**Risk Management in Global Supply Chain**

**There are four quantitative questions in the assignment:**

**First question **is an application of the newsvendor problem in the context of buy-back procurement contract and quantity flexibility procurement contract.

**Second question **is the design of postponement strategy in Benetton**. **

**Third question **is capacity planning at Seagate

**Fourth question **is related to our discussion of choice of procurement contracts in the presence of spot market for a commodity input

**(5 points)**Geoff Gullo owns a small firm that manufactures ”Gullo Sunglasses.” He has the opportunity to sell a particular seasonal model to the retailer Land’s End. It is estimated that this season’s demand for this model will be normally distributed with a mean of 250 and a standard deviation of 150. Land’s End will sell those sunglasses for $100 each and can dispose the unsold sunglasses at the end of the seasons free of charge.- a)
**(1 point)**Currently Geoff offers a price of $25 for each unit of sunglasses to Land’s End. How many units Land’s End would buy from Geoff and what is Land’s End’s expected profit? - b)
**(1 point)**Geoff considers a different purchasing option for Land’s End. In particular, Geoff offers to set his price at $30 and agrees to buy back each unit of unsold glasses at the end of the season from Land’s End at a unit price of $20. How much Land’s End would buy from Geoff and what is Land’s End’s expected profit? - c)
**(1.5 points)**If we compare the purchasing option in a) and purchasing option in b), which purchasing option should Land’s End choose? Why is Land’s End profit higher in that option (compared to the other option)? Is this option also preferred by Geoff Gullo (please assume that unit production cost of Geoff Gullo is normalized to zero)? Why (not)? - d)
**(1 point)**Geoff considers a different purchasing option for Land’s End. In particular, Geoff agrees to let Land’s End first reserve the sunglasses before the season starts for a reservation price of $22. Land’s End then can ask for the delivery of sunglasses within the reserved capacity for an exercise price of $3 for each unit after the season’s demand is realized. How much Land’s End would buy from Geoff and what is Land’s End’s expected profit? - c)
**(1.5 points)**If we compare the purchasing option in a) and purchasing option in d), which purchasing option should Land’s End choose? Why is Land’s End profit higher in that option (compared to the other option)? Is this option also preferred by Geoff Gullo (please assume that unit production cost of Geoff Gullo is normalized to zero)? Why (not)? In calculating Geoff Gullo’s expected profit please consider how much Land’s End reserves first and then how much Land’s End exercises later. **(5 points)**Benetton is selling blue and green colored sweaters from a unit price of $200. The demand for each sweater is normally distributed with mean 250 and standard deviation 80. Any leftover sweaters at the end of the selling season can be salvaged from unit price of $50. The production of sweaters involves two sequential processes, dyeing, which has a unit cost of $25 and knitting, which has a unit cost of $45.- a)
**(1 point)**Given that Benetton has to produce each sweater well in advance of the selling season (facing demand uncertainty), how many blue and green colored sweaters should Benetton produce? What is the profit? - b)
**(2 points)**Benetton is considering postponing the coloring of sweaters until they have a better understanding of the demand for each color. To achieve this, they need to change the order of the production process—knitting first—and produce a generic white color sweater which then they will color (in blue or green) if there is demand for that color. In this case, because coloring is done only if there is demand for that color, Benetton does not salvage colored sweaters, but they salvage generic white sweaters if there is any leftover at the end of the selling season. The salvage value for the generic sweater is $40. Consider the case where the knitting and dyeing cost remain the same. Should Benetton implement this postponement strategy? How many generic white sweaters should they produce in advance of the selling season? What is the profit? - c)
**(2 points)**Benetton would like to understand the impact of demand correlation on their production volume and profitability with the postponement strategy—currently they are assuming that blue and green color demands are independent. Please re-calculate the production volume and profit in part ii for the cases where correlation between blue and green color demands is 0.25, 0.5, 0.75 and 1. What happens to the production volume and profit when correlation increases? Why? **(5 points)**Consider the Seagate case example and assume the same capacity investment costs and contribution margins for Cheetah and Barracuda. Seagate has a new demand forecast with the following scenarios:

Pessimistic: 100 (Cheetah), 550 (Barracuda) with probability ¼

Most Likely: 400 (Cheetah), 400 (Barracuda) with probability ½

Optimistic: 600 (Cheetah), 150 (Barracuda) with probability ¼

- a)
**(1.5 points)**Consider the benchmark case where Seagate invests in dedicated (separate) testing facility for each product. What are the optimal capacity investment levels for Cheetah and Barracuda assembly and testing facilities? What is the optimal profit? - b)
**(1 point)**Consider now the case where there is flexible (joint) testing facility for Cheetah and Barracuda. Currently, Seagate is proposing to invest in 400 units of Cheetah assembly, 400 units of Barracuda assembly and 800 units of testing facility. Explain why the proposed capacity investment plan is not optimal (in answering this question make a comparison of demand coverage with this portfolio and the optimal capacity portfolio in part a). - c)
**(1 points)**Using a mathematical model you find that the optimal capacity plan with flexible testing facility is to invest in 600 units of Cheetah assembly, 550 units of Barracuda assembly and 800 units of testing facility. Explain why this plan works better than the original proposal in part b (in answering this question make a comparison of demand coverage with this portfolio and the proposed portfolio in part b) - d)
**(1.5 point)**Seagate has an updated demand forecast with the following scenarios:

Pessimistic: 100 (Cheetah), 150 (Barracuda) with probability ¼

Most Likely: 400 (Cheetah), 400 (Barracuda) with probability ½

Optimistic: 600 (Cheetah), 550 (Barracuda) with probability ¼

Using a mathematical model you find that the optimal capacity plan with flexible testing facility under this new demand forecast is to invest in 400 units of Cheetah assembly, 400 units of Barracuda assembly and 800 units of testing facility. Does the flexibility of testing facility benefit Seagate in this case? Why (not)? To answer this question, please make a comparison with the dedicated (separate) testing facility benchmark case where Seagate invests in 400 units of Cheetah assembly and testing and 400 units of Barracuda assembly and testing. What is the demand coverage under the flexible system and the dedicated system? What has changed in the updated demand forecast in comparison with the original demand forecast?

**(5 points)**Consider a cocoa processor who sources cocoa beans from a single supplier using quantity flexibility contract (r,e) where r denotes the unit reservation price and e denotes the unit exercise fee. The processor uses the cocoa beans to produce cocoa butter with selling price of $120 per kg. The processing cost is normalized to zero, so the only cost is the procurement cost of the cocoa beans. Let us assume there is 1-1 conversion between cocoa beans and cocoa butter, i.e., 1 kg of beans yields 1 kg of cocoa butter. The processor can source the cocoa beans from the supplier in advance of the spot market and from a spot market on the day. The processor has a spot price forecast w, $ per kg, for cocoa beans with the following scenarios:

Scenario A: $150 with probability ¼

Scenario B: $100 with probability ½

Scenario C: $50 with probability ¼

- a)
**(1 point)**A supplier (Supplier1) is offering the contract (51, 38). Is it profitable to order from this supplier? Why (not)? - b)
**(1 point)**There is another supplier (Supplier2) offering the contract (55, 37). Which supplier should the processor choose to order from? Why? - c)
**(1 point)**What if Supplier2 offers (65,23)? Which supplier should the processor choose to order from? Why? - d)
**(2 points)**Suppose the processor has a new spot price forecast w, $ per kg, for cocoa beans with the following scenarios:

Scenario A: $180 with probability ¼

Scenario B: $100 with probability ½

Scenario C: $20 with probability ¼

The processor is still trying to decide between Supplier1 offering the contract (51, 38) and Supplier 2 offering the contract (65,23). Which supplier should the processor choose to

order from? Why? In comparison with your answer in part c, did your answer change? Why (not)?