1. 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

2. Page 2 Competing on Quality We model the situation where sellers compete on quality rather than price. A seller has constrained capacity available of different qualities. 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?

3. Page 3 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 Month 6 Slots 1-3 Mos. 12 Slots 3-6 Mos. 34 Slots ?

4. Page 4 Example: SF Giants Baseball 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.

5. Page 5 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

6. Page 6 Why not charge for better quality? Competitive reasons System constraints Desire to maintain price simplicity and/or stability Customer acceptance/market custom Upgrade strategy

7. Page 7 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.

8. Page 8 Decision in Each Period Class 1 (Capacity = s 1 ) Class 2 (Capacity = s 2 ) Which class of capacity to offer to each customer segment in order to maximize expected revenue? Accept with Prob. p 11 Accept with Prob. p 12 Accept with Prob. p 21 Accept with Prob. p 22

9. Page 9 Comparison with Revenue Management Revenue Management“Quality Management” Fixed Capacity Uniform QualityDifferential Quality Differential PricesUniform Price Manage Fare AvailabilityManage Quality Offerings Maximize RevenueMaximize Profitability Since price is the same for each transaction, maximizing revenue is the same as maximizing total sales.

10. Page 10 The Model n customer types, m product classes, s j > 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 p ij. What policy maximizes total expected revenue (capacity utilization)?

11. Page 11 Key Assumptions Each customer segment has the same preference order over classes, that is, p i1 > p i2 >... > p im, 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

12. Page 12 Dynamic Programming Formulation In each period t a customer of type i arrives with probability r i (t) Value-to-go function: V(t,s) = V(t+1,s) + r i (t) max (p ij (1 - Δ j V(t+1,s) ) + ) Σ i=1 m where: s: vector of remaining capacities 0: first booking period T: last booking period Δ j V(t,s) ≡ V(t,s) – V(t,s-e j ), where e j = j th n-dimensional unit vector

13. Page 13 Some Structural Results 0 ≤ Δ j V(t,s) ≤ 1. Offer some product to every arrival. Δ j V(t,s) ≥ Δ k V(t,s) for i < k. Better products are more valuable. Δ j V(t,s+u) ≤ Δ i V(t,s) for u > 0. Value decreases with capacity. Δ j V(t,s) ≥ Δ i V(t+1,s). Value decreases as time passes.

14. Page 14 Special Case: Single Customer Segment A single customer segment with acceptance probabilities p 1 ≥ p 2 ≥ … ≥ p 1. 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.

15. Page 15 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 Δ j V(t,s) ≥ Δ k V(t,s) for i < k.)

16. Page 16 Special Case: Two Products Multiple segments but two products. Define r i ≡ p i1 / p i2 > 1 and order customer segments such that r 1 > r 2 >... > r m. 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.

17. Page 17 Segment “Nesting” (Two-Product Case) Segmentp i1 p i2 riri 1.10∞ 2.9.19.0 3.5.15.0 4.8.24.0 5.6.51.2 6 1.91.1 7.5 1.0 Optimal policy: Each period with s 1 > 0 determine k such that segments i < k are offered product 1 and segments (if any) i > k are offered product 2.

18. Page 18 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!

19. Page 19 Simulation Results: Model Parameters Two segments T =20 Arrival rates: r(t) = (.4,.4), all t. Acceptance Probabilities p ij : Segment 1 = (.7,.1) Segment 2 = (1,.9) Parameterize on starting capacity S 1 varies from 0 to 20 S 2 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?

20. Page 20 Two-Product Optimal Action Space Offer Product 1 Offer Product 2 (S 1 ) (S 2 ) The offer to segment 2 depends upon time and available inventory. For the first period:

21. Page 21 Dependence on Segment 1 Acceptance Probability Offer Product 1 Offer Product 2 p 1 =(.3,.1)p 1 =(.4,.1)p 1 =(.7,.1) Dependence of optimal first period Segment 2 offer on Segment 1 acceptance probabilities:

22. Page 22 Simulation Simulate effect of alternative policies: Optimal Best-first heuristic Random choice Simple Simulation 5 units of capacity per product 10-20 periods

23. Page 23 Example Simulation Results Period Sales 2 Segments, 2 Products 3 Segments, 4 Products

24. Page 24 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.

25. Page 25 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.