This paper describes a multi-range robust optimization approach applied to the problem of capacity investment under uncertainty. In multi-range robust optimization, an uncertain parameter is allowed to take values from more than one uncertainty range. We consider a number of possible projects with anticipated costs and cash flows, and an investment decision to be made under budget limitations. Uncertainty in parameter values -- in our case, the cost and net present values of each project -- could significantly impede the real-life viability of the suggested investment plan. We set up the multi-range robust optimization so that the possible values taken by the uncertain parameters match the three possible values of the cost or net present value distributions in the stochastic programming approach that we use as benchmark. While the stochastic programming approach suffers from tractability issues, the robust optimization approach solves the same capacity investment problem in seconds. We also show how to compute the project prioritization list to substantially decrease computation time.
Technical report, Lehigh University, Bethlehem, PA.