A comparative analysis of Mixed Integer Linear Programming models for the problem of scheduling tasks in the flexible jobshop environment with blocking constraints

The Flexible Blocking Job Shop Scheduling Problem (FBJSP) is an NP-hard combinatorial problem that extends the traditional job shop scheduling problem by incorporating machine flexibility and blocking constraints. The FBJSP is relevant in many sectors such as semiconductor manufacturing and hospital surgical centers. This study develops and compares two Mixed-Integer Linear Programming (MILP) models for the FBJSP, aiming to minimize total tardiness. The first
model is an adaptation of Birgin et al. [2014], which was selected for its proven good performance. The second model is an adaptation of Dauz`ere-P´er`es et al. [2024], which represents a more recent development. Numerical experiments were conducted using 80 instances adapted from the literature. An extensive analysis of the results obtained from both models was carried out.