Finding Admissible Bounds for Over-subscription Planning Problems

When given a plan by a satisficing planner, it is usually not intuitive as to how close it is to the optimal solution. However, real world planning problems often require some metric on which to optimize, especially when goals are soft and resource constraints are involved, as is the case in oversubscribed planning problems. Unfortunately, little effort is given to find how close any plan may be to an optimal solution value. We set out to answer this shortcoming by providing a way to encode a relaxed version of over-subscribed planning problems in an integer program (IP) formulation. The solution to this formulation gives an admissible bound on the optimal solution value and can be further relaxed by dropping its integer constraints for better scalability.