As a manager of a company you are facing the following challenge: You need to co

Question

As a manager of a company you are facing the following challenge: You need to complete the following 6 tasks on a single resource (machine) Tasks: Processing l ime.4 Due date 2 10 13 Moreover: You have the following precedence relations: a) (20 points) Find a sequence that will Minimize Maximum Lateness. What is that Lateness? b) (10 points) Now forget all about the precedence relations. The 6 jobs can be done in any order! Find the sequences that will achieve the following objectives: Shortest Makespan (Cmax time of finishing the last project) Minimal number of tardy projects. Minimal mean completion time of all the projects Minimal mean lateness of all projects

Explanation / Answer

(1) Given the precedence diagram, we have arranged the tasks in non-decreasing order of their due dates. By doing so, we will arrive at the sequence which will minimize tardiness.

So the sequence of job scheduling will be

A -> C -> B -> D -> F -> E. The lateness would be 17.

(0+3-1+4+5+6 = 17)

b)

Makespan is the time taken to finish all projects. We will use SPT or Shortest Processing Time first to schedule the jobs as SPT will guarantee minimum average flow time. Arranging the tasks using SPT, we get the following

(i) Shortest Makespan is 24 using Shortest Processing Time.

(ii) Minimal No. of Tardy Projects = 4 (A, D, C, E)

(iii) Minimal Mean Completion time of all the projects = (2+5+9+13+18+24)/6 = 11.83

(iv) Minimal mean lateness of all the projects =

(-8-3+5+4+12+11)/6 = 3.5

Processing Time Due Date Completion time Lateness A 4 4 4 0 C 5 6 9 3 B 3 8 7 -1 D 4 9 13 4 F 2 10 15 5 E 6 13 19 6

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