A branch-and-cut algorithm for the integrated employee timetabling and hybrid job-shop scheduling problem with time lags and setup times

Abstract

This paper addresses a real-world manufacturing scheduling problem that integrates employee timetabling with production scheduling. The employee timetabling problem considers skill requirements, employee availability, and legislative regulations. The production scheduling problem is modeled as a re-entrant hybrid job-shop, where jobs may revisit machines multiple times. The problem includes further complexities such as time lags, sequence-dependent setup times, and machine availability constraints. To address these challenges, a novel time period-based modeling approach is introduced. By discretizing the planning horizon into work periods, the proposed formulation ensures that each employee is assigned to a single machine per period, thereby reducing frequent transitions, improving workforce stability, and enhancing operational feasibility. Furthermore, we develop an enhanced decomposition and cut generation method, which goes beyond conventional single-cut strategies by applying multiple problem-specific cuts per iteration. These cuts are designed to exploit the hybrid structure and inherent symmetries of the problem, significantly refining the solution space and accelerating convergence. This approach is embedded within a newly developed Branch-and-Cut algorithm, leading to substantial gains in computational efficiency, especially for large-scale instances where classical MILP and CP methods underperform. Overall, the proposed formulation and algorithmic framework provide a scalable, efficient, and practically viable solution to complex integrated scheduling problems in hybrid job-shop environments.