In this paper it is presented an improvement of the branch and bound algorithm for the permutation flow shop problem with blocking-in-process and setup times with the objective of minimizing the total flow time and tardiness, which is known to be NP-Hard when there are two or more machines involved. With that objective in mind, a new machine-based lower bound that exploits some structural properties of the problem. A database with 27 classes of problems, varying in number of jobs (n) and number of machines (m) was used to perform the computational experiments. Results show that the algorithm can deal with most of the problems with less than 20 jobs in less than one hour. Thus, the method proposed in this work can solve the scheduling of many applications in manufacturing environments with limited buffers and separated setup times.

In this paper, the flow shop with blocking and sequence and machine dependent setup time problem aiming to minimize the makespan is studied. Two mixed-integer programming models are proposed (TNZBS1 and TNZBS2) and two other mixed-integer programming models, originally proposed for the no setup problem, are adapted to the problem. Furthermore, an Iterated Greedy algorithm is proposed for the problem. The permutation flow shop with blocking and sequence and machine dependent setup time is an underexplored problem and the authors did not find the use of mixed-integer programming models for the problem in any other work. To compare the models, a database of 80 problems was generated, which vary in number of machines and jobs. For the small sized problems, the adapted MILP model obtained the best results. However, for bigger problems, both proposed MILP models obtained significantly better results compared to the adapted models, proving the efficiency of the new models. When comparing the Iterated Greedy algorithm with the MILP models, the former outperformed the latter.

This paper addresses the minimization of makespan for the permutation flow shop scheduling problem with blocking and sequence and machine dependent setup times, a problem not yet studied in previous studies. The 14 best known heuristics for the permutation flow shop problem with blocking and no setup times are pre-sented and then adapted to the problem in two different ways; resulting in 28 different heuristics. The heuristics are then compared using the Taillard database. As there is no other work that addresses the problem with blocking and sequence and ma-chine dependent setup times, a database for the setup times was created. The setup time value was uniformly distributed between 1% and 10%, 50%, 100% and 125% of the processing time value. Computational tests are then presented for each of the 28 heuristics, comparing the mean relative deviation of the makespan, the computational time and the percentage of successes of each method. Results show that the heuristics were capable of providing interesting results.