Integrated Scheduling and Location Considering Machine Mobility

In this study, we address a new dynamic scheduling-location problem (DSLP), which is that incorporates movable machines. The objective is designed to optimize job scheduling and machine placement dynamically. For this strongly NP-hard problem, we formulate the problem as a mixed-integer linear programming (MILP) model. To further improve its computational efficiency and tighten the lower bounds for faster convergence to optimal solutions, we propose several valid inequalities based on the characteristics of the DSLP. Numerical experimental results for a case and randomly generated instances demonstrate significant improvements in system efficiency by allowing machine movement. The findings highlight the potential of extending traditional location scheduling frameworks to include dynamic elements, offering new insights and practical implications for complex industrial applications.