Supply Chain Management

Lecture 25

Semester Outline

• Tuesday April 20 Chap 15• Thursday April 22 Simulation Game briefing• Tuesday April 27 Review, buffer• Thursday April 29 Simulation Game

Outline

• Today– Chapter 15

• Sections 1, 2

• Homework 7 – Online today– Due Thursday April 29 before class

• Homework submitted before April 29 will be graded and returned on April 29

• Thursday – Simulation game briefing

What is Revenue Management?• Revenue management is the practice of differential

pricing to increase supply chain profits– A strategy that adjusts prices based on product availability,

customer demand, and remaining duration of the sales season will result in higher supply chain profits

What is Revenue Management?• Revenue management is the practice of differential

pricing to increase supply chain profits– A strategy that adjusts prices based on product availability,

customer demand, and remaining duration of the sales season will result in higher supply chain profits

• Revenue management, also called yield management, and sometimes smart pricing, is a technique to optimize revenue from a fixed, but perishable inventory

Revenue Management

Newsvendor problem:Maps demand into capacity

Revenue Management:Maps capacity into demand

What is Revenue Management?• Revenue management, also called yield management,

and sometimes smart pricing, is a technique to optimize revenue from a fixed, but perishable inventory

• Is revenue management possible for…– Airline tickets– Cruise travel– Restaurants– Hospitals– LTL trucking companies– Apartment rental– Incoming MBA class– Vending machines

Revenue Management and Vending Machines• Coca-Cola announces that it is

considering vending machines that will boost prices during hot weather.– “Coca-Cola is a product whose utility varies

from moment to moment. In a final summer championship, when people meet in a stadium to enjoy themselves, the utility of a chilled Coca-Cola is very high. So it is fair it should be more expensive. The machine will simply make this process automatic.”

Douglas Ivester, Chairman and CEO

Conditions for Revenue Management• The value of the product varies in different market

segments– Airline seats: leisure versus business travel

• The product is highly perishable or product waste occurs– Fashion and seasonal apparel– High tech products

• Demand has seasonal and other peaks – Cruise travel

• The product is sold both in bulk and on the spot market – Owner of warehouse who can decide whether to lease the entire

warehouse through long-term contracts or save a portion of the warehouse for use in the spot market

Why Revenue Management?

• Success stories– American Airlines increased annual revenue by over $1 billion

through revenue management– Marriott hotels increased annual revenue with $100 million

through revenue management– National Car Rental was saved from liquidation through

revenue management– Canadian Broadcasting Corporation increased revenue with $1

million per week

Airfare example

p1000

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q

800600400200

Choose the fare that maximizes the area

(revenue) of the rectangle

Airfare example

1000

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800600400200

Choose the fare that maximizes the area

(revenue) of the rectangle

Maximum revenue = 500*500= $250,000

Consumer surplus

Unaccommodated

demand

p

q

Airfare example

1000

1000

800

600

400

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800600400200

Choose the fare that maximizes the SUM of areas

of the rectanglesEconomy class

Business class

Maximum revenue = 333*(333 + 667) =

$333,000

p

q

Airfare example

1000

1000

800

600

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800600400200

Choose the fare that maximizes the SUM of areas

of the rectanglesEconomy class

Economy plus class

First class

Maximum revenue = 200*(800+600+400+200)

= $400,000Business class

p

q

Airfare example

1000

1000

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800600400200

Maximum revenue = $500,000

Perfect price discriminationCharging a different price to a different buyer

for the same product without any true cost differential to justify the different price

p

q

Is Revenue Management Price Discrimination?• The same product sold at different times for different

prices is not necessarily price discrimination, because at different times...– The production or distribution costs may be different– Inventory costs were incurred to keep the product in stock until a

later time– Consumers value products differently at different points in time– The product value may change over time, such as perishable or

maturing or seasonal products, fashion goods, antiques.– Interest is earned if product is sold at an earlier time– Locking sales in early reduces uncertainty

Revenue Management for Multiple Customer Segments• If a supplier serves multiple customer segments

with a fixed asset, the supplier can improve revenues by setting different prices for each segment– What price to charge each segment?– How to allocate limited capacity among the segments?

Prices must be set with barriers such that the segment willing to pay more is

not able to pay the lower price

Revenue Management

• Hotels, airlines, opera houses hope this tool will help them maximize sales and profits– “The real beneficiary of revenue management has

been the consumer”

Clearly, customers for which revenue management has decreased the cost of air travel, have benefited from revenue management. Could customers for which revenue management has

increased the cost of air travel, also have benefited from revenue management?

What is Revenue Management?

p1000

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p1000

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Example 15-1: Pricing to multiple segments• A contract manufacturer has identified two customers

segments for its production capacity—one willing to place an order more than one week in advance and the other willing to pay a higher price as long as it can provide less than a week’s notice for production. The customers that are unwilling to commit in advance are less price sensitive and have a demand curve d1 = 5,000 – 20p1. Customers willing to commit in advance are more price sensitive and have a demand curve of d2 = 5,000 – 40p2. Production cost is c = $10 per unit. What price should the contract manufacturer charge each segment if its goal is to maximize profits?

Example 15-1: Pricing to multiple segments

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Price

Dem

and d1 = 5,000 – 20p1

c = 10

Example 15-1: Pricing to multiple segments

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Price

Dem

and

d1 = 5,000 – 20p1

c = 10

Profit

p - c

Pricing Multiple Segments

• Assume that the demand curve for segment i is given by– di = Ai – Bipi

• The goal of the supplier is to price so as to maximize profits– Max (pi – c)(Ai – Bipi)

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Price

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and

Profit

Pricing Multiple Segments

• The optimal price for segment i is given by– pi = Ai/2Bi + c/2

Example 15-1: Pricing to multiple segments• For segment 1:

– pi = Ai/2Bi + c/2 pi = 5,000/(2*20) + 10/2 = $130

– Profit (pi – 10)(5,000 – 20pi) = (130 – 10)(5,000 – 20*130) = $288,000

• For segment 2:– pi = Ai/2Bi + c/2 pi = 5,000/(2*40) + 10/2

= $67.50– Profit (pi – 10)(5,000 – 40pi)

= (67.5 – 10)(5,000 – 40*67.5)

= $127,650Total profit $415,650

Example 15-1: Pricing to multiple segments• If total capacity is limited to 4,000 units, what

should the contract manufacturer charge each segment?– For segment 1: p1 = $130

• Demand d1 = (5,000 – 20p1) = 2,400

– For segment 2: p2 = $67.50

• Demand d2 = (5,000 – 40p2) = 2,300

– Total demand = 2,400 + 2,300 = 4,700

Total demand exceeds production capacity of 4,000

Pricing Multiple Segments

• The goal of the supplier is to price so as to maximize profits– Max ∑k

i=1 (pi – c)(Ai – Bipi)

– Subject to:∑k

i=1(Ai – Bipi) Qpi 0

Maximize profits

Production capacityPrice

c 10Q 4000Segment Price Demand Profit1 141.666666651042 =5000-20*B4 =(B4-B1)*(5000-20*B4)2 79.1666666744792 =5000-40*B5 =(B5-B1)*(5000-40*B5)Total =C4+C5 =D4+D5

Example 15-1: Pricing to multiple segments• If the contract manufacturer were to charge a

single price over both segments, what should it be?

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and

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and

d1 = 5,000 – 20p1 d2 = 5,000 – 40p2

d = (5,000 – 20p) + (5,000 – 40p) = 10,000 – 60p

Example 15-1: Pricing to multiple segments• For segment 1 and 2:

– p = Ai/2Bi + c/2 p = 10,000/(2*60) + 10/2 = $83.33

– Max (p – c)(A – Bp) Max (p – 10)(10,000 – 60p) = (83.33 – 10)(10,000 –

60*83.33) = $366,650

Differential pricing raises profit from $366,650 to $415,650

Revenue Management for Multiple Customer Segments• If a supplier serves multiple customer segments

with a fixed asset, the supplier can improve revenues by setting different prices for each segment– What price to charge each segment?– How to allocate limited capacity among the segments?

What if demand is uncertain?

The Park Hyatt Philadelphia

• 118 King/Queen rooms.

• Hyatt offers a pL= $128 (low fare) targeting

leisure travelers.

• Regular fare is pH= $181 (high fare)

targeting business travelers.

• Demand for low fare rooms is abundant.• Let DH be uncertain demand for high fare

rooms. • Assume demand for the high fare (business)

occurs only within a few days of the actual stay

How much capacity should Hyatt save for the higher priced segment?

Allocating Capacity to a Segment Under Uncertainty• Basic tradeoff between committing to an order

from a lower-price buyer or waiting for a high-price buyer to arrive later on– Spoilage occurs when the capacity reserved for

higher-price buyers is wasted because demand from the higher-price segment does not materialize

– Spill occurs if higher-price buyers have to be turned away because the capacity has already been committed to lower-price buyers

Allocating Capacity to a Segment Under Uncertainty

• Expected revenue = sales probability x sales price

Never sell a unit of capacity for less than the expected revenue

$128 $181.00 = 1.0 x 181

$128 $162.90 = 0.9 x 181

$128 $144.80 = 0.8 x 181

$128 $126.70 = 0.7 x 181

Allocating Capacity to a Segment Under Uncertainty

RH(CH) = Prob(demand from higher-price segment > CH) x pH

Expected revenue = sales probability x sales price

Never sell a unit of capacity for less than the expected revenue

$126.70 = 0.7 x 181

Allocating Capacity to a Segment Under Uncertainty

RH(CH) = Prob(demand from higher-price segment > CH) x pH

pL = Prob(demand from higher-price segment > CH) x pH

Prob(demand from higher-price segment > CH) = pL/pH

Expected revenue = sales probability x sales price

Never sell a unit of capacity for less than the expected revenue

$128 $126.70 = 0.7 x 181

Allocating Capacity to a Segment Under Uncertainty

Prob(demand from higher-price segment > CH) = pL/pH

CH = F-1(1 – pL/pH, DH, H)

Prob(demand from higher-price segment CH) = 1 – pL/pH

Prob

CH pL/pH1 – pL/pH

Example: Allocating Capacity to a Segment Under Uncertainty• Assume that demand for rooms at the high rate is

normally distributed with mean 102 and standard deviation 20.8. Also assume that the high rate is 181 dollars and low rate (discount rate) is 128 dollars– Determine probability that expected marginal revenue of higher

rate class will exceed marginal revenue of lower rate class• pL = 128

• pH = 181

• 1 – pL/pH = 1 – 128/181 = 0.2928

– Convert that probability into the number of rooms• NORMINV(1 – pL/pH, DH, H) = NORMINV(0.2928, 102, 20.8)

= 91 Hence, 91 rooms should be reserved for the high rate class

Example 15-2 Allocating Capacity to Multiple Segments• ToFrom Trucking serves two customer segments. One

segment (A) is willing to pay $3.50 per cubic feet but wants to commit with only 24 hours notice. The other segment (B) is willing to pay only $2.00, but is willing to commit to a shipment with up to one week notice. With two weeks to go, demand for segment A is forecast to be normally distributed, with a mean of 3,000 cubic feet and a standard deviation of 1,000. How much of the available capacity should be reserved for segment A?

Example 15-2 Allocating Capacity to Multiple SegmentsRevenue from segment A pA =

Revenue from segment B pB =

Mean demand for segment A

DA =

Standard deviation of demand for segment A

A =

Capacity to be reserved for segment A

CA =

$3.50

$2.00

3,000

1,000

F-1(1 – pB/pA, DH, H) =F-1(0.4286,3000,1000) =2,820

Example 15-2 Allocating Capacity to Multiple Segments• ToFrom Trucking serves two customer segments. One

segment (A) is willing to pay $3.50 per cubic feet but wants to commit with only 24 hours notice. The other segment (B) is willing to pay only $2.00, but is willing to commit to a shipment with up to one week notice. With two weeks to go, demand for segment A is forecast to be normally distributed, with a mean of 3,000 cubic feet and a standard deviation of 1,000. How much of the available capacity should be reserved for segment A?

How should ToFrom change it decision if segment A is willing to pay $5 per cubic foot?

Example 15-2 Allocating Capacity to Multiple SegmentsRevenue from segment A pA =

Revenue from segment B pB =

Mean demand for segment A

DA =

Standard deviation of demand for segment A

A =

Capacity to be reserved for segment A

CA =

$5.00

$2.00

3,000

1,000

F-1(1 – pB/pA, DH, H) =F-1(0.6, 3000, 1000) =3,253