Design of Capacity-Expandable Product for Competing buyers Yue Jin, Qiong Wang, Ulas Ozen, Mustafa Dogru April, 2008.
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Design of Capacity-Expandable Product for Competing buyers
Yue Jin, Qiong Wang, Ulas Ozen, Mustafa Dogru
April, 2008
2 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Outline
Motivation
Modeling of the problem
Analysis and findings
Discussion
3 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Lucent Compact Lite
800mm (31.5”)
450mm (17.7”)
NT Village
857mm (33.75”)
471mm (18.5”)
NT Village1030/3030 vs. Lucent BTS4400
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Nortel 3030 vs. Lucent 4400CDMA 850 NAR ID DC Cost Comparison
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
$18,000
1C3S 2C3S 3C3S 4C3S
LU 4400
LU 4400 w/EVDO
NT 1030
NT 3030
NT 3030 w/EVDO
+13% Error Bar
5 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Design decisions
Should we choose software-enabled capacity expansion design or hardware-enabled design?
Research focus:
What factors would affect our design decisions in addition to the cost factors?
Manufacturer Buyer
Service Provider
End-user
6 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Modeling of the problem – Manufacturer
Software-enabled design
q≤K: Software-enabled design has a strict upper limit on available capacity
C(q) = cs q + f(K): fixed cost incurred for initial delivery of products
f(K) = f*K: fixed cost is proportional to capacity upper limit
q
f(K)
K
cs
C(q)
f(K’)
K’
cs
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Modeling of the problem – Manufacturer
Hardware-enabled design
Hardware-enabled design doesn’t have a strict upper limit on available capacity
C(q) = ch q: fixed cost is negligible
f*K
K
cs
q
C(q)
ch
Cost equivalence condition:
cs+f=ch
8 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Modeling of the problem – Manufacturer
A monopoly manufacturer
Two-part tariff to the buyers: an upfront fee T and a per unit incremental price r
Cost of a buyer for using capacity q: T + r q
Modelling of the problem - Buyers
The layout of the network is determined by the service providers in advance of the purchase decision of the base stations. On each node of the network, the service providers place one unit of base stations
9 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Modeling of the problem - Buyers
N identical buyers compete in the end-user market by playing a Cournot game
Software-enabled design
Hardware-enabled design: no capacity upper limit constraint
Kq
qrqqNp o
q
s.t.
]))1(([ Max
Price in end-user market
Incremental price
Capacity used
Capacity upper limit
10 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Modeling of the problem – End user
Linear demand curve: p = θ – N q
Uncertainty in end users’ willingness to pay
D
P
p
Nq
θ
θ’
Nq’
11 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
Buyer maximizes his profit
His solution
His expected profit
Kqqrqpq s.t. ))(( Max
KqN
rqrKN
* otherwise, ;1
* ,)1( if 0
(T, r)
K
p(f K, cs)
Manufacturer Buyer
Service Provider
End user
Nq
Θ
TqrqpE *])*)([(
12 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
Manufacturer maximizes his expected profit
Upfront fee
Manufacturer gets the system expected profit
*]))[(( Max ,,s qcrEfKTN sKrT
(T, r)
K
p(f K, cs)
Manufacturer Buyer
Service Provider
End user
Nq
Θ
*]))*)([(( Max ,s qcqpEfKN sKr
*])*)([( qrqpET
13 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
Buyer maximizes his profit
His solution
His expected profit
qrqpq ))(( Max
1*
N
rq
(T, r) pch
Manufacturer Buyer
Service Provider
End-user
Nq
Θ
TqrqpE *])*)([(
14 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
Manufacturer maximizes his expected profit
Upfront fee
Manufacturer gets the system profit
*]))[(( Max ,h qcrETN hrT
*])*)([( qrqpET
(T, r) pch
Manufacturer Buyer
Service Provider
End-user
Nq
Θ
*]))*)([(( Maxh qcqpEN hr
15 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
rs < rh: rs (rh) is the optimal incremental price for software-enabled (hardware-enabled) design; Ts > Th.
][][ **sh pEpE ][][ **
sh qEqE
Price at end user market
θ
p
Software Hardware
Quantity of end user served
θ
q
Software Hardware
],[ if ,1
N
rK s
16 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
Manufacturer's profit
θ
Software Hardware
Buyer's profit
θ
Software Hardware
17 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
System profit
θ
Software Hardware
Manufacturer's profit
θ
Software Hardware
18 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
There exist some cases where Πs > Πh
even when software-enabled design doesn’t have cost advantage, i.e., under the cost equivalence condition: cs + f = ch
If θ is small, rs increases the amount
of end user served
if θ is large, the capacity upper limit helps dampen the competition between the buyers
Depending on f, Πs may be greater than Πh even without cost advantage
f*K
K
cs
q
C(q)
ch
Profit
f
Software Hardware
19 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
Without considering market implication of different designs
Decide designs under given prices (T, r)
Let θ0 = (N+1)K+r. Under the cost equivalence condition cs + f = ch,
If θ< θ0, T – fK + (r-cs)q = T + (r-ch)q – f(K-q) < T + (r-ch)q
If θ> θ0, T – fK + (r-cs)K = T + (r-ch)q – (r-ch)(q-K)< T + (r-ch)q
Πs > Πh only if software-enabled design has (substantial) cost advantage, i.e. cs + f < ch
With considering market implication of different designs
Πs may be greater than Πh even without cost advantage
20 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Analysis and findings
KM > N KO: KM (KO) is the optimal capacity upper limit when there is a monopoly buyer (when there are N identical buyers)
Optimal capacity upper limit decreases as f increases
Capacity Upper Limit
f
21 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Discussion
f(K) = f*K, upfront cost is proportional to capacity up-limit
A monopoly manufacturer
N identical buyers compete in the end-user market by playing a Cournot game
Linear demand curve: p = θ – N q
22 | Presentation Title | Month 2006 All Rights Reserved © Alcatel-Lucent 2006, #####
Discussion
Q&A
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