Prelim 2 – Module 6: Revenue Management

Question 1

Arrival
-explanation
-example accommodation
-example reduction

Answer 1

Customer arrivals are independent decisions, not evenly spaced

Provide generous staffing or hold high inventory

Require reservations

Question 2

Capability
-explanation
-example accommodation
-example reduction

Answer 2

Level of knowledge and skills vary, resulting in some hand-holding

Adapt to customer skill levels

Target customers based on capability

Question 3

Request
-explanation
-example accommodation
-example reduction

Answer 3

Uneven service times result from unique demands

Cross-train employees

Limit service breadth

Question 4

Effort
-explanation
-example accommodation
-example reduction

Answer 4

Level of commitment to coproduction or self-service varies

Do work for customers

Reward increased effort

Question 5

Subjective preference
-explanation
-example accommodation
-example reduction

Answer 5

Personal preferences introduce unpredictability

Diagnose expectations and adapt

Persuade customers to adjust expectations

Question 6

d =

Answer 6

Some random variable that we are guessing (often demand, could be #of no-shows)

Question 7

x =

Answer 7

Our decision variable (e.g., amount of inventory to choose)

Question 8

Cu =

Answer 8

Unit cost of being too low (underestimating d)

Question 9

Co =

Answer 9

Unit cost of being too high (overestimating d)

Question 10

To minimize expected cost ____

Answer 10

Choose the highest value of x such that 𝑃(𝑑<𝑥)≤𝐶𝑢/(𝐶𝑢+𝐶𝑜)

This is known as the critical fractile (or critical ratio) solution

Question 11

Salmon fillets are delivered to Establishment on Monday and Thursday mornings. They have a shelf life of three days. The salmon entrée sells for $19. Suppose the fillets cost $5 each, and other food costs are negligible. How many fillets should we purchase given the following demand information?

Monday-Wednesday demand has mean=22.7; st dev.=7.5

Thursday-Friday demand has mean=12.7; st dev.=4.0

Answer 11

𝐶𝑢=$19−$5=$14
𝐶𝑜=$5
𝑃(𝑑<𝑥)≤𝐶_𝑢/(𝐶𝑢+𝐶𝑜) =14/(14+5)=0.737

norm.inv(0.737,22.7,7.5)
27.45 filets is the optimal number to procure

norm.inv(0.737,12.7,4)
15.24 filets is the optimal number to procure

Question 12

You are planning security personnel for a festival. You need one officer for every thousand attendees. The number of attendees is a random variable following a normal distribution with a mean of 40,000 and a standard deviation of 10,000. Hiring in advance costs $200 per officer. Hiring at the “last minute” costs $500. How many officers should you hire in advance?

Answer 12

𝐶𝑢=$500−$200=$300
𝐶𝑜=$200
𝑃(𝑑<𝑥)≤𝐶𝑢/(𝐶𝑢+𝐶𝑜) =300/(300+200)=0.6

𝑁𝑂𝑅𝑀.𝐼𝑁𝑉(0.6,40,10)=42.53 officers (either 42 or 43 officers)

Question 13

You are the Director of Revenue Management for the Service Ops hotel, an upscale hotel with 100 rooms. The net revenue on each stay is $200, and all 100 rooms have sold for an upcoming night’s stay. There is no cancellation fee for your guests. Your analytics software has tracked last-minute cancellations among guests and has determined the likelihood of each possible number of cancellations, as shown in the table to the right.

You have the opportunity to overbook some number of your rooms to avoid losing the $200 if guests cancel. If you overbook too many rooms, you have to “walk” guests. You believe the expense of walking a guest – from booking a room, offering extras, and reputation costs – is $800. How many rooms should you overlook?

What is the largest x such that 𝑃(𝑑<𝑥)≤0.2 (create table)?

Answer 13

𝑐𝑢=$200; 𝑐𝑜=$800
𝑃(𝑑<𝑥)≤𝐶𝑢/(C𝑢+𝐶𝑜) =200/(200+800)=0.2

For x=3, 𝑃(𝑑<𝑥)=0.08≤0.2
For x=4, 𝑃(𝑑<𝑥)=0.22>0.2
Therefore, overbooking three rooms is the optimal solution.

Question 14

You are the Director of Revenue Management for the Service Ops hotel, an upscale hotel with 100 rooms. The net revenue on each stay is $200, and all 100 rooms have sold for an upcoming night’s stay. There is no cancellation fee for your guests. Your analytics software has tracked last-minute cancellations among guests and has determined the likelihood of each possible number of cancellations, as shown in the table to the right.

You have the opportunity to overbook some number of your rooms to avoid losing the $200 if guests cancel. If you overbook too many rooms, you have to “walk” guests. You believe the expense of walking a guest – from booking a room, offering extras, and reputation costs – is $800. How many rooms should you overlook?

What if Co = $400?

What is the largest x such that 𝑃(𝑑<𝑥)≤0.33?

Answer 14

For x=4, 𝑃(𝑑<𝑥)=0.22≤0.33
For x=5, 𝑃(𝑑<𝑥)=0.41>0.33

Therefore, overbooking four rooms is the optimal solution.

Question 15

Managing Demand: Other Strategies (5)

Answer 15

1. Offering price incentives and dynamic pricing
2. Promoting off-peak demand
3. Developing complementary services
4. Reservations systems
5. Overbooking

Question 16

Managing Capacity (6)

Answer 16

1. Scheduling to a forecast
2. Increasing customer participation
3. Creating adjustable capacity
4. Sharing capacity
5. Cross-training employees
6. Using part-time employees

Question 17

What is yield management?

Answer 17

A variable pricing strategy to maximize revenue from a fixed, perishable resource

Question 18

When is yield management most useful? (5)

Answer 18

1. Relatively fixed capacity
2. Perishable inventory
3. Product sold in advance
4. Fluctuating demand
5. Low marginal sales costs and high capacity change costs

Question 19

Blackjack Airline sells its 95 coach class seats on a Boeing 737 to two customer classes.

Full-fare pays $69. Number of these passengers is normal random variable with mean of 60 and st dev of 15.

14-day advance-purchase special pays $49. High demand.
How many should it reserve for full-fare passengers?

Draw a graph.

Answer 19

C𝑢=$69−$49=$20
C𝑜=$49
𝑃(𝑑<𝑥)≤𝐶𝑢/𝐶𝑢+𝐶𝑜 =20/(20+49)=0.29

We should reserve 𝑁𝑂𝑅𝑀.𝐼𝑁𝑉(0.29,60,15)=51 seats for full-fare customers.

Graph should be inverse bell curve (x-axis is d, y-axis is P(d)). μ is 60 (mean), x=51. Shade area before.