Example 6 There are three jobs to be processed by a machine

Example 6 There are three jobs to be processed by a machine. The setup time depends on the previous job being processed. Schedule the jobs such that total processing time is minimized. Setup time Job Job 1 Job 2 Job 3 None 5 913 815 5 12 2

Solution

TOtal Processing time is L

In no particular order

Setup TIme ( Job1) + Setup TIme ( Job2) + Setup TIme ( Job3)

In total there total 6 ways to this Setup

the orders could

Job1 > Job 2 > Job 3

Job1 > Job 3 > Job 2

Job2 > Job 1 > Job 3

Job2 > Job 3 > Job 1

Job3 > Job 1 > Job 2

Job3 > Job 2 > Job 1

Now we can calculate the setup time in each of the processes

Job1 > Job 2 > Job 3 = 5 + 9 + 15 = 29

Job1 > Job 3 > Job 2 = 5 + 13 + 12 = 30

Job2 > Job 1 > Job 3 = 3 + 8 +13 = 24

Job2 > Job 3 > Job 1 = 3 + 15 + 5 = 23

Job3 > Job 1 > Job 2 = 8 + 5 + 9 = 22

Job3 > Job 2 > Job 1 = 8 + 12 + 8 = 28

Based on this the total processing time is minimized when we start with Job 3 followed by Job 1 and then Job2 with total processing time of 22