Operation Research Case study

1. Old Oregon Wood Store
Case Analysis

2. Preparation Assembly Finishing Packaging
Tom Surowski Leon Davis
George Brown
Cathy Stark
Process for Old Oregon Wood Store
General information
• Process shows general allotment of people
• One person is required for each step
• Each person can do each task – Timing shown in next slide
• May or may not optimal solution

3. Time taken in each stage for each person

4. Fastest way to manufacture with the crew:
Stage Preparation Assembly Finishing Packaging
Tom 100 60 90 25
George 80 80 60 10
Leon 110 90 80 10
Cathy 120 70 100 25
Using Hungarian method for assignment
Column reduction Row reduction
20 0 30 15
0 20 0 0
30 30 20 0
40 10 40 15
5 0 30 15
0 20 0 0
30 30 20 0
30 0 30 5
Min value: 5
Intersection: 20, 0

5. 0 0 25 15
0 25 0 5
25 30 15 0
25 0 25 5
Final table:
Assignment:
Stage Preparation Assembly Finishing Packaging
Tom 100
George 60
Leon 10
Cathy 70
Total Time 100 70 60 10
From the allocation,
Total time = 100+70+60+10 = 240
Assuming 8 working hours a day, total number of tables = 480/100 = 4.8 tables

6. If another person Randy is added
Timing for Randy
Stage Preparation Assembly Finishing Packaging Back up
Tom 100 60 90 25 0
George 80 80 60 10 0
Leon 110 90 80 10 0
Cathy 120 70 100 25 0
Randy 110 80 100 10 0
New assignment table after joining of Randy
To balance the table, we have to add a dummy column

7. Solving using Hungarian method:
Stage Preparation Assembly Finishing Packaging Back up
Tom 60
George 80
Leon 80
Cathy Back up
Randy 10
Total time 80 60 80 10
If Randy is hired,
Total time = 80+60+80+10 = 230
Saving of time = 240-230 = 10 with Cathy as back up

8. Moving Cathy
• Cathy’s first preference is finishing
• Cathy’s second preference is preparation
• Ignore Randy
Assignment in which Cathy is given finishing
Stage Preparation Assembly Finishing Packaging
Tom 100 60 90 25
George 80 80 60 10
Leon 110 90 80 10
Cathy 120 70 100 25
Assigning remaining 3jobs to remaining 3 persons:
Stage Preparation Assembly Finishing Packaging
Tom 60
George 80
Leon 10
Cathy 100
Total time 80 60 100 10
Total time:
80+60+100+10
= 250

9. Stage Preparation Assembly Finishing Packaging
Tom 100 60 90 25
George 80 80 60 10
Leon 110 90 80 10
Cathy 120 70 100 25
Assignment in which Cathy is given preparation
Stage Preparation Assembly Finishing Packaging
Tom 60
George 60
Leon 10
Cathy 120
Total time 120 60 60 10
Assigning remaining 3jobs to remaining 3 persons:
Total time = 120+60+60+10 = 250

10. Utilizing Packaging function
• We can combine packaging and finishing operation to utilize packaging function
• Considering 5 crew member i.e. Randy is included
Stage Preparation Assembly Finishing &
Packaging
Back up Total time
Tom 100 60 115 0 275
George 80 80 70 0 230
Leon 110 90 90 0 290
Cathy 120 70 125 0 315
Randy 110 80 110 0 300
• George is taking least time. So he can complete the table alone
• Table made by George is = 480/230 = 2.09
• Time taken by other crew members = 100+80+90 = 270
• Bottleneck process is preparation (100 min)
• Table made by other crew member = 480/100 = 4.8
• Total number if table produced = 4.8 + 2.09 = 6.89
• Crew can make almost 7 table a day

11. Solver approach
Job-Employee Assignment Problem
Time of each assignment
Tom George Leon Cathy
Preparation 100 80 110 120
Assembly 60 80 90 70
Finishing 90 60 80 100
Packaging 25 10 10 25
Tom George Leon Cathy Job Available Job Assigned
Preparation 1 0 0 0 1 = 1
Assembly 0 0 0 1 1 = 1
Finishing 0 1 0 0 1 = 1
Packaging 0 0 1 0 1 = 1
Emp. Available 1 1 1 1
= = = =
Emp. Assigned 1 1 1 1
Total time 240
Job
Job
Employee
Employee

12. Thank You