ, the decision variable relies on both the primary disturbance w and the introduced vector, enjoying a richer parameterization, and can be consequently less conservative than the classic affine disturbance prediction.Due to the RHC nature of MPC, it is important to guarantee that the optimization problem remain feasible at all times, as the evolution of the state trajectory is not admissible otherwise.…”

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

“…Additionally, the computational effectiveness of this data-driven DRO method was demonstrated via process network planning and batch production scheduling . Recently, a data-driven DRO model was developed for the optimal design and operations of shale gas supply chains to hedge against uncertainties associated with shale well estimated ultimate recovery and product demand [119]. However, the moment-based ambiguity set is not guaranteed to converge to the true probability distribution as the number of uncertainty data goes to infinity.…”

“…Data-driven stochastic programming has several salient merits over the conventional stochastic programming approach. However, there are few papers on its PSE applications in the existing literature [117,119]. As the trend of big data has fueled the increasing popularity of datadriven stochastic programming in many areas, DRO emerges as a new data-driven optimization paradigm which hedges against the worst-case distribution in an ambiguity set, and has various applications in power systems, such as unit commitment problems [125][126][127][128], and optimal power flow [129,130].…”

Waste high‐density polyethylene recycling process systems for mitigating plastic pollution through a sustainable design and synthesis paradigm

“…Recent works combine these two viewpoints to address environmental sustainability through fixed technologies when conducting techno‐economic analysis (TEA) and life cycle assessment (LCA) 22 . However, the lucrative pathway for the open‐loop recycling process of waste HDPE evaluated depends on the market condition 23 . To address this concern, it is important to investigate the sustainable design of waste HDPE recycling process systems in consideration of the economic performance and environmental impacts.…”