PROBLEM 1.Multi-Supplier Decision Making

Suppose that you are planning to purchase 100 units of a product. To do so, you can purchase the product from one of the three suppliers available. That Is, if you choose a supplier, you will buy the whole 100 units from the same supplier. When you purchase the product, some portion of the products can be damaged during delivery. You can return the damaged products to the supplier and they will partially refund you for the damaged product. However, different suppliers have different refund policies and they only accept limited number of damaged products. The specifications of the suppliers are as follows:

• Supplier 1: It sells the product for $15 per unit. It refunds you $7 per each returned damaged product. It can refund you for at most 15 units of damaged products.
• Supplier 2: It sells the product for $16 per unit. It refunds you $12 per each returned damaged product. It can refund you for at most 25 units of damaged products.
• Supplier 1: It sells the product for $17 per unit. It refunds you $15 per each returned damaged product. It can refund you for at most 30 units of damaged products.

Upon previous observations on delivery, you have estimated that 10% of the products you purchased will be damaged with probability 0.45, 20% of the products you purchased will be damaged with probability 0.30, and 30% of the products you purchased will be damaged with probability 0.25. You will sell any undamaged product for $30 per unit in your store. The delivery cost and return cost back to the supplier are negligible. You want to decide which supplier to purchase 100 units of the product to maximize profit. You profit will be equal to revenues gained from selling undamaged products minus the purchase cost paid to the supplier plus the money you get refunded for damaged products.

a) Formulate a decision analysis problem by constructing the payoff table with the information given above. That is, describe your alternatives, states of natures, and calculate the payoff (profit) for each alternative and state of nature pair, and note the prior probabilities for each state of nature.

b) Based on the maximax criterion, which supplier you would purchase 100 units from? Show how you reach to your solution.

c) Based on the maximin criterion, which supplier you would purchase 100 units from? Show how you reach to your solution.

d) Based on the maximum likelihood criterion, which supplier you would purchase 100 units from? Show how you reach to your solution.

e) Based on the Baye's decision rule, which supplier you would purchase 100 units from? Show how you reach to your solution.

f) What is the expected value of perfect Information for you?