Capacity Allocation to Support Customer Segmentation by Product Preference

Guillermo Gallego Özalp Özer Robert Phillips Columbia University Stanford University Nomis Solutions

4th INFORMS Revenue Management and Pricing Conference MITJune 11, 2004

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Competing on Quality

We model the situation where sellers compete on quality ratherthan price. A seller has constrained capacity available of differentqualities.

• Customers pay a uniform price for capacity regardless of quality. • Customers belong to different segments, known to the seller. • Segments differ in their strength of preference for different qualities. • When a customer arrives, the seller can choose which quality class to offer. • The buyer’s probability of purchasing depends on the quality (class) she is

offered.

What is the seller’s strategy for maximizing contribution?

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Who should be offered the slots?

• Individual Owner/Operator• Very time-sensitive

• Small local fleet• Somewhat time-sensitive

• Large fleet• Not time-sensitive

Delivery Lead Time:Slots Available:

< 1 Month6 Slots

1-3 Mos.12 Slots

3-6 Mos.34 Slots

?

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Example: SF Giants Baseball

Giants offer 13 ticket pricesbased on section.

For a recent game, 69 price points were listed on-line withclear price differentiation basedon quality within a section.

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Other Examples

• Made-to-Order Manufacturing: Short vs. long lead-times• Planned Upgrades: Sell some (but not all) high-quality inventory at

lower price• Hotels: “Ocean view” vs. “parking-lot view”• Airlines: Aisle vs. middle seat• Concerts: Better seats within sections• Contract Manufacturing: Must allocate capacity to OEM’s at same

price.• Free or Bundled “Value-Added” services: with limited capacity

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Why not charge for better quality?

• Competitive reasons• System constraints• Desire to maintain price simplicity and/or stability• Customer acceptance/market custom• Upgrade strategy

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Alternative Allocation Approaches

• Best-first: Allocate best capacity to customers arriving first

• On-request: Allocate best capacity to customers who request it.

• Customer-based: Allocate the good stuff to particularly loyal or “strategic customers”.

• Revenue Maximization: Allocate in order to maximize total revenue.

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Decision in Each Period

Class 1(Capacity = s1)

Class 2(Capacity = s2)

Which class of capacity to offer to each customer segment in order to maximize expected revenue?

Accept with Prob. p11Accept with Prob. p

12

Accept with Prob. p21

Accept with Prob. p22

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Comparison with Revenue Management

Revenue Management “Quality Management”

Fixed Capacity Fixed Capacity

Uniform Quality Differential Quality

Differential Prices Uniform Price

Manage Fare Availability Manage Quality Offerings

Maximize Revenue Maximize Profitability

Since price is the same for each transaction, maximizingrevenue is the same as maximizing total sales.

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The Model

• n customer types,• m product classes, • sj > 0 is capacity of product class j,• i = index over customer types,• j = index over product classes,• common price P=1 for each sale,• customer of type i arrives,• we observe his type, offer class j,• customer accepts with probability pij.

What policy maximizes total expected revenue (capacity utilization)?

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Key Assumptions

• Each customer segment has the same preference order over classes, that is, pi1 > pi2 > . . . > pim , all i.

• Appropriate when “quality’’ is generally agreed upon• Early delivery vs. Late delivery

• Aisle seat vs. Middle seat.• Not appropriate when preferences differ by segment

• Smoking vs. Non-smoking room

• Color of automobile.

• Customers book ahead of time and are served simultaneously• Time-varying independent arrival probabilities by segment (Lee and

Hersh type model)• Each arrival has demand for a single unit of capacity

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Dynamic Programming Formulation

• In each period t a customer of type i arrives with probability ri(t)

• Value-to-go function:

V(t,s) = V(t+1,s) + ri(t) max (pij (1 - Δj V(t+1,s) )+)Σi=1

m

where:s: vector of remaining capacities0: first booking periodT: last booking period

Δj V(t,s) ≡ V(t,s) – V(t,s-ej), where ej = jth n-dimensional unit vector

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Some Structural Results

• 0 ≤ ΔjV(t,s) ≤ 1. Offer some product to every arrival.

• ΔjV(t,s) ≥ ΔkV(t,s) for i < k. Better products are more valuable.

• ΔjV(t,s+u) ≤ ΔiV(t,s) for u > 0. Value decreases with capacity.

• ΔjV(t,s) ≥ ΔiV(t+1,s). Value decreases as time passes.

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Special Case: Single Customer Segment

A single customer segment with acceptance probabilities

p1 ≥ p2 ≥ … ≥ p1 .

Optimal policy: “Best first” is optimal. That is, offer products in order of decreasing acceptance until availability of each is extinguished or the end of the time horizon is reached, whichever comes first.

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Special Case: Deterministic Acceptance

Behavior of customer segments is deterministic, that is a customer of type i will accept any product j= 1,2,…,i and reject any product j = i+1, i+2, …, m with probability 1.

Optimal policy: Offer worst available capacity that the customer will accept. (Follows immediately from Δj V(t,s) ≥ ΔkV(t,s) for i < k.)

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Special Case: Two Products

Multiple segments but two products.

Define ri ≡ pi1 / pi2 > 1 and order customer segments such that r1 > r2 > . . . > rm.

Optimal Policy: If it is optimal to offer class 1 to segment k, then it is optimal to offer class 1 to all i < k. If it is optimal to offer class 2 to segment k then it is optimal to offer class 2 to all i > k.

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Segment “Nesting” (Two-Product Case)

Segment pi1 pi2 ri

1 .1 0 ∞

2.9 .1 9.0

3.5 .1 5.0

4.8 .2 4.0

5.6 .5 1.2

61 .9 1.1

7.5 .5 1.0

Optimal policy: Each period with s1 > 0 determine k such that segments i < k are offered product 1 and segments (if any) i > k are offered product 2.

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Implications with Two Products

• A customer who will only accept the higher quality product will always be offered it if it is available.

• A customer who is indifferent between the two products will always be offered the lower quality product if it is available.

• What is offered other customers will depend upon time, relative availability, and anticipated future demand.

Implication for customers: Try to convince seller that lower quality products are unacceptable in order to obtain a better offer!

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Simulation Results: Model Parameters

• Two segments• T =20• Arrival rates: r(t) = (.4, .4), all t.

• Acceptance Probabilities pij:• Segment 1 = (.7, .1)• Segment 2 = (1,.9)

• Parameterize on starting capacity • S1 varies from 0 to 20

• S2 varies from 0 to 15

Segment 1 is always offered product 1 if it is available. Key question iswhich product to offer Segment 2?

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Two-Product Optimal Action Space

0

5

10

15

20

0 5 10 15

Capacity 1

Cap

acit

y 2

Offer Product 1Offer Product 2

(S1)

(S2)

The offer to segment 2 depends upon time and available inventory. For the first period:

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Dependence on Segment 1 Acceptance Probability

0

5

10

15

20

0 5 10 15

Capacity 1

Cap

acit

y 2

Offer Product 1Offer Product 2

p1=(.3,.1) p1=(.4,.1) p1=(.7,.1)

Dependence of optimal first period Segment 2 offer on Segment 1 acceptance probabilities:

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Simulation

• Simulate effect of alternative policies:• Optimal• Best-first heuristic• Random choice

• Simple Simulation• 5 units of capacity per product• 10-20 periods

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Example Simulation Results

0

1

2

3

4

5

6

7

8

9

10

10 11 12 13 14 15 16 17 18 19 200

5

10

15

10 11 12 13 14 15 16 17 18 19 20

Capacity

Optimal

Best First

Random

Period Period

Sal

es

Sal

es

2 Segments, 2 Products 3 Segments, 4 Products

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Simulation Results

• Best-first is a good heuristic, providing substantial gains over random allocation.

• The optimal policy increases sales over best-first by amounts from .5% to 8.5%• With more segments, the value of optimization goes up• Best first is good

• With little time left relative to capacity • With lots of time left relative to capacity

• Optimization makes a substantial difference in the ``intermediate range’’

• Improvement from optimization increases more with additional segments than additional products.

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Extensions

• Extension to multi-class/multi-product cases.• Dynamic fulfillment models (e.g. lead-time differentiation)• Simultaneous price and quality selection• Value of segmentation – how much does ability to segment gain

relative to selling to aggregate segments?• Customer strategies and equilibrium – customers should seek to

be perceived as having high acceptance ratios. They especially want to be perceived as likely to reject low-quality offerings.