Heart Valves SuppliersRaymond Valencia

Kevin Meono

Brandon Blaydes

Outline

• Problem Statement• Summarization• Formulation• Input Values• Optimal Solution• Sensitivity Analysis• Unit Cost of Supplier 1• Demand for large valves

• Report to Manager

Problem Statement

• 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.

SupplierCost Per Value ($)

Percent Large

Percent Medium

Percent Small

1 5 40 40 20

2 4 30 35 35

3 3 20 20 60

Summarization

Cost Per Value ($)

Large Medium Small

Max valves that

can be purchased

Supplier 1 5 40% 40% 20% 700

Supplier 2 4 30% 35% 35% 700

Supplier 3 3 20% 20% 60% 700

Demand 500 300 300

Sign Restriction

Formulation

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

.2

Large MediumSmall

S.T.

O.F.

Input Values

Solution

Optimal Solution

Amount Cost

Supplier 1 700 $3,500

Supplier 2 700 $2,800

Supplier 3 50 $150

Total 1450 $6,450

Minimal Cost

Sensitivity Analysis

• Unit Cost for Supplier 1

• Demand for large valves

Unit Cost for Supplier 1

New Solution

Table Representation

Unit Cost ($) Min Cost ($)

3 5050

4 5700

5 6450

Graphical Representation

3 4 54500

5000

5500

6000

6500

Min Cost ($)

Unit Cost ($)

Min

Cos

t ($

)

Demand for large valves

New Solution

Table Representation

Demand Min Cost ($)

495 6375

500 6450

505 6525

510 6600

515 6675

520 6750

525 6825

Graphical Representation

495 500 505 510 515 520 5256300

6400

6500

6600

6700

6800

6900

Min Cost ($)

Demand

Min

Cos

t ($

)

Report to Manager

  Cost per Value ($) # of Heart Valves to purchase

Total contribution

Supplier 1 5 700 $3500Supplier 2 4 700 $2800Supplier 3 3 50 $150Total   1450 $6450

Minimum cost: $6450

Purchasing Order:

• 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.

Requirements met

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 300 415 √ fulfilled

  Maximum amount of heart valves available per supplier

Actual amount of heart valves received from suppliers.

Supplier 1 700 500 √ not exceeded

Supplier 2 700 535 √ not exceeded

Supplier 3 700 415 √ not exceeded

• fulfilled the required amount of valves of each size that has to be purchased every month.

• 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.

Sensitivity Analysis

Original, Supplier 1 Unit Cost $5

Output if Supplier 1 Unit Cost $4

Unit Cost = $3

Original, Supplier 1 Unit Cost $5 Supplier 1 Unit Cost $3

Availability=800 valves

Availability of pig valves is 700 per supplier

Increase availability of pig valves to 800 per supplier

Questions?