Improving scheduling robustness via preprocessing and dynamic adaptation

We study methods to improve scheduling robustness under processing time variation. We propose a two-stage scheme that preprocesses the scheduling data to create a skeleton of a schedule and then completes it over time through dynamic adaptation. We focus our attention on the classical job shop scheduling problem. Preprocessing starts at the beginning of the planning period (at the time of scheduling) when a priori information becomes available on processing time uncertainty. We first decompose the job shop scheduling problem into network-structured subproblems using Lagrangian relaxation. For each subproblem, we introduce stochastic constraints that capture the processing time uncertainty. We incorporate the stochastic information in such a way that the subproblems retain their efficient network structure. Using a subgradient search algorithm, we iteratively improve the lower and upper bounds obtained from the Lagrangian relaxed problem, which produce a partial sequence of critical operations. This so-called Lagrangian ranking defines a preprocessed schedule where the complete scheduling is determined dynamically over time, adapting to changing shop conditions. We test the robustness of the two-stage scheme through extensive computational experiments. We show that the scheme significantly outperforms deterministic scheduling methods and dynamic dispatching rules with minimal computational burden.