DO NOT DO THIS WITH CHATGPT OR AI

Assume that there is a household electronics product that has a lifetime of one year. After the year is over, the product does not sell anymore $($possibly because of the launch of a new and better version which we do not model$).$ There is a single replenishment opportunity for this product before observing the demand $($Newsvendor model assumptions!$).$

The yearly demand is normally distributed with a mean of $1450$ and a standard deviation of $800.$

The supply chain consists of a retailer and a supplier. The retailer faces the random demand and gives an order to the supplier. The supplier takes the order and produces it $($forced compliance$).$ It has no capacity limit$.$

The product sells at $10000$ TL per unit which is fixed throughout the year. There is a shortage penalty of $6000$ TL$/$unit for each unit short charged to the retailer. At the end of the year, on$-$hand inventory has no salvage value.

The supplier produces the product at $3000$ TL$/$unit$.$

What is the centrally optimal order quantity and the corresponding expected profit? $($Assuming that the supplier and the retailer are owned by the same company$).$

Assuming that the supplier and the retailer are different companies what is the order quantity that the retailer is going to order if the supplier charges a wholesale price of $5550$ TL$/$unit$?$ What are the corresponding $($expected$)$ profits of the retailer and the supplier?

The supplier now offers a buy$-$back contract where she still charges a wholesale price of $5550$ TL$/$unit but offers to buy the remaining items at the end of the year at $1500$ TL$/$unit$.$ What is the order quantity? What are the corresponding expected profits of the retailer and the supplier? Is this a better contract than the one in part $(2)?$

The supplier now offers a revenue sharing contract where she offers a wholesale price of $4500$ TL$/$unit but asks for $20\%$ of retailer's expected revenue $($s$=0\mathrm{.}80).$ What is the order quantity? What are the corresponding expected profits of the retailer and the supplier?

Compare the results of $1-4$ and discuss why the chain is not coordinated by these contracts with the given contract parameters?

Find a pair of coordinating revenue share parameters $($w$,$s$)$ such that both the retailer and the supplier do better than their profits in part $(2)($under a wholesale contract$).$

Please upload your solution from this interface. Your submission should contain two parts:

A well written report $($pdf file$),$

Your computations $($excel or others$)$ in a single zipped file.

The total size of each file submission cannot be larger than $2$ MB$.$

Hint: There are several ways to compute expected profits in this setting. You can use the formulation in the notes and use the loss function tables; you can simulate the profit function for an approximation $($see various Newsvendor simulators on the internet$)$; you can use a software like Matlab or R that can evaluate the expected sales, S$($q$),$ numerically.