5) Five jobs must be processed on a single machine. The time required to process

Question

5) Five jobs must be processed on a single machine. The time required to process each job and the due date for each job are shown. Time to Job Perform JobDue Date of Job (Minutes) End of minute 4 End of minute 8 End of minute 12 4 End of minute 15 End of minute 11 Construct the branch-and-bound tree in orderto determine the order of jobs that minimizes the total delay. Please show all your work, and write your reason for fathoming any node. Clearly show the optimal solution; otherwise you won't receive any points.

Explanation / Answer

So we see the best fit for all the branches and bounds the scenarios

Provides the best solution with min total delay.

Eng Block Processing time Flow in Flow out Sch Cust Pick up Tardiness FCFS 1 3 0 3 4 0 1 2 3 4 5 2 6 3 9 8 1 Avg flow time 14.6 3 8 9 17 12 5 WIP 3.173913043 4 4 17 21 15 6 Avg job lateness 4.8 5 2 21 23 11 12 Makespan 23 Completion 73 Avg Tardiness 4.8 Eng Block Processing time Flow in Flow out Sch Cust Pick up Early/Late (negative) SPT 5 2 0 2 11 0 5 1 4 2 3 1 3 2 5 4 1 Avg flow time 10.8 4 4 5 9 15 0 WIP 2.347826087 2 6 9 15 8 7 Avg job lateness 3.8 3 8 15 23 12 11 Makespan 23 Completion 54 Avg Tardiness 3.8 Eng Block Processing time Flow in Flow out Sch Cust Pick up Early/Late (negative) EDD 1 3 0 3 4 0 1 2 5 3 4 2 6 3 9 8 1 Avg flow time 13 5 2 9 11 11 0 WIP 2.826086957 3 8 11 19 12 7 Avg job lateness 3.2 4 4 19 23 15 8 Makespan 23 Completion 65 Avg Tardiness 3.2 Current day 0 Job Date Order Received Processing Days Needed Date Order Due, End of Day __ Days left Critical ratio Priority Flow in Flow Out Tardiness 1 3 4 4 1.333333333 1 0 3 0 2 6 8 8 1.333333333 2 3 9 1 Avg flow time 14.6 5 2 11 11 5.5 5 21 23 12 WIP 3.173913 3 8 12 12 1.5 3 9 17 5 Avg job lateness 4.80 4 4 15 15 3.75 4 17 21 6 Utilization 0.315068 Makespan 23 Completion 30 Completion 73 4.80

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