# Solution Library

# Supply Chain Example Problems

**Question**

1. On consecutive Sundays, Mac, the owner of a local newsstand, purchases a number of The Supply Chain Digest, a popular weekly magazine. He pays 25 cents for each copy and sells it for 75 cents. Copies he has not sold during the week can be salvaged for 10 cents each. Mac's newsstand sees a weekly demand for the magazine to be approximately uniformly distributed with the range [50; 200]. Assume that the publisher of the SC Digest incurs only 13 cents to publish a copy of the magazine.

- Determine the optimal number of copies that Mac should purchase each week.
- Determine the optimal number of copies by performing marginal analysis through enumeration.
- Determine the expected overage, shortage and the associated expected profit.
- Determine the expected profit for the publisher if the publisher doesn't take any action.
- Determine the expected profit for the supply chain if the publisher buys Mac's business.
- Determine the expected profit for the publisher if the publisher pays 25 cents for buying back each unit that Mac did not sell.
- Determine the expected profit for the publisher if the publisher pays 12 cents for buying back each unit that Mac did not sell.
- (Bonus - 1 point) Determine the optimal profit for the publisher and the associated buy-back price, if the publisher sets the price.
- (Bonus - 1 point) Determine the optimal profit for Mac and the associated buy-back price, if Mac should negotiate a price.

2. (Bonus - 1 point) Solve the above problem assuming that the weekly demand for the magazine to be approximately normally distributed with mean 125 units and standard deviation 25 units.

- Determine the optimal number of copies that Mac should purchase each week.
- Determine the optimal number of copies by performing marginal analysis through enumeration.
- Determine the expected overage, shortage and the associated expected profit.
- Determine the expected profit for the publisher if the publisher doesn't take any action.
- Determine the expected profit for the supply chain if the publisher buys Mac's business.
- Determine the expected profit for the publisher if the publisher pays 25 cents for buying back each unit that Mac did not sell.
- Determine the expected profit for the publisher if the publisher pays 12 cents for buying back each unit that Mac did not sell.
- Determine the optimal profit for the publisher and the associated buy-back price, if the publisher sets the price.
- Determine the optimal profit for Mac and the associated buy-back price, if Mac should negotiate a price.

3. Solve the above problem assuming that the weekly demand for the magazine to be approximately exponentially distributed with mean 125 units.

- Determine the optimal number of copies that Mac should purchase each week.
- Determine the optimal number of copies by performing marginal analysis through enumeration.
- Determine the expected overage, shortage and the associated expected profit.
- Determine the expected profit for the publisher if the publisher doesn't take any action.
- Determine the expected profit for the supply chain if the publisher buys Mac's business.
- Determine the expected profit for the publisher if the publisher pays 25 cents for buying back each unit that Mac did not sell.
- Determine the expected profit for the publisher if the publisher pays 12 cents for buying back each unit that Mac did not sell.
- (Bonus - 1 point) Determine the optimal profit for the publisher and the associated buy-back price, if the publisher sets the price.
- (Bonus - 1 point) Determine the optimal profit for Mac and the associated buy-back price, if Mac should negotiate a price.

4. Blue Skies Airlines has decided to apply the capacity-controlled discount fares model to one of its flights. This flight can accept 500 reservations for seats in the main cabin. The flight attracts a large number of business travelers, who typically make their reservation within a few days of the flight but are willing to pay a relatively high fare of $1120 for this flexibility. However, the substantial majority of the passengers need to be leisure travelers in order to fill up the plane. Therefore, to attract enough of these travelers, a very low discount fare of $330 is ordered to passengers who make their reservations at least 14 days in advance and satisfy certain other restrictions (including no refunds).

- (Bonus - 1 point) Assume that the arrival of business travelers follow normal distribution with mean 350 and standard deviation 100. Determine the optimal number of seats that should be reserved for business customers.
- Assume that the arrival of business travelers follow uniform distribution [250,450]. Determine the optimal number of seats that should be reserved for business customers.
- Assume that the arrival of business travelers follow exponential distribution with mean 350. Determine the optimal number of seats that should be reserved for business customers.

5. Transcontinental Airlines has a daily flight (excluding weekends) from San Francisco to Chicago that is mainly used by business travelers. There are 480 seats available in the single cabin. The average fare per seat is $600. This is a non-refundable fare, so no-shows forfeit the entire fare. The enterprises optimization group at Transcontinental has observed that only 90% of the customers who make reservations for this flight actually show up to take the flight. If overbooked, customers will be bumped to another flight. When a customer is bumped, the airlines arranges to put the customer on the next available flight to Chicago on another airline. The company's average cost for doing this is $900. In addition, the company gives the customer a voucher worth of $400 for use on a future flight.

- a. Determine how many reservations should be accepted for this flight by performing marginal analysis.
- b. If the probability of showing up is 75%, then determine how many reservations should be accepted for this flight by performing marginal analysis.

**Summary**

These questions belong to Supply chain management. These are some of the example supply chain problems which help you to practice various assumptions and combinations. The answer has solutions to all the assumptions in detail.

**Total Word Count 1834**

## Comments

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