Patent ID: 7873530

Claim:
An apparatus, comprising: a calculator programmed to determine an optimal solution to a stochastic linear programming problem, or stochastic mixed-integer linear programming problem, with conditional value at risk (CVaR) constraints, as executed by a processor on said apparatus, said optimal solution being determined by generating a sequence of solutions that converge to said optimal solution; and a constraints module, as executed by said processor, to generate new constraints for a next iteration, wherein said optimal solution is determined using a sequence of steps as follows: a first solution x is provided as an initial estimate of said optimal solution; the CVaR value in each CVaR constraint is estimated by using a current solution x to estimate order statistics for each constraint; a linear program, or a mixed-integer linear program (if the problem is a stochastic mixed integer linear program) is constructed based on the estimated order statistics; said linear program or a mixed-integer linear program is solved; binding constraints are determined from a dual of said constraints and retained for a next iteration, or alternatively, all binding and non-binding constraints that have been added sequentially are retained across iterations.