(269e) A Robust Method for Process Design Under Uncertainty

Process design is traditionally formulated as an optimization problem with an objective function and constraints with deterministic data. This makes it amenable to classical mathematical techniques for solving such problems. With uncertainty in the data, the resulting changes in form of the constraints and objective functions generally require new solution approaches which motivate current research in optimization today.

Robust optimization is a relatively new product of that field of research with the goal to minimize the worst-case performance of a given system under all possible realizations of the driving uncertainties. In its traditional implementation, constraints of the problem are assumed to be hard i.e. no violations of the constraints are to be tolerated [1]. This formulation is attractive primarily in that it offers deterministic guarantees in the performance of the system. However it suffers from two major limitations: first it offers solutions that tend to be too conservative in general for the elimination of risk it provides; second, the reformulation leads to an increase in the structural complexity of the base problem of the system under consideration [2].

A modified robust approach has been developed which addresses those limitations [3]. First, it provides for less conservative solutions by allowing for the probabilistic violation of the constraints ? the degree of violation being in the control of the decision maker. Secondly, the reformulation of the problem ensures that under modest conditions for the uncertainty sets, the robust reformulation remains in a tractable class of problems.

In this presentation, we describe this new approach in greater detail and demonstrate its applicability to process design by looking at an example of the optimal sizing of a chemical reactor with uncertain reaction kinetics, raw material and product prices. Furthermore, we compare the resulting sizing decisions to those from other approaches to process design under uncertainty ? chance-constrained optimization, stochastic optimization and dynamic programming ? and illustrate the superiority of the new approach.

References

[1]. Ben-Tal, A., Ghaoui, L. E., and Nemirovskii, A., ?Robust Optimization?, Princeton University Press (2009), pp 1-25

[2]. Johnson, M.P, Norman, B., and Secomandi, N., (eds) ?Tutorials in Operations Research? , INFORMS (2006), pp 95-122

[3]. Bertsimas, D., and Sim, M. ?The Price of Robustness?, Operations Research, Vol. 52, No. 1. (2004) pp 35-53