V$=12345$ VS$=15//////$ O'Neill Inc, designs and manufactures fashionable water$-$sports apparel and equipment; however, for some of

their products, they outsource manufacturing to Xtex. Consider such an item for which O'Neill's seasonal demand

forecast is a Normal distribution with mean $($V$//10+9000)$ and standard deviation $30$ xx$($V$\_($S$)+90).$ For this

item, XTex charges $$(140+$V$\_($s$)//2)$ per unit $($including transportation$).$ O'Neill sells each unit for $$(220+$V$\_($s$))$

during the season and can sell the leftovers at the end of the season for $$(60-$V$\_($S$)//2)$ per unit on average. Assume

that, for the units produced for pre$-$season orders, XTex's unit cost is $60\%$ of their selling price.

$[18]$ Assuming a single order for the season, how many of these items should O'Neill order? Calculate the

resulting expected profits for both O'Neill and XTex.

To improve their ability to meet demand, suppose O'Neill brings a proposal to XTex. Accordingly, if O'Neill needs

any extra units during the season, XTex will quickly deliver them and get $20\%$ higher unit price than pre$-$season.

Assume XTex's unit cost for in$-$season production orders is $75\%$ higher than that of pre$-$season orders.

$[18]$ Considering this proposal, calculate the expected profits for both O$^(\text{'})$ Neill and XTex.

HINT: This is not a "read$-$react" type question.

Suppose XTex makes a counter$-$proposal with a pair of contract alternatives as described below. For each

of the contract alternatives, determine the resulting expected profits for both O'Neill and XTex. Then,

state which of these two contract alternatives would o'Neill select.

a$)[16]$ Buyback Contract: For leftovers, XTex would reimburse O'Neill up to $50\%$ of the purchase price.

If O'Neill wishes to buy any extra units during the season, XTex will deliver them at $$190$ per unit.

b$)[16]$ Options Contract: O'Neill would purchase options at $$25$ and exercise at $$(125+$V$\_($S$)//2)$ per unit.

If O'Neill wishes to buy any extra units beyond the options created, XTex will deliver them at $$170$

each. Assume that XTex can salvage any leftover items at $$45$ per unit on average.

$[$SPECIAL BONUS: $10]$ So far, we have always assumed the supplier produces exactly the quantity

ordered from them. Now, consider the options contract above. Suppose that regardless of O'Neill's

decision of how many options to buy, XTex can freely decide how many units $($options$)$ to actually

produce, and that O'Neill will have to accept and pay for whatever number of options XTex produces.

How many units would XTex produce? What are the resulting expected profits for O'Neill and XTex?

Note: Special Bonus points will NOT count towards the midterm make$-$up$.$

$[14]$ Take into consideration XTex's capability to quickly produce and deliver in$-$season orders $($described

above before question $2).$ To maximize the total supply chain profit, how many units would XTex be asked

to produce pre$-$season and in$-$season? What is the resulting expected total supply chain profit?

$[18]$ Design a revenue$-$sharing contract $($find its parameters$)$ that maximizes $0^(\text{'})$ Neill's profits while giving

XTex exactly the maximum of their expected profits in questions $1,2$ and $($the best selected by $0$ 'Neill in$)3.$

$[10]$ Referring to the environment, constraints, and approaches in their decision$-$making process, explain

the characteristic differences between i$)$ Newsvendor model, ii$)$ read$-$react.strategy, iii$)$ make$-$to$-$order,

and iv$)$ multi$-$period inventory models.