Scheduling class!!!

Problem form the book: Theory, Algorithms and Systems, Fifth Ed by Michael L Pinedo. Chapter three.

PLEASE TRY TO GO STEP BY STEP SO I CAN UNDERSTAND THE PRODECUDERE AND KNOW THE PROCEDURE AND THE REASON OF THE STEPS NOT JUST THE ANSWER.

::::::::::::::::::::::::::::::::::::::::::::::::::BACKGROUND TO SOLVE THE PROBLEM AND MAY BE USEFUL::::::::::::::::::::::::

- Processing time (Pj) 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.

- Release date (rj) The release date rj of job j may also be referred to as the ready date. It is the time the job arrives at the system, i.e., the earliest time at which job j can start its processing.

- Due date (dj ) The due date dj of job j represents the committed shipping or completion date

- Weight (wj) The weight wj of job j is basically a priority factor, denoting the importance of job j relative to the other jobs in the system. For example, this weight may represent the actual cost of keeping the job in the system. This cost could be a holding or inventory cost; it also could represent the amount of value already added to the job.

- Makespan (Cmax) 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).

- Maximum Lateness (Lmax) The maximum lateness, Lmax, is defined as max(L1, . . . , Ln). It measures the worst violation of the due dates.

- Total weighted tardiness ( WjTj) this is also a more general cost function than the total weighted completion time.

3.26. Consider 1 wjTj. Prove or disprove the following statement: If Pi