FORMULATIONS FOR THE JOB SEQUENCING PROBLEM WITH SEQUENCE-DEPENDENT SETUPS AND INVENTORY CONSTRAINTS

This work addresses the problem of minimizing makespan in single-machine job scheduling, considering release dates, sequence-dependent setup times, and inventory constraints. Four distinct mathematical formulations were proposed to represent the problem: the first based on position-indexed variables; the second on arc-indexed variables; the third on arcs combined with inventory levels; and the fourth on arc-time indexes. To evaluate the performance of each model, experiments were conducted on a set of 450 generated instances. The results indicate that the arc-indexed formulation showed the best overall performance, being the only one capable of solving instances with up to 50 tasks and achieving the optimal solution in 154