A branch and bound and parallel genetic algorithm for the job shop scheduling problem with blocking

In this paper, we study the job shop scheduling problem with blocking where the objective is to minimise the maximum completion time (i.e. makespan). To solve this non-polynomial-hard problem, we propose three algorithms. First, we propose a combination of a branch and bound algorithm with alternative graphs. We investigate the performance of this proposal to get an optimal solution in a reasonable time. Next, we develop two methods based on genetic algorithms (GAs): sequential and parallel GAs. In the former, we propose two different ways to encode the individuals: binary code using alternative arcs and priority rules code. In the latter, we propose a parallelisation of the GA, where the master computer is dedicated to the steps of selection, crossover and mutation, and the other computers (slaves) are concerned with the computation of the individual’s fitness. At the end of this paper, we discuss the different results.