(581c) An Optimization-Based Framework for Process Planning Under Uncertainty with Risk Management

Authors: 
Chachuat, B., Imperial College London
Khor, C. S., Imperial College London
Giarola, S., Università di Padova


The process systems engineering (PSE) community has been instrumental in carrying out a key role in extending the systems engineering boundaries from a sole focus on process systems to the incorporation of important business issues. The latter involves the inevitable consideration for uncertainty in decision-making that gives rise to a need for risk management in enhancing the robustness of process planning activities under numerous possible operating scenarios. In current challenging and volatile political and economic environment, the process industry is exposed to a high degree of uncertainty that renders the production planning task to be a risky and complex optimization problem that typically requires high computational expense.

This work proposes a computationally-tractable, optimization-based framework for risk management in mid-term process planning under uncertainty. In general, the two major methodologies for addressing optimization problems under uncertainty are recourse-based two-stage or multi-stage stochastic programming [1,2] and robust optimization [3,4,5]. In this work, the latter is employed with a scenario-based approach adopted to represent uncertainties in the stochastic parameters. The problem is formulated as a recourse-based two-stage stochastic program that incorporates a mean-risk structure in the objective function. Two risk measures, with origins in the insurance and finance industries, are considered, namely Value-at-Risk (VaR) [6] and Conditional Value-at-Risk (CVaR) [7]. We account for uncertainty in prices of crude oil and commercial products, market demands of products, and production yields. However, since a large number of scenarios are often required to capture the stochasticity of the problem, the model suffers from a curse of dimensionality since the model size scales exponentially with the number of scenarios and the uncertain parameters. To circumvent this problem, we propose a framework with relatively low computational burden that involves the following two major steps. First, a linear programming (LP) approximation of the risk-inclined version of the planning model is solved for a number of randomly generated scenarios. Subsequently, the VaR parameters of the model are simulated and incorporated into an LP approximation of the risk-averse version of the planning model, which is a mean-CVaR stochastic program [8].

The proposed approach is illustrated through a petroleum refinery planning case study to demonstrate how solutions with relatively affordable computational expense can be attained in a risk-averse model in the face of uncertainty.

Bibliography

1.&nbsp&nbsp
Birge, J. R., and F. Louveaux (1997). Introduction to Stochastic Programming. New York: Springer-Verlag.

2.&nbsp&nbsp
Kall, P., and S. W. Wallace (1994). Stochastic Programming. New York: John Wiley & Sons.

3.&nbsp&nbsp
Ben-Tal, A., and A. Nemirovski (1998). Robust convex optimization. Mathematics of Operations Research 23(4):769-805.

4.&nbsp&nbsp
Ben-Tal, A., and A. Nemirovski (1999). Robust solutions of uncertain linear programs. Operations Research Letters 25(1):1-13.

5.&nbsp&nbsp
El Ghaoui, L., F. Oustry, and H. Lebret (1998). Robust solutions to uncertain semidefinite programs. SIAM Journal on Optimization 9(1):33-52.

6.&nbsp&nbsp
Tsang, K. H., N. J. Samsatli, and N. Shah (2007). Capacity investment planning for multiple vaccines under uncertainty: 2. Financial risk analysis. Food and Bioproducts Processing 85(C2):129-140.

7.&nbsp&nbsp
Verderame, P. M. and C. A. Floudas (2010). Operational planning of large-scale industrial batch plants under demand due date and amount uncertainty: II. Conditional Value-at-Risk framework. Industrial & Engineering Chemistry Research 49(1):260-275.

8.&nbsp&nbsp
Rockafellar, R. T. and S. Uryasev (2000). Optimization of conditional value-at-risk. Journal of Risk 2(3):21-41.