HD28
.M414
\
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
SUBCONTRACTING. COORDINATION. FLEXIBIUTY,
IN AGGREGATE PLANNING
AND PRODUCTION SMOOTHING
Lode Li
Sloan School of Manage me nl. Masitachusetts Institute ofTechnology
and
Morton Kamien
J I.. Kellogg Graduate School of Management. Northwestern Unwersity
#202e-88
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
.^'f
3 >?««.!»=:„
SUBCONTRACTING. COORDINATION. FLEXIBILITY,
IN AGGREGATE PLANNING
AND PRODUCTION SMOOTHING
Lode Li
Sloan School of Management, Massachusetts Institute of Technology
and
Morton Kamien
JX. Kellogg Graduate School of Management. Northwestern University
#2026-88
Subcontracting, Coordination, Flexibility,
And Production Smoothing
Mcirtnn
.1.
I.
In Aggregate Planning
Kaiiiirn
L. Krllogfc C'rafluato Srlionl of Maimfjciiicnt
Noitliwostci'ii University
Evanstnii. Illinois 00208
Loflr Li
Sloan Sriiool of Mana^cnirnt
Masparlinsctts Instituf'^
CaniluKlRr.
A]iiil,
f>f
MA
T<"rhnolopy
02139
1988
Abstract
W(" ])ropnpr a moflrl in wliirli sulirontractinp ran
planninc; ?tratop;y.
The
])o<;sil)lc
iiiarkrt
their transaction rnsts are discussetl
nisnis in
whirh films rofirdinate
inerlianisnis
if
cost fmictions
tory,
lie cxi'licitly
and non-market sulieontrarhnj^ inechanisnis and
We show
that a set of feasible
theii- jirodiirtion
the transaction costs are e(iual.
ability in jiroduction
ai-e
derived
suhmntraetins nierha-
via snl)ronti-arts rar(~to-(loiiiinates other
We
then study an exanii)le with (jnadratic
and a rnnrdinrtticn snhcontract; linear decision
and subcontracting];
consiflcird a? a jirodnction
In the exanii)le,
rules for jiroduction. inven-
suhcontractinR n'duces the vari-
and inventory. The same interpretation can be used
manufacturing resources.
for Hexibility of
1.
Introduction
Suh'-nntifirtiiif:
proflnrtioii
make
the prime cnntractdr's
in
nn item or srrvice
"tlic pinciirciiuiit of
is
ciwii
spcrifirationp availal)Ie to the sn])pliei'
can be
integration,
anrf horiz.ontal
vertiral
self-sufficient
in
its
all
(.1.
icciuircs
wliicli
Day
S.
is iii>riii;\lly ra]i;il)In
tlir
of ("roiKimir
cnntractor to
iniiiic
Desi)ite a hiRli degree of hotli
(195C)).
very doulitfnl wlietlier any mo'lern business enterjjrise
is
it
and
facilities
wliirli
Even ignoring the
activities
raw materials and the
of
])in-ciiase
use of distribution systems to dis])ose of Hnal j)ro(lucts, most comi)anies ajijiear tn dei)eiid u])on
other ])rodiicers
for-
dependence,
this
jierformance of
"th(~
some work and
least
at
extii-mely im])nrtant role that subcontracting ])lays in industry has been
(Sammil ami Kelley
recogni7,ed in the past few years as never before"
many
oliservers (Williamson (1985), Piore
exti^nsively used in the industries
firms, etc.)
and Sabel (1984))
and/or industrial
where manufacturing technologies have
for
i)oint
out that subcontracting
adjustment of labor force
plaiming (Holt
Bitran and
Hax
et
size,
(1900),
al.
(1977). etc
),
little
Sobel (1971).
has been said
into the production ])lanning models.
al)f)ut
among
subcontracting
In particular,
as.
strategies
holding inventory,
Despite the ennrmous work on aggregate
pricing anrl jirruiiotions
(19!38).
more
H(-xibility increases
an imjiortant o])lion
is
other ]>r"duction smonthing strategies such
Manne
is
to reali/c greater value of flexibility.
lie|j)s
aggregate production and cajjacity jilaniung (Schroeder (1981))
fcir
Because
gicatei- flexibility.
has also been long recogni7,(vl that subcontracting
can be user! as a sulistitute
hi particular,
(198(1))
rlistricts (.lajiaiK-se tr)ol makei's, Italian textile
the feasibility of subcontracting while subcontracting
It
Reflecting the extent of
servi(es.
how
Thomas
(1971).
Hax and Meal
(1975),
to formally incorjiorate subcontracting
I'nlike the alternatives
such as invent(]ry and adjustment
of jiroduction cajiacify, the feasibility of subcontracting dejiends not only on the decision of the
firm
itself,
interests.
but also on the willingness of other, jiossibly c(un])eting. firms
The
shift
from in-plant-))riiduction to milside
economic institutions empbiyed by firms
We want
We
to
sniirces
who may have
indicates a major shift
more
title of
between "make-oi-buy" decisions and "make-oi-subcoiitract"
Vertical Integration are
For examjile, Toyota
relies
more
of design decisions to lay the efficient
on many small firms
for the s\i])])ly of ])arts
those small firms are frecpiently namefl as "sul)contractors".
subcontracting relations of this kind can be treated
relations with raw material supjiliers.
subcontract'' decisions
we
decisions.
which
imt
is
in
the
How<'ver.
same way
products which are regularly prorluced
w(-ll
in their
own
1
facilities
Firms
From
the
length inider
of a firm.
on a ])ermanent basis, aud
managing the jiermanent
as that
the ciincern "f this
as \\iv subcontractors.
in
boundary
])ai)er.
refer to in this jiaper are tactic or operational decisions
the dynamics of the jirime producer as
the
strict definition.
viewpoint of ojierations managemiMit. the former that WilliamsDii (1985) discusses
the
in
markets and/or relational cmitracting.
to em]ihasi7,e that subcontracting discussed in this pajier has
fhfferentiate
conflicting
of
managing the
The
"iiiake-or-
which depend on
conti'act out parts or final
on a temjiorary basis due to certain
''phorks
111
or
s]i(it-iiiai'kct
tlic s]int-c(iiitrartiiif;
we
In this ])a])cr,
iiip:
show
Wc
use a dyiianiir
first
iirof^raniiiiiui::
ways
])ossil)le
namely, the
a ])artirnlar set of subeoiitrarts,
apjiroach to ilhistiate
ordinnticn subcontract
via the subcontract.
niiniinizeil
more desirable than any other subcontract,
socially
production
j)laii
can be determined
our
in
the rfinidinntinn snbcontrartinp; can be
(1900)
and
[ilanniiij^ morlcl,
The example
als<i
and hence, contribut(>s
method
(liven a
i-asily inclurletl
ccinal
We
also
Here, a ro-
contractor and
])riiiie
of subcontractinp;, the o])timal
model
We
into
Holt. Modi?liaiii. Mutli
tjir
then
slif)w
linear decision rules are obtained for juoduction
by an example that
Variability
is
and Simon
and subcontracting.
i-educcs the variability in jiroduction
to jiroduction siiioof hinp;.
.
Moreovei', the riuiiiliiintinn subcontracts arc
ctiiice])tual
shows that subconf ractin<:
tlic fcapil)iiity
suhront raets. Pareto-doiiiinatcs
rnnn///;afi'ijj
so defined that the joint ])ioduction costs of the
is
how
to ])rodiire a feasiMe snl)rontrart
any other subroiitrart, assninint^ the transaction costs of suhcoiitractiii!^ arc
subconh'actor are
tlic
ti-aiisar tiniis.
fletenunied and the
is
dismssril in this piipcr arc cither
i-;irts
fnriinilatc a ])rofi\irt ion ])lanniii)^ iiinfici tliat (-X]>hfitly rcmsidcrs puhcoutract-
as a ]ilaniiinK tool,
of a siibenntrart
Alsn. snliront
('iivirninnnit
flir ofoiioiiiic
and inventory,
smaller as the correlation of the
production requirements and the subconti-actins costs decrease,
2.
A Conceptual Planning Modpl with Subcontracting
In this section,
The main
subcrintractiiig
oj)timality
all
we introduce
a
to discuss the issues rec^arding
and
illustrate concejits of feasil)ility,
imrjiose of this section
and dominance relations
the decisions that
dynamic prop;rammin^', model
liav(^
is
to develo])
W(- adojtt vei'y <;en(~ral notation to incoi-porate
of subcontracts
been discussed
jiroduction
in th("
])lanninfi: literature
but do not sjiecify
rigorous mathematical assumjitions to assure the existence or uni([ueness of a solution.
we take
a unitjuc solution for granted. For sim])lirity.
we
assume there
also
In effect,
two ])roduction
are only
organiz.ations in the market, and the insights devfdoped in this section can be extended to the
situation witli
Two
more
firms.
j-irorluction organi^.ations,
firm
<
duction rcfiuirement stream, {D',.\
assume that the technologies
2"s
of th(^
production rcfiuirement with
tion i:ilanning setting, firms
its
f
and
1
2,
< T)
?
.
are in the market, each faces a frirecastcnl jiro-
=
1.2.
two firms are good substitutes,
jii-oject tlic
information and capacity constraints
tlic
t.
where
/,'
is
iin-aniiig. firm
existing technology and vice versa.
work
For
i
As
I
-
1.2,
iilaniii!:
denote by
jieriod
{P,'.!',) firm
ran
fulfill
firm
in the tyjiiral jiroduc-
force sizes. jH'oduction rates, overtime,
invfMitory levels in an aggregated iH-oduction unit for each
jieriod
For subcontracting to be possible, we
t
undertime and
based on the current
Ts decision variables
in
a vector of the decision variables which directly affect the jiroduction cost of
next jieriod and T/
period cost. Typically.
is
/,'
a vector of the decision variables whicji rlo not directly affect tlie next
may
include inventory levels by the end of jieriod
2
f
and work force
size at
/;
PI )n^y inrhuic innihirtidii
cost
vn\ the variHl)les in
is
vari;il)h's ;iik1
rniistraiiit
and
tion
,
must
state vai'ial)!es
D],
we assume
+
/
C.','_^,
7/
(
information (or
/;
,
for
)
=
j
the
us(^
the set of rdiistraints that the docisioii
Ix'
ej(f,'.
/,';
DJ,
/,'_,
To
)
ca])aeity
,
(Usniss the produc-
tlie
minimal
same
tlie
The
discoiuit factor
That
exi)ert(-d
/?
(0
<
/?
<
We
1).
For sim])licity.
each firm has (omiiletc information
is.
and
historic state variahles (ivquirements. inventory
same
belief re;;aidni5^ future re(|uirements, f^iven the
forecastinp; nu'thod)
Ix-
is
can he determined recursively
,
This assumjition
achieved through h'arniiiK,
Moreover, the sniicontractinf, mechanism
tnithfiil resjionses (see
Le
1,2.
'^^/i
cui'rent
and share
),
"
assume that firms know
v/c
t.
show that
to
However, complete information may
tionships.
t
a situation with comjihte information
data, work force sizes, etc
>
whifh on the next ixni'ul
effect of
on ronchtional on histoiiea! information aliout the i)roduction
1
ahout each others cost functions and
availal)ie
/,'_i)
tli(^
satisfy, for exaiii]i|e, the iiiveiitdiy liahiiice ciiiist raiut
siil)rontrartinp; derisions in ])eiifid
dynamic proj^ramminK
use
/,'.
Lot the jtnuhirtioii rost of jieiiod
etr.
requirements, denoted Ly
will
Let /;,(r/.
/,,
produrtion costs from
total
i;itc, ovcrtiiiic. aiifi iiinicitiiiic.
may
itself
Hurwicz (1072), Myerson (1979). and
may
sig;nallinf<,
l)c
too striui^ent.
and long-term
I'ela-
jirovide incentives for firms to give
also Section 4 for
more discussion on
tlie i.ssne).
essence, siihcontractinp
Ill
a snl)roiitract as a
Qi
jirire
a reallocation of jiroduction reipiirements
and quantity
jiair
[pi.Qi]
\hc subcontracting quantity from firm
is
U Qi >
firm 2
0.
and firm
trivial sulicontractiiig in
firm 2 gives the
will
is
subcontracts
2
which firm
1
same amount back
1
dejieiid
to firm
—Qt
\{
I
to firm
The
1.
0)
jiart
We
0.
of
may
define
and
i)ric(>
its
rule nwt
the
jirorluction to firm 2
and
exj)licitly
costs of subcontracting
Subcontracting
We
subcontracts ([uantity Q, to
I
Q( <
firms
the sulicontractiiig
is
firm
re.,
2.
to firm
(>
/>(
subcontracts a certain
eliminate this case as an ojitiinal solution
parties.
\vlier(>
among
we introduce
later
incur additional costs to both
Following Williamson, we categorize sul>contracting costs into jihysical costs (which usually
on the sul)contiacting ([uantify Q/) and transaetioii costs
Ti(Qt) (T,(0)
=
n),
includ(-s
subcontracting quantity
includes time and
in
the shi]uiient, handling,
arldition to
manpower
engineering and monitoring costs of the
production costs.
recjuiri-d for
Th<" variable costs, denoteil by
The
ti-ansa<'tion
costs, fleiioterl
by
F,,
generating and im])lem<'nting a subcontract (negotiation,
bargaining, comjMiting, drafting, and safeguarding against opi)ortuiiism, etc).
There are many
jiossibie
ways
to generate a su])coiitract
negotiation and bargaining for an agn-einent.
a (subcontracting) meriianis/d.
firm
1
intends to sul)contract
The
It
following
We
is
,
ranging from a simjile market game to
call a jjarlicular
way
of
producing a subcontract
an examj'le of subcontracting iiu'chanism, Sujipose
asks firm 2 to submit a
liid
/),
Based on the subcf)ntracting
])ricc
jif.
firm
(irriciop
1
how
to pul)roiiti;\rt vi;i tin- fullowiii'^ prdRraiii.
iiinrli
rl(r;.i;:D^ - Q,.
mil.
if
+ JuQ, + TAQ,)
,)
-^
.dl
ftf'!,
.
ij)
r,'.i;.Q,
oAr^.il.D] -Q,.i]_^)>{y
.^.t.
Drnotr the solution
of tlir ])ro^r;vm hy r/(7'/), l}{]>i)-
a function of state variables, but
subrontractinK prire
mm
Q,>().
j>f
romitiufi;
c^r^.Ir.D^
wo omit them
on
-
lli)
f 'citaiiily,
Qi(j>t)-
Firm
for notational sim])li(ity
best resjionse of firm
tlie
4 QiiPi).
-md
ViQiipf)
+
the solution
2
then ran
is
also
set
the
to the jirire. Tims, firm 2 solves
1
+
T,{Q,{pi))
pf'Uiillil'')' ^t)
r/.if.r<
g^ir^.llD^ + Q, {}>,). ll^) >
s.t.
Siipposr
/)*
is
for a
and quantity
it
n.
Then, a sulirontrart
tini'
would
aeeejit
The
rorresiuiiiding optimal produetinn derisions
determined
is
name
rould
I
(H course,
a prire and
that ])iire
at
subeontraet geniMateil by
Qii}'*))
deteiiinned ac<'ordm(^ly.
is
subrontrartiuR m(~rhanism (indexed by
sjierified in the
{]>'
For examjiie. firm
juissible
then firm 2 rould res])nn(l with the (|naiitity
hi general,
>
with subcontrat
meel anisms for suljeontrartinp; are
Jirire
;»,
the optimal in the alxive jtroRram
anfl the ]>roduetion jilan (for jteriod f)
otliei'
n,
.S").
tlu'
resultm(.r costs
denote by
w(-
and Qf the
;i^
merhanism and by
foi'
both
T/"
.
/,'"
the
jiarties are
where
Note
th;,t C','-
exrlude the transartion costs
F, sinre
they do not affert the optimization and hence,
can be treated separately.
Obviously, a subccHitract
without
subcoiitractin',';.
is
feasible
if it
yields each firm at
To establish the no subcontracting^
most the cost
sf;ifus tpw.
we
it
rould be
smr
solve the following
of
two
programs.
Program
i:
.r7,(r;./;.D;./;_,)>n.
,..f.
for
i
=
1.2. aufl flenote the
Definition 2.1.
A
Definition 2.2.
A
I
=
subcontract
subcontract
is
fe,Tsj7./e if
is
C','*.
Q]^
^
and
Cp <
fra/jsarhojia/Zy frasi/i/r
if
(",'
Qf /
for
(1
i
=
1.2
anrl (V,^
+
F,
<
r;,"
for
1,2.
The
(see
minimal costs by
feasibility, in fact, follows directly
Luce and Raiffa (1957)). For a
fixecl
from the notion
of iiiiUviiJu:il ratin/i;i/ity of
subcontracting mechanism S. a ])roduction
game theory
jilan
can be
derived via the
to set nil the !>tntus
deeisious followinj-^
sulirontrart
C]
=
ri'rnisivc r(iiii]iul at ion
followiii>;
(']'
<]iin.
tin-
si)erifie(I
i\il<-s
in
,
<
f>
—
t
1,7
=
above prorednre.
On
let
W(- liave fixed
=
C,'
period
=
1.2.
We
That
set
th(-
is,
meclianism
.S''
if
=
1,j
(']^
the
If
.
Otherwise,
1.2]
mechanism
This mechanism
let
dominance
.S''
lar^c
relations
C]^
if
may
feasililc
mechanisms can be very
dominates mechanism
.'^
<
C]^'
neith<'r firm prefers S' to S.
moment
transaction costs aside for the
-
f
and obtain
next establish certain
mechanism
say a
iloiiiinates
•S'
We
2
n'jieat the jirorednrc.
the otluM- hand, the set of feasibh- subcontractin-;
amoHR snbcontractinK mechanisms We
i
and
1
aiul
I
imply firms cannot find a transactional
and any ^wcn mechanism may not be the "best".
for
-
/
the snlirontrartinj^
rloes not
it
<
E\(V,^\D',.k
Prnprams
and cniresiinndinK jirodnrtion
snlirontraet in^ nuTlianisiii
1.2). (lO liark to
be transactionally infeasible. However,
merhanism.
tlie
Hist solve
t.
siilxont ract
tlic
r(iiii]iiite
transact ionally feasible, tlien
is
ElC^y \D\
In the
Sernnd,
Foi- rarli ])cri"d
Let
us look at
a set
of snbcontracts
generated as follows. First, solve a jiropram.
Program
0:
mm
s.t.
and
let
f^i'
C]'^'
Lemma
rrnnf.
=
,],{r;. /;.
and
C^,'
('',"
2.1.
0.
'
ci{r;'\i;'': D]
<
d] - Hr)Q,. /;_,)
solution coustitutefl by
assertion in the
lemma
th(-
-
+
n^)Q',' r;^,)
nii'l ('','
C','*
+
(",'
<
T,{Q'/)
C'/'^
is
+
+
(^J^
follows immediately
at a feasible solution to Pi-op;ram
Definition 2.3. A sulicontiact
quantity are determiner! by Qi
is
=
_ c^' - 0{cr +
;i^
1
=
,
Q;
which
i. 2.
valuables with sujierscript
/?^';, ,(//''. Ij'').
miy
fi^r
and
Pro^iams
Similarly.
,
is
C'/'
1
and
any Qi
4
'"',
2 ])his
sum
rj'
f)
is
;/ir,-ii,-i7ij.s;;j
evaluated
Qi =
0. anrl
since h[\) 4-^(2)
if tlic
a feasible
at
hence, the
=
Program
m(Thanism
subcontracting
i)rice
and
- rf _
)
(1
-
o)((:r
+
r.J'
first
0) evaluated
constittited by the solution (generated by
is
S.
a feasible solution to
the value function of
is
+ Cf"' =
("ertalnly. r/^"*
su/uo/jfr.-irfjn/'
2 jilus
cancelled in the
(\ be the
.
the optimal solution of the jiropram,
at
called a rc)nrdin:itif<ii subcontract
Q','
/^^•;+, (/;./'))
the value function of Pioi^ram
o])timal solutions to
(noticing in (2.1) that transfer value.
(;/•
T,{Q,) f
n.
d(~cision
feasible solutions fo Proi^rams
In jiarticular.
>
+
be firm Ts cost function evaluated
CJ' + Cj'
Note that the
ProRram
f{r.)Q,.ri,)
be the ojitimal value. corres])ondin<r
o[itima! solution,
i.e.,
-
}_^{r]ir;.!;.D]
- c ;-) - (cf - cf-)
and
<
for n
It
if
fl
can
<
Qi'
<
f)
easily vcrificfl the siilirontractiiip
1)0
and
<
(^,'
niauipulatiou to
Lemma
^- 0.
(//
if
1
*
f',
if
>
Q/
siiuo
hy
iniiinc'rafivr
is
costs iiioic to produce luoic.
it
<
that Cj'
iioticiii;',
Also,
C^]'
takes
it
'
little
f^et
Tlir tntal casts t« firms
2.2.
])ri(('
mid
1
2 uinlrv a fonidinntion suh'-nntiHrt with
pnrnmrtci
are
cr
=
-
('V
(i
In fact, to obtain a cotnihtuilinn suhcontract,
ojieratiiiK
jirice to
with coin])lete coordination as
Proposition 2.1. A
The
Procf^
rnnrijiiuttion siilu-Dntinrt
thrm
niiy incrhnnisin.
first jiart
Lemma
liy
cf
=
2.1.,
f:p. This
is
is
(I'l
always
thei-e
must
note that (!'
exists a
doable since
^
r:,"'
+(':f''
=
such that
?
('','
Lemma
2
by
C,',
<
C',''
> r:p u
Fii'st
of
all,
it
is
a set of
are e(jual. Secondly, unlike other subcontractinj_'
over,
is
socially
Propcsition
is
pinjity if
2.2.
an J only
The
a
=
(2.2).
4
C,','
()
.
2
tlmt siiliriniliFirt
and
I
l^y
.
2 2.
For any subcontract mechanism
C-'^
and
r'''"
C.',
=
,
foi-
=
C.',
_;'
r;;'
^
-
Set
r.
—
—(",]'
<
cj'
d'^'
such that
d'
c;p
if
—C!\
= l
/?
<
C',
,
since
undnminated subcontracts
mechanism,
if
wlieth("r the set
to test
ti-ansaction costs
results ni an uni(|ue subcontractinpj
minnni'/.rs thr total cusl
it
if
iin-
of ])roduction.
More-
of transactionally feasil^le
emjity or not.
Sujijiosr tlir trnnsnrtian costs nf coaiiJinnti'iii snhi-ontincts nir less thnn or
rqunl to that of any other
Prnnf.
moic desuable
we can use rnovdinntuni subcontractni;;
subcontracts
Lemma
f^cncvAtrd
discussion, we can see that the cnn/v/inafion subcontracts constittite an
subcontracts.
outcome which
fincl
1.
From the above
jKii'tant set of
sii}trniitr:\rf
wliii-li iIi<iniiiHtcs
Thini, under the coordination subcontract with jjarameter 0'
again by
For a
frnsi}<li\
of the proposition follows directly from
jiart,
mie firm, and then
in
.
exist a rcnKJinntion siiiirontrnct
To prove the second
S,
+ cf' —
q\iantity by
Hist deteiiiiinr snlicontract
fiiiiis
they were two de])ai-tiiients
if
divide the total cost savings, ('j'
+ rr -r,f)
-(>){(}'
if Q^," j^
siilirfintrnet
and
+
r:/'
"if" jiart directly follows
.
Tlien. the set of ti:ins:irtioiinlly fe:isihle .su/icnjifracf.s
df >
C','
Proposition
+
2.1
F,
+
To
not
Fj.
n-et
tin-
the transaction costs in the cost savings and divide C'* +''',*
price similar to that in Definition 2.3.
j.s
—
"only
if"
jiart,
we
—
F\
—
amon^
C',^
Fi
sim])ly include
firms via a
I
Wc now
iiroccrd to
fliscussinn alxnit thr ti-ansiictioii costs nhitifl tn diffcirut sul)rontrarting
,i
TIk' iiliysical costs of sulicoiiti-iictiiiK nsnally
iiicrlia.iiis]iis.
sulicontract
That
^diciatccl.
is
is
why wc
The
pi-o(lncc(i.
assumption
against, the
Let ns see
in general.
effoit
general consmisus
devoted
is
tc)
tiian single jilant
drastically
cost
more
why
As we can
models.
is
hard to
may reduce
liiKh
1
and
2.
conce])tual
transaction costs.
That
mij^ht take
nnvhanisms
not
ai-e
model. Piof^ram
Thus, the comjiutational
That
more
is
A
lot of
flifficult
usually not
of the transaction
jiart
However, the jiarameter
in
the
negotiation and bargaining, and
Ion;::
as f^tntiis
is
quo
to nail
down
it
This
is
the
of rtuniliii;ifi"u subcontracts.
jiartii's.
iciiutation effects, or regulations
the difficulties of dividing the benefits from subcontracting and lower the transaction
moi-(>
Williamson
(lOST))
mentions that
emj)liasis on building an intimate ]M'rsrinal
than on drafting and safeguanhng a
more extensively on subcontiacting than
is
contiact
rletailed
triie in
siu-cessful .lajianese
iidations
between contracting
This exjilains
The
the lhiite<l States,
man-
why
.Iapan(\se rely
discussion in this section
and proves their success.
ju'edicts
Subcontracting, Coordination, Flexibility and Production Smoothing In
whicli a
market mechanisms
ipjnore the
may have
situations, long-term relationshijis bc-tweeii
ufacturers place
3.
we can not
lience,
oui'
in
s])ecify
costs of rnnrdiupitinu subcontiactinjr.
pai'ties
in
liave low transaction costs.
nuxlerate for the ritardinntinii suhcontracts
major cause of high transaction costs
many
and
see,
than Piograms
way
on liow a sulicontract
will (li'jicnd
moflels and com]iutationally, they
jilannin'';
firms miglit have to use outcfuiies of other
In
,
the coordiiuition suliconti-acts
multi-plant
subcontracts
citordinntiitn
market nieclianisnis
tliat
in Projiosition 3.2
(Hfficult
relativ(^ly
is
is
tlic
treat tlic varialilc costs of sul)contractniK as iiiochainsni-
Out the transaction costs
in<lc])rnilcnt in the aluivc (hscnssion.
is
do not dcix-nd on
the jirecerling discussion,
subcontracting
in
we can
cfniceptually.
see,
We now
any jilainnng model
us(- a
sim]>le
thei-e
is
example
no
to
difficulty
in
An Example
considering
show how subcontracting
smooths juoduction.
Holt. Modigliani.
chiction cost function
framework
ties,
in
and
more
it
in
is
Muth and Simon
and deiiv a linear decision
our discussion because
simjib' to analyze, but
realistic
(1900) projios'- a (|uadiatic approximation of a firm's
models.
tlie
cpiadratic
rule for aggr<'gate plainiin''.
a])])ioximation avoids
(
We
ado])t
of quadratic costs
is
that
their
(uiibinatorial difficul-
the (|ualitative insights obtaininl in the framework
Another arlvantage
])ro-
])i-evail
the optimal solution for
the uncertainty case can be obtained directly from the solution of the ceitainty case as long a?
the cost function
is
jiositive definite.
this "certainty equivalence"
Holt, Modigliani.
Muth and Simon
j)rf)j)erty in their ('hajiter G.
Also, then-
is
(lOGO) discuss and jirovc
evidenc(- that linear rules
are optimal or nearly ojitimal not only for ipiadratic cost functions but also for
functions (Schneeweiss 1971, 1974).
7
more general
cost
To avoid rninplcx
we further
notiitinn,
roiistauf aiul lalior a-ljiistiiiciit rosts
stage jinuliirtidn
for firm
rf)f^ts
i
i.
ai<-
=
firms iiiniut
assiiiiir tli:i(
Tlicirfor.-.
iK^t'liKil'l'-
\]\r
;iiii
wnik finer
Hnll
fnllr.wiii;-
.!
size irlafivM^ly
(1900), thr
al.
1.2, ate
(3.1)
whoiT
D]
is
the pnidnctioii rate for ])riiocl
t,
I]
the produftioii rctinirriiient in ])ciiod
i,
and
r,'
is
W<- ran solve
two
tlie
same apjiroaeh
LGmma
3.1.
CV-,.
'^
=
7.
'
I>y
I'-vcl
the riid of
tlir
jHTiod
(,
an- constant cost i)aranif^tcrs.
single firm ])rol)lenis
.'^
hy
invciitoiy
flic
is
F(n-
/;.
i
=
t.
i
Mutli and Simon (lOGD)
as in Holt, Modi<;liani.
=
?
+ r; - D] -
/;_,
In ])artienlar,
1.2,
(U{i -
+
/\,)
(-i-(/o
-
i.-U{l
-
+
/\,)
+
(^'.,(1
(
-4,
-
^_^
^'r„)l
+
^T„.
(3.2)
(4, ,^^
-
A,)
+
r:4,)(/'
^,
- r„)l + d; + r„ -
(3.3)
2(-i,
if
r —
>
CO. wiif-rr A, (0
<
A,
<
Ij is fiir
f'l.A?
If
-
(2r:„
nf
i<<<)t
+
r;4,)A,
suhcontrartinp; strategies are eonsideretl, then
add more rondjinatorial
difficiilti(^s
F,
=
D.
?'
=
-
tlie
r'„
=
o.
(3.4)
transaction costs of snlirontracting will
the transaction costs are negiccted
if
This can he a gonrl a])i)roximatir)n when
1.2
By Proposition
long-term rolationshij).
(pi;iijrntii- r(ju:iti(iii.
to the analysis, as ilhistratcd in Section 2
the prolilcm hecoines relatively sim])le
assume
siuDlIn
2.1,
and
2 2..
tlie
On
the other liand,
For ilhistration. we
two firms have a good
suhcontracts are not rmiy
cnnrdinntiitii
Therefore, wc
always transartionally feasible, but also rareto-doiiiinate any
otli(-r
can reasonably expect that firms
follr)w a certaui r(iniihi>:iti"ii
subcontracting mechainsm. By the
dynamic j)rogramming juocedure
describeil above, for each period
are,
C,
=
ElC'i^lD',.!'
C} +
r.f
=
<
f
-
E[(^j"
l.t
+
=
1.2).
(/
subcontracts.
-
1).
Thus, the exi)ect(-d future cost
('r\D',..'^
<t-l.t =
8
l.2]
=
the ex])ected future ccists
in
E\C','\D\..''
Brogram
<t.i =
(for
1,2].
t
-
1) is
Honrp,
liy
''(crtainty {•i|iiivMl(-iirc"
flir
only need to solve
argument,
in ordci' to
wv
plan,
Mii- i>])tiiiial iiid'lurtioii
fiii'l
program.
tlic fnllowin;',
T
r^
g,.r;,/;,-=i.2,f=i
3.5)
il, + r; - Dj
-
Q, =
Ti{Qi) + T^iQi) ran also hr
jirovidrci
—
assnniin!; that Ti ((^) t-T'2((V)
the consideration
<\\Q
,?
first
=
t
= 1,2
3.C)
T.
\
hy a quadratic funrtion centered
a])]iroxiiiiat(v|
with the
In coiiiiiarison
he ohtaiiKvl
still
sinjd"'
numher
snl<contractin<r), this ])roKram has twir(- the
r)f
Qi's: tlie exjilicit linear decision rnle can
The
If.
at
0.
i.e.,
firm i)rol)leni (witliont
of decision variahles p\ns
fairly easily.
ord(M' conditions yield
-
r-u(f,V,
r,') -
r,'„(/;
-
-
r.'ci/;;
=
q,))
n.
(3.7)
(3.8)
(uP' ~
^4if'ci(//
-
r;c,(D,'
-Qt)) - <\2Pj
(3.9)
where
P,'
=
T/
-
("'2,,
=
(^i
-
Q> = ^[^^4i(^'Ci)'^'
where
C = CuiCaif +
for
in
P'l
terms of
Pi
r'
+
+
=
Z?(
Cn +
r7i2.
(3.9) to
be
(3. in)
^'42^'C2/fl.
.solvinp;
them
we have
-
il-l
-
^'22)
+
-
f'lJ/;
/,'-,
-
^"21)
^41^'0l//
+
[(^'4i(^'0i)'
.
Rewrite
^-'5,
- ('nP' - (\i<'ui] +
(iiP,'
\{(\7{(\7? + (\7)Pi +
^'12(A'
D^ + Dj
-
SnhstitutinK (3 10) into (31)) and (3 G) and
("n
^-
+
where
+
H
/;
''i^P]
+
(^'
+
^'12)(//
-
//-,
-
('21)
+c'i2
r.'n
Pf =
=
^3,72('i,. ;uid /;
(42(^^,2)'^;
/,'_i.
^-
=
-
Cr42(r:c2)^
and
/,'
^'2,
^-11)^^
-
+ ^'nC? + {(
UsiiiK efinations (3.10), (3 11)
/,'
^
(-nni' - ili -
f>22)
- (Ai(\ill + ^Vc2/7l-
the total ]Hoduction retinirement in i)eriod
of differeure erjuations of
(3.11)
^'42^'C2/,^1.
and
(3.12).
/
(312)
and
('
=
wr can obtain from
^'AiI/'Ci)
(3.7)
and
+<^m2(^'02)
(3.8) a
+
system
as followinp;.
ai/;+i
-
(2r,,
+
hi)ll
+
a,//_,
+
dilf+i
-
('/i
+
'I7
+
<)l!
+
'hij-i
+ ^l =
"•
(313)
«2/7+i
-
(2^2
+
l>2)lf
+
^2/7-1
+
''2/;+,
-
(''1
^
'h
+
')/;
+
'/1//-1
+>!? =
"
(3 14)
where
+
for
7
=
1
.
2
J 7^
.
Solving
/,'
and
7[.
methods
7
=
(U,('o,D]).
linear differeiire etjnatidiis (3.13)
tlie
and
we can
(3 14),
nl)tain the (h^cision rules for
derision rnics for ])i(ulurtinn and sulxdntraetinj^ follow directly.
For general
of polvinR linear difference erinations. see Miller (10G8)
We now
for
+
D',)
7
tlie
and
-
^'n(^-i,(Z?;+,
1. 2.
look at the situation in which firms liave syiiimetiic cost fmictions
;t
=
ecjuations (3.13)
7.
1
=
a
and (3.14)
is
=
a,, h
h,.
d
=
d,
and
-=
/„
/,;.
foi
sum and
easy to solve. Takuip; the
7
=-
1,2
Let C^
=
(7;.,
Then, the system of
rhtfcriiice of (3 13)
and
(3.14).
we
obtain the following; two system of dith'rence e(iuations,
where V,
=
//
+
(a
+ d)U,^i -
(2(a
+
d)
+
h
+
r)ir,
+
(a
+
d)U,_i + A] 4
[a
-
-
(2(a
-
d)
+
//
-
e)V,
+
(a
-
r/)r,_i
If
r/)V',+ i
and
V,
=
//
-
Each
/,'
of (3 IG)
and
(3 17)
is
=
0.
(3.1G)
+ A\ ^ A] =
0.
(3.17)
/I;
a sin<.dc varial)le linear differenrc
efpiafions which can he solved easily. OhserviuR that
ri
+ r/= <\{2{(U((\? -^(\)
4
(>^)
+
f'n).
+
r
= (UW('i{('<if +
n-
d
=
h
('i{2{(^i{(\f 4 ^'4^'c)
b-r. = (',{2ni
and etjuations
(3.11), (3.12)
Let X and A*
lie
and
+
f-n).
+(';n).
we have
(3.10).
tiie
folhwin;^.
the smaller roots of
CiA^
repjjectively.
f'l)
Note that A = A* when
-
f'n
(2r;i
=
+ Ci)X -r, =
OO.
10
n.
(3. is)
Lemma
3.2.
F<>r
i
=
1.2.
oc
+
=
^''
^'i(/n-f'5)l +
c;,(2-\) +
-
(r:,(l
r;,
-
A)
f's.
(3.2(1)
E^''^''^^'+^ - ^i+i) + ^*<'oDU
(^,){I„
-I
^
+ aD] +
C,)]
(1
(h
- n)D] + C2
f
(3.2i;
26i
"^
1
(3.22)
ifT
—
>
oo. w/jnr'- A
;s
tlm suinUrr nu.f of (3 IS),
fm
=
?'
J. 2.
j 7^
7.
(3.23)
D;
=
^
^
~
'
<*i,
D,
p,D\
4
(1
p,]Ol
-
= -d
P,
-(
+
^'n(^'i(2- A)
2ni(U{c^{(-^ + i)(2_ A*)
=
+
(3.24)
r'4)
+ rn(r:,(2-
i)
^
Ai
^).
for
.
= .D,.(1-.)P,,
v=
f
>
A')
+
r4)'
2.
^'''^
2(rMr,)^^r:.)-,r„
'
or cqiiivalrntly.
i);
=
7,d; +
-
(1
7,)r/.
D;
AZ?,
=
-
£>/
D;.
Noti(<' that
invrntory of firm
in (3.3)
ami
.=!nm of its
AD, =
ill
i
- Dj.
Z?;
the hIiovc
in the
Iciiiiiia.
same
vrry
:in<l
=
(\D',
7,
=
-
(\(^cD',.
AD, = D] -
we
liii(~ai'
iiiti'iitioiially
form
as tliosc
(3 4) rxrrpt that instead of nsinp only its
own demand and
the otlier
fiiin s
demand
+
/?,„
(! --/?,)(
1
-
(3.2G)
,,),
(3.27)
Dj.
write
it
nsc^
flic
in
derision nil<s of piiulnrtidii and
a siiiiHc-finn
own deniand
Tiie
i>laiiiiiiiK ])r()l)lciii
forerasts, firm
weip;lit.>!
on
its
7
a?
uses a weighted
own demanrls mrreases
as the cost of snliront raeting (^'n) increases, the derision rules roiiverge to those of a single firm as
('n ai>]>roarhes infinity,
of the
two
and
at
tjie
in tlieir d(Misioii rules
other extreme, firms sim])ly use the aiitjimetic average
when
C'd
=
0.
11
demand
Lemma
3.3.
zrif
fioiii
i<<
Tlir wrifrJits.
r\.
of the
—
two
rr'^,
{ /J,'
(nv\D^.Dj] =
aii'l
firniaiul streams.
Proposition
For
3.1.
/','
,
<
^
=
whm
e(/tja/)7jes hnli} c\njy
nf invrntmy nu<I jir"(hirt inn
fi/'His
f/erj-ease a;)(/ file
=
j
1,2
tlie
first
result
same exeept
same exjieeted
as f'd inricnsos
is
iii(ir])<Mi'l('iit
n\\<\
<
;ia Z"/)^'
—
;is
liy
jx'ii"'! to jicTind. /?[DJ]
where- p
is
—
ft,
tlic ((nrcl.-itioii cooffiriciit
fjnfis.
"f
= 00
("i,
Tlint
eiq\']^o.
<
Vnr\r;'']
Var\I\].
I
/"ii/if
Vnr\ri\.
is. si;/i'-finfr;i'-fi/ir^
as thr anlirontrnrtiiif; ens^
js
nat
icijnrr-s
ti<(> liiyli <ir
Hirrrases as
<iu;\iitity
v:iii:i}iihty
and
jiroiUirtion
ronrhitiou corfBcicnt of
tlir
ilrcrrn^cs.
C,',,.
simjily nntirinp Miat
thr
thr ilrnmiiils of thr
M<>rr(<vrr. t]\r v:iri:iiirrs of iiivriitnry
tlic s^dirontinrtiuf:; cast.
oln'imis
1.
E\ri"] = E\rii
E[ii\.
p
>
t
from
th''
lules witli
;iiifl
witliniit siiliroiitrrirtini^
twi firms iiave the
for usinp; {hlfereiif (lemaiifl forerasls. hut ii<'maii']s f^r tlie
vahie.
To prove the
seroiifi result,
Var\D]\
note that
fii'st
= Var\P,D]^
=
P^Var\D',\
-
{\
+
Pi)D\\
-
(1
p,)''Var\D',\ ^ 2/?,(l
rT'-2/?,(l -/y,)(i
Sivoiul,
nnr
linlf to
1
vanaji'T of thr suJx-oiitrnrtiuf;
dcinniid. p. (irrrrasrs find
are
inrirn^r fmin "iic
1,
1} nrc
nir imt jirrfrrtly (imsitivrly) rnrirlntri]
Proof. Tlie
>
t
Hrin:^ hnvitii^ syiiuurtrir rosf
Var\r/']
thr
>
f
.
prr^ for
—1 <
E[r^']
a.u<i
f"r
nii'l 7,,
inHiiity.
Appuiiir thnt thr dcinaii'ls
Vnr\D',]
p,
-
~ p ,]< Uw\D',
.
(2.28)
D',\
pW-
we rewrite
1=0
+ 21=0
Note that we assume iiifiependeure
(in(h'pen(hnit of p
Far[DJ)
is
and
C^,)
inereasinp: in p
Vnr\Di] = Vrtr[D;]
solely via Far[£)J).
if
In-twe-eu jieriods
and
tliat
I[
and
/,"
has the same huear form
and have demands D] and D] respeetively. By (2.28)
and
and only
C',,
if
/7
sinee
=
I
/?,
or
The rnnrlusion with
=
1/2 wlien
n„ = co
(P,
=
r.',,
1)
^
And
and
p,
is
anrl
inrreasinR in
12
C'n.
Var[f;'") dejx'nrls on p
respeet to the jiroduction deeision rule ran
proved.
Lemma
l)e
3.3..
and
and Oq
similarly
To ralruhito the
nf
vr\ri;iiicc
AD, =
Q[
note
.
- DAD,,
{2p,
tliat
AD, =
-
(r,(27,
1)
Thrrofon-. Kar[(yj'] must he soino jjositivc term inultiiilird
=
Vrtr(AD,l
wliicli (Icrrcapps as
/)
+ V nr\D\\ -
^^«r[D;]
iiirroaso?, aii'l tlic ])ositivo
- (\(\{2p, - 1))AD,.
V ar\[\D,\.
l)y
2r.'o„[D;. D/j
term
2(1
-
^)r7^
dccri'HsiiiK finirtion of C,^.
tkw
is
=
Imt
I
From
the jn-oiiositinn.
we rnn
s(-c
tlint
siihroiitrartiiic;
ran
;il)snrli
plauniiiR strategies such as inventory. As a result, hoth iirothirtion
rednred.
show that
we do
If
more comiireliensive
a
sulicontractinp; heljis to
exercise to inchuh'
stal)ili7,e
ignore snhcontracting as a jilanning strategy
and when
corri'lated
the case that
demands
The model we
technology.
are
In
examined has the
As we mentioned
In the first case,
when
an" ni'gatively coirclatcd
liavc
good substitutes
work force
in
for the jihysical
the output of firms recjuires
the other case, the jiresence of
flexible"
as well
and im])lement
inter]iret ation
we assume
])ossibility
force
It
then,
jih-nniiinj;.
we can
])articularly costly to
is
a suhcontract
.
It
is
usually
the ])roducts of firms are substitutes.
if
s(>cond
the beginning,
six.e
inventory varial)ihtics arc
firms' ])rodiirtion n-quirements arc negatively
tln'
relatively easy to underwrite
is
it
th<'
aii'l
work
as dci other
tlic v;\ri;il>ility
to acc(-ss tlie value of flexible
Thi'rc co>ild be
of subcontracting,
two
cases.
technology that firms currently have.
similai-
tjie
two firms
that the technologies of the
manufacturing tethnology mak<'s firms
aljlc
to
fulfil
jiroduction ref|uiremcnts wdiich need tiaditionally different technologies. Therefore, facing flcniands
with traditionally different technology re(|uirements.
dcdicat("d t("chnologics but
it
is
it
is
is
iiifeasibh- to
have subcf)ntracting with the
feasible with the flexible technologies.
profluction ])lanning with two departments having
technologies,
it
demands
that
In the context of intrafirm
re(|uire
infeasible to cfioidinate the jirofluction reepiirements of
dc(licat(-d technologies
but
it is
ti-aditionally
different
two dejiartments with the
feasible to flo so with the flexible technologies
Having
this in
mind,
the single-firm ])roblems discussed above re]i|-escnt the o])timal plan with the dedicat("tl technologies,
while the nnilti-firm jnfiblem i(^])reseuts the ojitimal jilan with ])erfect flexible technologies, for both
inter-
and intra-firm situations.
We
can conclude that the
such as inventory and subcontracting to reduce
tlie
flexibility
mills.
order.
new system
flexible speciali^.atifin, as opposerl to standaiflizf^l
French and Italian
textili^ fiiiiis.
Piore and Sabel (1984)
rcai'rangements and
th("
i)f)int
search for
and Japanese
also a substitute for strategies
variability of j)roduction.
Piore and Sab(d (1984) ])resent a biilliant study of a
system of
is
tool
mass
of industrial ])roduction. a
])roductif)n
makers are exemjilary
American mini
of this
new
steel
industrial
out that technological innovation, constant subcontracting
new
jiroducts are the structiuing elements of the systems of
13
In the partinibu- cxaiiiijlcs of Frciicli
flcxililr ?]i('ciali7,ation.
nf (leiiianci results in
tlic
nmstant rearrangement
<if
and
Italian textile firms, tlu- variahiiity
snlxoutrartin!'; patterns: every jirime rontrartor
rtmld becniiie a snluDnt rarf or. every snlirnntraetor a prime enntraetur
close roiation? l)etween sulirontrartin<;
and
Hexiliility
Tlie evidenee indicafcs the
and between sul)eontrartinK and rnordination
of interorganization iM-ndnetion.
4.
Discussion
Variability in ])rnrluetion recinirements lias added moi-e comjilexity for researrhers and j)rarti-
tioners in produrtion ])lanninr:
Th(^
sinnnthiiie:.
The second
first
is
and srhednlinp;
through the
second
catppory. iiricing. promotion or
many ways
ai'c
in
is
falls in
the second cateiniry
Cnnrihuntinji subcontiacts. on
and Pareto-doniinate
all
tlu^
second
when the other
When
in^:
twf) categories of
(non market) mecha-
the numbei- of contracting
outcomes
l)ut
have
lf)w trans-
hand, yield the most total cost savings
othei
]iossible subcontracts, but
There are
roiitiacl
small, market meelianisms usually lesult in less desirable
action costs.
advance.
usuallv im])ossil)le).
wjiich a subcontract can be ])rodured
nisms. C^onrfJinnt if III subcontracting
is
(it
in
r)ther imjiortant strate<^ies in tlie
Subeontractin;'; ])lays an imjiortant role
I'c-jection
j)rn<lticti(m
Subcontractinp; as a production
itself
mechanisms: maiket mechanisms and iclational
sul)conti-actiiig
parti(^s
There are
rate(^oi-y
to eliminate th(< varial)ility comjiletely
fail
There
which represents j)roflnction
of inventory,
ns(>
thronsh modification of the demand jiattern
is
]ilannin?: strategy falls in the
stiatepies
There are mainly two ways to achieve
may
Considering
hav>- high transaction costs.
subcf)ntracting in ]>iofhiction planning, we need a cai<'ful study of the forms of subcontracting
mechanisms and
thiMr costs
Nevertheless, rdoidiuntidii subcontiactinjr can
the set of feasible subcontracts
To have subcontract
to forecast thiur
When
it is
also
own
in'-';
nonem]>fy and
is
as a
planning
question here
hi
is
how
s
cost clata
demand
which
is
is
not difficult to do
"correctly" than to do
In
firms o))tain other firms" jirivate information
lie
iiidu' cs
may
Firms do not only need
in
those situations
lead to the consensus on inhuiiiation
if
As we arguecl
subcontracting
Sul)contiacting recjuires additional coin])utation
14
for
if
sometimes,
each individual firm. Firms
r(ii)tili:witii>u
they don
t
subcontract.
have
it
in
the
The
first
look for an ojitimal subcontract
In
befori'. learning
is
hi jiarticular,
truth-telling behavior, naimdy, incentive
subcontracts (Huiwic/, (1972) aiul Myerson (1070))
informational losses
whether
formulated as a game with incomjih'te
snludutracting via rtdational contracting, one
within a subset of feasible subcontracts which
coiii])atible
it
crucial in determining a
subcontracting via markets, the situation can
iiiforinatioii.
test
subcontracting (juantities.
liidit"
we need more information
the prorlucts of firms are good substitutes, this
need each other
least
procluction i-eijuirements but also need the other parties d<'mand informatir)n.
easier to jn'edict total industry
place,
tool,
jiroject the
at
general,
firms
would incur
and re])utation
efF(-cts will
carried out on a long-term basis.
For exam]ile. we nee<l to solve a multi-firm
]A:\u
ill
WIk-h
(U'lor to Bii<! a /'(uirilmnfuni sulicontrart
this iiicicHse
miiqint
111
;\t
lull
is
As
iii(>i|(m;iI('.
in
nur
tlir
i-xniiiplr.
saiiK' liurar rule as in sint'lc-fii in i)r('l>lrni aii'l siiii]>ly ic])lacc
of the ic^quiromcnts of the
two fiims
\\'licn
the
liur'hui of a C(uir(liii:tti<in snl)roiitrart will Ix-
numlxT
heavy,
nuinli'T nf jiartics in cnntrjict
aii'l
we inn
the
is siii;ill,
src tliat firms nsr tlic very
icciiiirciiK-iits ]>\ tlic wciglitcf]
sum
of jiartics iiicii'ascs. tlu' coiiiiJUtational
sonu' sim])lr maikct
mechanism may be
prefcralilc.
rriciiiR
tion.
a very iiii]ioitaiit stratef.^y
is
(iiic
certainly shoiihl consider in oiKaiiiz.inp;
j)rocliic-
Kamieii, Li and Samet (1988) study a one-shot piiciiK: ^njuc with sul)contractiiip;. There, we
identify that firms
to
which
both firms
may
use sulicoiil rart mtr as
Considering
jjiicinp; as
means
of collusion to achieve a ])rice
a stratcf^y in pr'KJuction planning:
is
more desirable
certainly an imi)f)rtant
item on our future research ajjenila
hi
sum, subcoiitractin;^
is
way
oik-
to reallocate prochiction
organizations and to achieve ])roduction smoothing;
tion costs,
and
h<'nc(\
is
socially desirable
firms are requiicd to ex]>aiid
There are
in this
])aper
tln'ir
it
is
Two
sip;ned.
here could be
Sulicontractin<^ usually lowers
To incoriHnate subcontractinj'
scojk of
jilaiiniii':
of
them
aic of most imjxn-tance.
Tliese
(juality.
two
Tin- secojirl
as])ects
is
tlieic iiiiKlit
The
first
"mana<z:in<j;"
,
one
is
we have not discussed
"sourcin;':"
and
maiiap;inp:
]>rincipal-aj:;eiit
.
in detail
namely, how to to
have tremendous impact on subcontracting costs. The criteria
etc.
Rep;ardins the
be nncontrollabh^ uncertainties, jirivate information (in'oblenis
subcontracts with the
and mechanism
jiroduc-
namely, how^ to mana^.v a subcontract
of aflverse selection), and/or unobseivable actions (])roblems of moral
sourciiig;
tf)tal
into production planniiif!;.
on-time delivery, conformance to (-n^ineerinjc s])ecification,
economic environment,
tli(-
to consider other a<';ents in the eroiuuny.
ma,iiy other issm-s concf-iniiif-^ subcontiaclinj: practice
seh-ct ((jualify) subcontractors.
once
re(|uuements amoni^ profiuctive
]iossi))le
a]i])lications of
desipii deserves further research.
15
ha/.ai-rl).
How
to deal with
economic theories such as
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(::,i„t:<l,.<w:
Fnms. Mnikrts.
RrlHtioiuil
(Um-
lo/:J|c>fi
Date Due
B^st^tm
DEC 29
2
i^AY
OCT.
198^
ly^JD
23199/
JUN.
09 \m\
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3
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