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Capacity Allocation to Support Customer Segmentation by Product Preference. Guillermo Gallego Özalp Özer Robert Phillips Columbia University Stanford University Nomis Solutions. 4 th INFORMS Revenue Management and Pricing Conference MIT June 11, 2004.

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Capacity allocation to support customer segmentation by product preference

Capacity Allocation to Support Customer Segmentation by Product Preference

Guillermo Gallego Özalp Özer Robert Phillips

Columbia University Stanford University Nomis Solutions


Revenue Management and Pricing Conference


June 11, 2004

Competing on quality
Competing on Quality Product Preference

We model the situation where sellers compete on quality rather

than price. A seller has constrained capacity available of different


  • 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?

Who should be offered the slots
Who should be offered the slots? Product Preference

Delivery Lead Time:

Slots Available:

< 1 Month

6 Slots

1-3 Mos.

12 Slots

3-6 Mos.

34 Slots


  • Large fleet

  • Not time-sensitive

  • Individual Owner/Operator

  • Very time-sensitive

  • Small local fleet

  • Somewhat time-sensitive

Example sf giants baseball
Example: SF Giants Baseball Product Preference

Giants offer 13 ticket prices

based on section.

For a recent game, 69 price

points were listed on-line with

clear price differentiation based

on quality within a section.

Other examples
Other Examples Product Preference

  • 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

Why not charge for better quality
Why not charge for better quality? Product Preference

  • Competitive reasons

  • System constraints

  • Desire to maintain price simplicity and/or stability

  • Customer acceptance/market custom

  • Upgrade strategy

Alternative allocation approaches
Alternative Allocation Approaches Product Preference

  • 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.

Decision in each period
Decision in Each Period Product Preference

Accept with Prob. p11

Class 1

(Capacity = s1)

Accept with Prob. p12

Accept with Prob. p21

Class 2

(Capacity = s2)

Accept with Prob. p22

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

Comparison with revenue management
Comparison with Revenue Management Product Preference

Since price is the same for each transaction, maximizing

revenue is the same as maximizing total sales.

The model
The Model Product Preference

  • 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)?

Key assumptions
Key Assumptions Product Preference

  • 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

Dynamic programming formulation
Dynamic Programming Formulation Product Preference

  • 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) )+)





s: vector of remaining capacities

0: first booking period

T: last booking period

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

Some structural results
Some Structural Results Product Preference

  • 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.

Special case single customer segment
Special Case: Single Customer Segment Product Preference

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.

Special case deterministic acceptance
Special Case: Deterministic Acceptance Product Preference

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.)

Special case two products
Special Case: Two Products Product Preference

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.

Segment nesting two product case
Segment “Nesting” (Two-Product Case) Product Preference

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.

Implications with two products
Implications with Two Products Product Preference

  • 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!

Simulation results model parameters
Simulation Results: Model Parameters Product Preference

  • 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 is

which product to offer Segment 2?

Two product optimal action space
Two-Product Optimal Action Space Product Preference

The offer to segment 2 depends upon time and available inventory.

For the first period:


Offer Product 2

Offer Product 1


Dependence on segment 1 acceptance probability
Dependence on Segment 1 Acceptance Probability Product Preference

Dependence of optimal first period Segment 2 offer on Segment 1

acceptance probabilities:




Offer Product 2

Offer Product 1

Simulation Product Preference

  • Simulate effect of alternative policies:

    • Optimal

    • Best-first heuristic

    • Random choice

  • Simple Simulation

    • 5 units of capacity per product

    • 10-20 periods

Example simulation results
Example Simulation Results Product Preference

2 Segments, 2 Products

3 Segments, 4 Products





Simulation results
Simulation Results Product Preference

  • 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.

Extensions Product Preference

  • 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.