469700 Combined Use of the Sample Average Approximation and the Analytic Hierarchy Process to Support the Design of Chemical Processes Under Uncertainty
Published research in the process systems engineering has addressed both flexible process design and design under uncertainty. The former methods rely on flexibility indices that are difficult to implement in practice when dealing with complex systems and do not consider probabilistic information, while the latter may lead to large-scale stochastic programming models containing many scenarios and leading to large CPU times. In addition, the overwhelming majority of methods within the second group tend to maximize the expected value of the cost/profit distribution, thereby providing no control on the potential economic outcomes in every plausible scenario. To overcome these limitations, this paper introduces a novel methodology for the synthesis of chemical processes under uncertainty that combines the sample average approximation  and the analytic hierarchy process . The approach presented comprises four main steps: i) uncertainty characterisation and generation of scenarios using sampling methods ; ii) process synthesis based on the sample average approximation algorithm to generate feasible potential designs, iii) evaluation of each design in the uncertain parameters space using both feasibility and probabilistic metrics to assess the performance of the designs; and iv) application of the analytic hierarchy process to identify the process design(s) that best reflects the decision-makers’ preferences.
The capabilities of the proposed methodology are illustrated through its application to two problems: the design of heat exchanger networks and the optimisation of a crude oil distillation system of a petroleum refinery, considering uncertainties in stream inlet conditions. The former is originally formulated as a monolithic equation-oriented mixed-integer nonlinear programming problem, while the latter is implemented in a simulation-optimisation environment that combines rigorous model in Aspen HYSYS with an external optimiser coded in MatLab. The results obtained demonstrate that the proposed methodology is capable of identifying solutions that are flexible and operable under a wide range of operating conditions, and which shows better overall expected performance than the nominal design. One major advantage of the proposed method is that, compared to approaches based on flexibility indices, it can be easily implemented in process simulators without the need to write the mass, energy balances and thermodynamic equations in an explicit manner (a step required to derive the KKT conditions of the problem and determine the flexibility index).
 Kleywegt, A. J., Shapiro, A. & Homem-De-Mello, T. (2001). The sample average approximation method for stochastic discrete optimization. Siam Journal on Optimization, 12(2), 479-502.
 Saaty, T. L. (1990). How to Make a Decision - the Analytic Hierarchy Process. European Journal of Operational Research, 48(1), 9-26.
 Diwekar, U. M. & Kalagnanam, J. R. (1997). Efficient sampling technique for optimization under uncertainty. Aiche Journal, 43(2), 440-447.