Inverse scheduling with controllable job parameters

Scheduling problems deal with how to sequence a list of jobs with the objective of minimizing some measurement of the job completion times. Inverse scheduling problems assume that a job sequence is given and the objective is to determine the minimal perturbation to the job parameters (e.g., processing times) so that the given sequence becomes optimal with respect to a pre-selected objective function. The objective of this paper is to study inverse scheduling problems. It will be shown that these problems can be formulated as linear programming (LP) problems even when, in some cases, the corresponding forward scheduling problems are not solvable in polynomial time. Several applications are discussed, including the generation of benchmark optimal solutions for NP-hard forward scheduling problems.