Convex programming for inverse scheduling problem with maximum lateness criterion

Abstract

This paper considers an inverse single machine scheduling problem, the forward version of which tries to minimize the maximum lateness (i.e., $L_{\max}$). In the forward version, with critical parameters such as due dates and processing times are certain and cannot be adjusted. While in this investigated inverse optimization problem, the due dates can be adjusted, and the goal of this problem is to find optimal adjusted due dates, with which the predefined schedule could be an optimal schedule. For this problem, we first analyse the property of the optimal solution when the due dates are certain. Then, with this property, we formulate a convex programming for the investigated problem, and devise a solution method accordingly. To the best of our knowledge, we are the first to provide solvable mathematical programming model for inverse scheduling problems. The validity of the mathematical model and the proposed solution method is demonstrated by a randomly generated instance.