Optimize Renting Times of Machines in Flow-Shop Scheduling

Laxmi Narain

This paper studies three-machine scheduling problems in the situation when one has got the assignment but does not have one's own machines and has to take machines on rent to complete the assignment. Minimization of total rental cost of machines may be the criterion in this type of situation. Here, we have considered a rental policy in which second and third machines will not be taken on rent at times when the first job is completed on first and second machines respectively but these machines will be taken on rent subject to some criterion. The objective is: for a given sequence obtain the latest times at which the machines should be taken on rent so that total rental cost is minimum without altering the total elapsed time. We have obtained a simple and efficient algorithm, without using Branch-and-Bound technique. Numerical example is given to illustrate the algorithm.