design of capacity-expandable product for competing buyers yue jin, qiong wang, ulas ozen, mustafa...

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


Lucent Compact Lite

800mm (31.5”)

450mm (17.7”)

NT Village

857mm (33.75”)

471mm (18.5”)

NT Village1030/3030 vs. Lucent BTS4400


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


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


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



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



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


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


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’



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 *])*)([(



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



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 *])*)([(



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



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



Manufacturer's profit

θ

Software Hardware

Buyer's profit

θ

Software Hardware



System profit

θ

Software Hardware

Manufacturer's profit

θ

Software Hardware



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



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



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


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


Discussion

Q&A

design of capacity-expandable product for competing buyers yue jin, qiong wang, ulas ozen, mustafa...

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