***DUMMY HOMEWORK***

MGMT 6010 Problem Set 3—Newsvendor and Revenue Management

1 Newsvendor Model

1.1 Green Mountain Sports

Green Mountain Sports sells a full line of outdoor clothing and accessories, including waterproof hiking boots. Due to competition, Green mountain can sell these hiking boots for only $54 but must pay suppliers $40 per pair. One order is placed per season; excess inventory is sold at a 50% price discount at the end of the season. At $54, estimated demand over the season is 400 pairs of boots with standard deviation of 300.

a. Given the prices and costs, how many waterproof hiking boots should Green Mountain order given its demand estimate?

b. Suppose Green Mountain orders 380 pairs of boots? What would the fill rate be?

c. Suppose Green Mountain orders 380 pairs of boots? What would the expected profit be?

d. Suppose marketing is unhappy with the order quantity in part a? They argue that Green Mountain should maintain a high service level and insist that enough boots be ordered to have at least a 98% fill rate. What order size corresponds to a 98% fill rate for these boots?

e. What is Green Mountain’s expected profit if it orders the amount calculated in part d?

f. The supplier has offered Green Mountain a 10% discount if it orders at least 800 pairs of boots. If the objective is to maximize profit, how many boots should Green Mountain order in light of this new information?

g. Billy Bragg, marketing analyst, has decided to use A/F ratios for ordering decisions. Billy is trying to determine the order size for a different product, the standard hiking boot. A pair of standard boot sells for $55 and, due to a competitive supplier market, can be purchased for $30. The boots do not go out of style, but do cost $2.50 to hold a pair over from one season to the next. Green Mountain anticipates that the $55 price and $30 cost will remain the same for the next season. Bragg collected data from 20 items that he felt had market behavior similar to the standard boot. His forecast for the upcoming season is that demand will be 1000 boots. Using the data shown below and the price/cost information above, what is the profit maximizing order amount for the standard boot?

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Actual Item Num Demand Forecast A/F Ratio

1 2512 2041 1.23 2 1003 916 1.09 3 32 264 0.12 4 829 1417 0.56 5 95 1946 0.05 6 2122 1184 1.79 7 165 418 0.39 8 769 1514 0.51 9 1120 595 1.88 10 762 872 0.87 11 1317 1667 0.79 12 366 1216 0.30 13 1009 1266 0.80 14 1501 778 1.93 15 1918 1599 1.20 16 2306 2042 1.13 17 2058 1170 1.76 18 794 1607 0.49 19 552 323 1.71 20 638 801 0.80

Table 1: Green Mountain Product Demand and Forecast Data from previous season. This information is also available in a file labeled “Problem Set 3 Boot Data.xlsx”

2 Revenue Management

2.1 GreenJet

Next week, GreenJet has a regularly scheduled flight from New Orleans to San Francisco that will be booked to capacity. Based on prior experience, the airline expects 25 customers (normally distributed with a standard deviation of 15) to cancel their reservations too late to resell the seat or to fail to show up for the flight (we will assume that the tickets are refundable so that no-shows represent lost revenue). Revenue from a ticket on the flight is $125. If more customers show up than GreenJet has seats, the policy is to put the customer on the next available flight (without bumping any other passengers) and to give them a free round-trip ticket that will cost GreenJet an average of $250 in lost revenue at a later date. Should GreenJet underbook or overbook the flight? By how many seats?

2.2 Problem 1 from Netessine and Shumsky

See the Netessine and Shumsky article for full details. This is a two-fare revenue management problem. Key parameters are full price is $200, discount price is $120. Full price demand is 70 with standard deviation 29 (assume normally distributed).

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Calculate the following:

a. Find the optimal protection level for full price rooms (the number of rooms to be protected from sale at a discount price).

b. Find the booking limit for discount rooms.

c. Suppose that for a short time, the hotel’s forecast of business customer demand is biased upward: the forecast of 70 rooms is too high and fewer business cus- tomers appear, on average. Qualitatively describe the economic consequences of using the protection level and booking limit derived in (a) and (b).

d. Suppose that for a short time, the hotel’s forecast of business customer demand is biased downward: the forecast of 70 rooms is too low and more business cus- tomers appear, on average. Qualitatively describe the economic consequences of using the protection level and booking limit derived in (a) and (b).

2.3 Problem 2 from Netessine and Shumsky

See the Netessine and Shumsky article for full details. An airline offers two fare classes for coach seats on a particular flight: full-fare

class at $440/ticket and economy class at $218/ticket. There are 230 coach seats on the aircraft. Demand for full-fare seats has a mean of 43, a standard deviation of 8, and the following empirical distribution:

Table 2: Empirical Distribution: Full fare demand

Full-fare Demand (Q) Probability Cumulative Full-fare Demand Prob[d = Q] Prob[d ≤ Q]

40 0.02 0.25 41 0.06 0.31 42 0.04 0.35 43 0.01 0.36 44 0.06 0.42 45 0.07 0.49 46 0.02 0.51 47 0.03 0.54 48 0.03 0.57 49 0.05 0.62 50 0.03 0.65 51 0.05 0.70 52 0.04 0.74 53 0.06 0.80 54 0.09 0.89 55 0.11 1.00

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Economy-class customers must buy their tickets three weeks in advance, and these tickets are expected to sell out.

a. Find the (i) protection level and (ii) booking limit for low-fare seats.

b. Suppose that unsold seats may sometimes be sold at the last minute at a very reduced rate (similar to USAirways’ “esavers” for last-minute travel). What effect will this have on the protection level calculated in (a)? The protection level (Q∗) will be:

Higher, Lower, The Same.

Why?

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