$$ Buy$-$back contracts: in this contract, the seller agrees to buy back unsold goods from the buyer for

some agreed$-$upon price higher than the salvage value.

$$ Buyer$$s risk is decreased and thus he is willing to order more $($buyer makes ordering decision$).$

$$ Supplier$$s risk is increased.

$$ The contract must be designed such that all parties benefit.

$$ Sunglass example

$$ The supplier Zamatia agrees to buy back any leftover inventory at the price of $$40$ per unit,

which is higher than the salvage value of $$25.$

$$ In this case, the retailer UV earns $115-75=$ $$40$ for each unit sold, and loses $75-40=$ $$35$ for

each unit of unsold. This is the information you need to apply newsvendor model.

$$ Zamatia earns $75-35=$ $$40$ for each unit sold and earns $75-35-40+25=$ $$25$ for each unit unsold.

$$ Given the above information, apply newsvendor model to determine the optimal order quantity

and calculate UV$$s expected profit.

$$ According to the order quantity determined above, calculate the profit of Zamatia.

Hint: apply the newsvendor model for the buyer to determine the optimal order quantity. Given this order quantity, calculate the expected sales and expected leftover $($unsold$)$ using the formulas covered in week $2($Performance Measures for a Given Order Quantity Q$).$ For the buyer, it earns $$40$ for each unit sold, and loses $$35$ for each unit unsold, you can now calculate the expected profit for the buyer. For the supplier, it earns $$40$ for each unit sold and earns $$25$ for each unit unsold, you can now calculate the expected profit for the supplier.

$1.$ Report the expected profit for the buyer.

$2.$ Report the expected profit for the supplier.

$3.$ Report the expected profit for the entire supply chain $($buyer $+$ supplier$).$