Reference no: EM132302362

Production Planning Case Study. Biological heart valves are bioprostheses manufactured from porcine hearts for human implantation. Replacement valves needed by the human population come in differentsizes. On the supply side, porcine hearts cannot be “produced” to specific sizes. Moreover, the exact size of a manufactured valve cannot be determined until the biological component of the pig heart has been processed. As a result, some needed sizes may be overstocked and others may be understocked. Raw hearts are provided by several suppliers in six to eight sizes, usually in different proportions depending on how the animals are raised. The distribution of sizes in each shipment is expressed in the form of a histogram. Porcine specialists work with suppliers to ensure distribution stability as much as possible. In this manner, the manufacturer can have a reasonably reliable estimate of the number of units of each size in each shipment. The selection of the mix of suppliers and the size of their shipments is thus crucial in reducing mismatches between supply and demand. The notation for parameters in this problem is as follows:

The variables of the problem can be defined as follows:

The Linear Programming model is given below to determine the amount from each supplier that will minimize the total cost of purchasing and processing subject to demand and supply restrictions.

The solver output for a dataset involving 8 valve sizes and 12 suppliers is given in the following table:

Using the above solver output, answer the following questions:

a) How many decision variables and constraints include in this LP formulation?

b) What is the monthly supply amount by each vendor? What is the total average purchasing and processing cost of raw hearts?

c) If you are asked to use the above solver output for planning purposes, what would be your recommendation? Discuss if you can group the vendors in three categories.

d) Can you estimate the missing values in reduced cost column? Explain and justify your answer.

e) How do you interpret the reduced cost of 5.22 for vendor 3?

f) What valve size would you characterize as the most critical size? Justify your answer based on the value of additional resources for different valve sizes.

g) What is your recommendation for inventory planning of valve size 4 and 7?

h) Can you estimate the missing value in Dual Value column? Explain and justify your answer.