MIP Models for Flow Shop Scheduling with Inter-stage Flexibility and Blocking Constraints

We investigate a scheduling problem inspired by a material handling problem arising at a production line of an Austrian company building prefabricated house walls. The addressed problem is a permutation flow shop with blocking constraint in which some machines are flexible, that is, there are a number of operations that can be processed on any of two successive machines of the system. This situation is usually referred to as multi-task or inter-stage flexibility. We propose four different MIP Models and test their efficiency and effectiveness on a number of randomly generated instances similar to those of the real-life application.