Flow shop scheduling with inter-stage flexibility and blocking constraints

We investigate a scheduling problem arising from a material handling and processing problem in a production line of an Austrian company building prefabricated house walls. The addressed problem is a permutation flow shop with blocking constraints in which the machine of at least one stage can process a number operations of two other stages in the system. This situation is usually referred to as multi-task or inter-stage flexibility.

The problem is inherently NP-hard; however, we identify some special cases that can be solved in polynomial time. For the general case, with an arbitrary number of machines, jobs, and operations per job, we propose a range of heuristic algorithms, with a particular emphasis on matheuristics based on two distinct mixed-integer linear programming (MIP) formulations of the problem. These matheuristics utilize the strengths of exact optimization techniques while introducing flexibility to address limits on computation time. To assess the performance of the proposed approaches, we conduct an extensive computational study on randomly generated test cases based on real-world instances.