1. Heart Valves Suppliers
Raymond Valencia
Kevin Meono
Brandon Blaydes

2. Outline Problem Statement Summarization Formulation Input Values
Optimal Solution
Sensitivity Analysis
Unit Cost of Supplier 1
Demand for large valves
Report to Manager
Outline

3. Problem Statement Supplier Cost Per Value ($) Percent Large
U.S. labs manufactures mechanical heart valves from the heart valves of pigs. Different heart operations require valves of different sizes. U.S. Labs purchase pig valves from three different suppliers. The cost and size mix of the valves purchased from each supplier are given in the Table [below]. Each month, U.S. Labs places one order with each supplier. At least 500 large, 300 medium, and 300 small valves must be purchased each month. Because if limited availability of pig valves, at most 700 valves per month can be purchased from each supplier. Formulate an LP that can be used to minimize the cost of acquiring the needed valves.
Supplier
Cost Per Value ($)
Percent Large
Percent Medium
Percent Small 1 5 40 20 2 4 30 35 3 60
Problem Statement

4. Summarization Cost Per Value ($) Large Medium Small
Max valves that can be purchased
Supplier 1 5
40%
20%
700
Supplier 2 4
30%
35%
Supplier 3 3
60%
Demand
500
300
Summarization
𝑿 𝟏 , 𝑿 𝟐 , 𝑿 𝟑 >𝟎 Sign Restriction

5. X1 = number of valves purchased from Supplier 1 X2 = number of valves purchased from Supplier 2 X3 = number of valves purchased from Supplier 3 MINIMIZE COST 𝑧=5 𝑋 1 +4 𝑋 𝑋 3 .4 𝑋 𝑋 𝑋 3 ≥ 𝑋 𝑋 𝑋 3 ≥ 𝑋 𝑋 𝑋 3 ≥300 𝑋 1 ≤700 𝑋 2 ≤700 𝑋 3 ≤700
O.F.
S.T.
Large
Medium
Small
Formulation

6. Input Values

7. Solution

8. Optimal Solution Amount Cost Supplier 1 700 $3,500 Supplier 2 $2,800
$150
Total
1450
$6,450
Minimal Cost
Optimal Solution

9. Unit Cost for Supplier 1
Demand for large valves
Sensitivity Analysis

10. Unit Cost for Supplier 1

11. New Solution

12. Unit Cost ($)
Min Cost ($) 3
5050 4
5700 5
6450
Table Representation

13. Graphical Representation

14. Demand for large valves

15. New Solution

16. Table Representation Demand Min Cost ($) 495 6375 500 6450 505 6525
510
6600
515
6675
520
6750
525
6825
Table Representation

17. Graphical Representation

18. Report to Manager Purchasing Order:
Cost per Value ($)
# of Heart Valves to purchase
Total contribution
Supplier 1 5
700
$3500
Supplier 2 4
$2800
Supplier 3 3 50
$150
Total
1450
$6450
Minimum cost: $6450
order 700 heart valves from supplier 1
order 700 heart valves from supplier 2,
order 50 heart valves from supplier 3 in order to obtain the minimum cost of $6450. Even though Supplier 1 cost the most, it has the highest percentage of the large valves which constitutes 45% of the orders.
Report to Manager

19. Size of Heart Valve
Minimum amount of heart valves required to fulfill demand.
Actual amount of heart valves received from suppliers
Large
500
500 √ fulfilled
Medium
300
535 √ fulfilled
Small
415 √ fulfilled
fulfilled the required amount of valves of each size that has to be purchased every month.
Maximum amount of heart valves available per supplier
Actual amount of heart valves received from suppliers.
Supplier 1
700
500 √ not exceeded
Supplier 2
535 √ not exceeded
Supplier 3
415 √ not exceeded
U.S. labs have not exceeded the supply that each supplier can provide.
Purchase order satisfies all the criteria
Provides the lowest possible cost under the limitations and current conditions.
Requirements met

20. Sensitivity Analysis Original, Supplier 1 Unit Cost $5
Output if Supplier 1 Unit Cost $4
Sensitivity Analysis

21. Unit Cost = $3 Original, Supplier 1 Unit Cost $5

22. Availability=800 valves Availability of pig valves is 700 per supplier
Increase availability of pig valves to 800 per supplier
Availability=800 valves

23. Questions?