Makespan minimization on a two-machine flowshop with an availability constraint on the first machine

This paper deals with the scheduling of a two-machine flowshop with an availability constraint on the first machine with the aim of minimizing the makespan. We investigate two mixed-integer programming (MIP) models for this problem. Then we propose a branch and bound (B&B) algorithm based on a set of new lower bounds and heuristics. We further provide the results of extensive computational experiments performed on randomly generated instances to show the efficiency of the proposed approaches. Our computational study reveals that most of the instances of size up to 100 jobs are optimally solved with the (B&B) method. However, the first MIP (MIP1) model is able to solve optimally instances of size up to 10 jobs and the second MIP (MIP2) model can solve instances of size up to 20 jobs. It has been shown that there is an impact of the unavailability start time period and instances with unavailability period at the middle of the time window are the hardest to solve. The impact of the length of the unavailability period on the performance of the (B&B) is also considered.