On two-machine Flow Shop Scheduling Problem with disjoint setups

We consider a variant of the Permutational Flow Shop Scheduling Problem with disjoint setups and makespan minimization. A mathematical model of the problem is presented and several properties on the feasibility of solutions are formulated. An elimination property is proposed, allowing to disregard up to 75% of the solution space. We also show an interesting connection between the number of feasible solutions and Catalan numbers. To solve the problem for a fixed job order, we propose two algorithms: Mixed-Integer Linear Programming exact formulation and a greedy heuristic algorithm. An empirical evaluation shows a promising efficiency of the heuristic, providing an optimal or near-optimal solutions for problem instances with low setup and job times time deviation.