MIP formulation for scheduling of a reconfigurable assembly line based on state machines and state transitions

A new mixed integer program is proposed to schedule a fully automatic, reconfigurable assembly line. The scheduling consists of sequencing and timing a set of pre-allocated assembly and transport jobs, while also inserting the necessary reconfiguration jobs. By modelling reconfigurations as state transitions of a state-machine, the formulation enables to exploit the full flexibility of the reconfigurable assembly line. To evaluate the performance of our formulation we solve a problem instance with Gurobi 10.0.0 and compare our exact formulation against a current state-of-practice heuristic. While substantially slower, our formulation results in a solution with a 11.5% shorter make span.