Optimization of Makespan in Job and Machine Priority Environment

Abstract

This paper analyses a specific case of permutation flow shop scheduling problem with job and machine priority. Sometimes, a particular job has to precede or succeed another job; or a set of jobs are to be together for a specific reason. Within the set of jobs also, there may be a condition that a particular job has to precede or succeed another job. In such case, the scheduling is done in two or more phases to optimize the makespan. In many occasions, the percentage utilization of a particular machine has to be increased due to several reasons. The machine may be costlier, rented, and highly precise or needs to be operated continuously. In the context of the permutation flow shop scheduling, the percentage utilization is calculated in terms of machining time compared with the makespan. For a fixed number of jobs, the total machining time for each machine is also fixed and reduction in the makespan only can increase the percentage utilization. On the other hand, splitting the machining times and regrouping may also help for achieving the objective. The problem is demonstrated with numerical examples. For trial purpose, the machining time of all the jobs that come before and after the priority machine are split (25% and 50%) individually and also in toto, and combined with the critical machine. The number of jobs and machines is kept the same. Consequently, the makespan and percentage utilization have been computed and compared with the original case.