System, Method, and Computer Program Product for Two-Stage Robust Optimization With Decision Dependent Uncertainty

A system, comprising:

• at least one processor configured to:
• generate a first-stage decision before determining one or more uncertain parameters of the first-stage decision;
• adjust a second-stage problem according to the one or more uncertain parameters, wherein the one or more uncertain parameters may be combined to represent a plurality of outcomes modeled as one or more possible scenarios in the second-stage problem, and the first-stage decision is optimized based on the one or more possible scenarios in the second-stage problem;
• generate a feasible region in the first-stage decision based on at least one possible scenario of the one or more possible scenarios in the second-stage problem, the feasible region forming a boundary for the first-stage decision;
• and
• provide a cutting set to narrow the feasible region of the first-stage decision to obtain an optimal solution that performs under a worst case scenario.

The system of 17, wherein the at least one processor is further configured to:

• determine the one or more uncertain parameters associated with the first-stage decision by solving a deterministic mixed integer linear program (“MILP”);
• determine a plurality of second-stage parameters by solving a set of MILPs, each MILP of the set of MILPs corresponding to at least one of the one or more possible scenarios in the second-stage problem, wherein an objective function of the two-stage RO formulation comprises a cost of the first-stage decision and a value of the uncertain parameters of a worst-case scenario;
• and
• optimize a solution to the second-stage problem with decision-dependent uncertainty that minimizes a worst-case cost over all possible realizations of the uncertain parameters.

A computer program product comprising at least one non-transitory computer-readable medium including one or more instructions that, when executed by at least one processor, cause at least one processor to:

• generate a first-stage decision before determining one or more uncertain parameters of the first-stage decision;
• adjust a second-stage problem according to the one or more uncertain parameters, wherein the one or more uncertain parameters may be combined to represent a plurality of outcomes modeled as one or more possible scenarios in the second-stage problem, and the first-stage decision is optimized based on the one or more possible scenarios in the second-stage problem;
• generate a feasible region in the first-stage decision based on at least one possible scenario of the one or more possible scenarios in the second-stage problem, the feasible region forming a boundary for the first-stage decision;
• and
• provide a cutting set to narrow the feasible region of the first-stage decision to obtain an optimal solution that performs under a worst case scenario.