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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Guillermo Gallego Özalp Özer Robert Phillips
Columbia University Stanford University Nomis Solutions
Revenue Management and Pricing Conference
June 11, 2004
We model the situation where sellers compete on quality rather
than price. A seller has constrained capacity available of different
What is the seller’s strategy for maximizing contribution?
Delivery Lead Time:
< 1 Month
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.
Accept with Prob. p11
(Capacity = s1)
Accept with Prob. p12
Accept with Prob. p21
(Capacity = s2)
Accept with Prob. p22
Which class of capacity to offer to each customer segment in order to maximize expected revenue?
Since price is the same for each transaction, maximizing
revenue is the same as maximizing total sales.
What policy maximizes total expected revenue (capacity utilization)?
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
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.
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.)
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.
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.
Implication for customers: Try to convince seller that lower quality products are unacceptable in order to obtain a better offer!
Segment 1 is always offered product 1 if it is available. Key question is
which product to offer Segment 2?
The offer to segment 2 depends upon time and available inventory.
For the first period:
Offer Product 2
Offer Product 1
Dependence of optimal first period Segment 2 offer on Segment 1
Offer Product 2
Offer Product 1
2 Segments, 2 Products
3 Segments, 4 Products