Minimizing the number of machine idle intervals with minimum makespan in a flow-shop

This paper considers a selected sequence in a permutation flow-shop. The objective is to minimize the number of machine idle intervals with minimum makespan (or total production time) for this selected sequence. There are at least two advantages of minimizing the number of machine idle intervals. The first reduces the number of times necessary to restart machines. The second achieves a longer period of idle time for each idle interval, and hence the idle time may be used more efficiently. An integer programming formulation is presented to provide the optimal solution. A heuristic algorithm is also proposed to solve large-sized problems. The heuristic finds the optimal solution for the three-machine case and is found to provide the optimal or near-optimal solution for other cases.