IFORMATION THAT MAY BE USEFUL: Pj MEANS: Processing time (pij): The pij represen
ID: 366911 • Letter: I
Question
IFORMATION THAT MAY BE USEFUL:
Pj MEANS: Processing time (pij): The pij represents the processing time of job j on machine i. The subscript i is omitted if the processing time of job j does not depend on the machine or if job j is only to be processed on one given machine.
Cmax MEANS: Makespan. The makespan, defined as max(C1, . . . , Cn), is equivalent to the completion time of the last job to leave the system. A minimum makespan usually implies a good utilization of the machine(s).
Prmu Means: Flow shops that do not allow sequence changes between machines are called permutation flow shops. In these flow shops the same sequence, or permutation, of jobs is maintained throughout. The results in this chapter are mostly limited to permutation flow shops.
6.1. Consider F4 | prmu | Cmax with the following 5 jobs under the given sequence J1,- -. ,J5- jobs j1 j2 js js jis Pij 5 3 6 4 9 P2j 4 8 2 9 13 PsJ 7 8 7 6 5 P4j 8 4 2 9 1 Find the critical path and compute the makespan under the given sequence.Explanation / Answer
Critical Path is 54. (A critical path is a chain of jobs whose earliest starting time is equal to the latest
starting time).
Makespan is detailed as under with the flow of operations as below:
5 3 6 4 9 36 4 8 2 9 13 48 7 8 7 6 5 53 8 4 2 9 1 54