An Approach to Flexible-Robust Optimization of Large-Scale Systems

Though Robust Optimization has proven useful in solving many design problems with uncertainties, it is not suitable for certain problems which have sequential options in the decision making process. In this work, an integration of a Real Option model with the Robust Optimization technique is presented. This approach aims to eliminate the shortcomings of robust optimization for sequential decision making problems. We provide an example of applying this new integrated model to the operational control of a single reservoir of the Oregon-Washington Columbia River system by optimizing the flexibility of the system. Flexibility for an engineering system is the ease with which the system can respond to uncertainty in a manner to sustain or increase its value delivery through decision-making. In this paper, we define flexibility as the amount of water left in the storage reservoir to produce electricity after meeting demand. Real Option analysis is an economic tool which helps to value the multiple courses of actions in a decision: that is to either sell the flexibility or hold it for future use based upon the future value of flexibility. Selling flexibility causes one to lose some future value because one may be forced to repurchase that flexibility from the market at higher prices later due to shortages; Real Options analysis values future purchases to support decision-making. Robust optimization focuses on for selling the flexibility in a daily market and gives an optimal result by maximizing net revenue, considering all the physical and operational constraints of the reservoir to avoid floods or other environmental calamities. Net revenue is defined as cost of selling and cost of future purchase of the flexibility. We provide an optimization result of 27 random inflow scenarios which gives high, medium and low flexibility to allocate using the integrated model. We compare the optimal solutions given by the integrated model with that given by robust optimization. The integrated real option-robust optimization model improves the revenue from allocating flexibility as much as 40 percent over the robust optimization result.