Convex programming model for inverse scheduling with adjustable release times

This paper proposes an inverse scheduling problem in a single machine system. The maximum completion time is concerned, the release times are adjustable parameters, and the processing sequence of all jobs is known and fixed. The aim of this inverse scheduling problem is to obtain optimal adjusted release times, which not only have a minimal derivation from the original release times, but also could guarantee the prefixed processing sequence to be optimal. To efficiently solve this problem, we first discuss the properties of optimal solutions of the 1|ri|Cmax problem. Then, we formulate the investigated inverse scheduling problem into a convex programming model. Based on this model, we further propose a solution method for the investigated inverse scheduling problem. A randomly generated testing instance demonstrates the efficiency of the formulated convex programming model and the proposed method.