Optimal scheduling of AGVs in a reentrant blocking job-shop

This work presents a mixed integer linear programming (MILP) formulation to find an optimal solution to a small instance of the complex scheduling problem in a make-to-order production. Minimizing the make span, the MILP generates the optimal schedule for the autonomous guided vehicles (AGVs) in a blocking reentrant job shop environment with different jobs. Feasible schedules for the machines and the AGVs are generated from different sized instances to evaluate the limits of the mathematical model. These results are compared to a priority rule based dispatching system, evaluated with a discrete event simulation. The comparison leads to the insight, that on the one hand optimal solutions cannot be calculated for most real world scenarios due to the complexity and on the other hand the application of a standard dispatching rule lead to poor performances neither of the technics are satisfying the need to generate an appropriate schedule. As a result possible solutions are presented.