Model 7: Results and Sensitivity Analysis

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

6. Solutions (cont.) • Storage needed for each month • Total storage costs: $51.50 • Total costs: $1164.75

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

11. Changing Storage Costs (cont.) • Storage needed for each month • Total storage cost: $28.25 • Total Cost: $1136.50

12. Observations from Changing Storage Costs • Storage level increases • Storage costs decrease from $51.50 to $28.25 • Regular time costs increase from $737.25 to $753.50 • Overtime costs decrease from $376.00 to $354.75 • Total costs decrease from $1164.75 to $1136.50

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

15. Changing Overtime Constraints • Storage needed for each month • Total storage cost: $96.00 • Total cost: $1204.25

16. Observations from Changing Overtime Constraints • Regular time costs increase from $737.25 to $759 • Overtime costs decrease from $376 to $349.25 • Storage costs increase from $51.50 to $96 • Total costs increase from $1164.75 to $1204.25 • Lower overtime constraints cause higher regular time production and higher storage

17. Questions;