1. Model 7: Results and Sensitivity Analysis
Presented by Brian Murphy and Scott Lichtor

2. Overview Sensitivity Analysis Overview Review of Model
Solution to the Model
Post-Optimality Adjustments
Changing Storage Costs
Changing Overtime Constraints
Conclusion

3. Sensitivity Analysis Overview
Linear programming problems are usually in the form:
Z=cTx
subject to Ax≤b
Where c is your cost vector, x is your decision variable vector, A is your inputs matrix, b is your constraint vector, and Z is your objective value.
After finding a solution, conditions of the problem may change (either A, b, or c may change).
Sensitivity analysis entails evaluating if your original solution is still valid with respect to the new conditions. If not, a new optimal solution can be derived that satisfies the new conditions without redoing the Simplex method.

4. Review of Model 7 Ice cream plant manufactures containers of ice cream
Meets the demand for ice cream parlors
Plant has overtime and regular time costs and constraints
Plant can store ice cream for use in later months
Storage has a per month cost, but ice cream can be stored indefinitely
Goal: minimize costs while satisfying constraints

5. Solutions to the Model Containers produced for each month
Total regular time production cost: $737.25
Total overtime production cost: $376.00
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Reg Time 75
100 90 80
Over-time 30 40 50 60

6. Solutions (cont.) Storage needed for each month
Total storage costs: $51.50
Total costs: $
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
No.
Containers
250 20 55 15

7. Observations Overtime production needed more in later months
Storage needed more in earlier months
Total storage costs relatively low.

8. Post-Optimality Adjustments
Parameters that can be changed:
Regular time and overtime production capacities (A matrix)
Regular time and overtime costs (c vector)
Storage costs (c vector)
Total demand (b vector)

9. Change Storage Costs
Suppose the storage costs decrease from $.1 per month to $.05 per month

10. Changing Storage Costs (cont.)
Containers produced in each month
Total regular time production cost: $753.50
Overtime: $354.75
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Reg. Time
100 90 80
Over-time 5 40 50 60 30

11. Changing Storage Costs (cont.)
Storage needed for each month
Total storage cost: $28.25
Total Cost: $
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
No. Containers
245 40 60 10

12. Observations from Changing Storage Costs
Storage level increases
Storage costs decrease from $51.50 to $28.25
Regular time costs increase from $ to $753.50
Overtime costs decrease from $ to $354.75
Total costs decrease from $ to $

13. Changing Overtime Constraints
Now, suppose overtime production constraints decrease to 40 for every month.

14. Changing Overtime Constraints
Containers produced in each month
Total regular time cost: $759.00
Total overtime cost: $349.25
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Reg Time
100 90 80
Over-time 35 40 30

15. Changing Overtime Constraints
Storage needed for each month
Total storage cost: $96.00
Total cost: $
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
No. Containers
200 65
120 30

16. Observations from Changing Overtime Constraints
Regular time costs increase from $ to $759
Overtime costs decrease from $376 to $349.25
Storage costs increase from $51.50 to $96
Total costs increase from $ to $
Lower overtime constraints cause higher regular time production and higher storage

17. Questions;