BASEMEN
HD28
.M414
Dewey
^5-
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
Design and Control
of
Multi-Location Distribution Systems/
Donald B. g.osenfield
Visiting Associate Professor
M.I.T. Sloan School of Management
Senior Consultant
Arthur D. Little, Inc.
April 1985
#1647-85
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
^Design and Control
of
Multi-Location Distribution Systems/
Donald B. 5.psenfield
Visiting Associate Professor
M.I.T. Sloan School of Management
Senior Consultant
Arthur D. Little, Inc.
April 1985
#1647-85
M.i.T.UBRI^nES
AUG
9 1985
RECEIVED
Intr oduct an
i
This paper examines the issues
distribution systems.
Mu
I
t
i
-I
procurement ot merchandise ar
in
the design and contra
ocat on distribution systems
materials from vendors
I
af multi-location
involve the
i
raui
i
the transport of the
same to plants) warehouses and distribution centers; the stocking of finished
goods or merchandise) and the del ivery of these goods to customers or reta
outlets.
i
I
Some of these distribution systems use distribution centers) which
consolidate and distribute merchandise to capitalize on the economies of scale
transportation) and others use warehouses) which serve to stock goods and
in
pass b y conso
i
I
I
i
date de
I
i
ver es
i
The design and control of these systems
involving facilities)
involve a range of questions
inventories) product flows and transportation.
In
addition) control of the movements and storage of goods require a greater
of sophistication than simple single
level
installation retail outlets or
manufacturing operations.
In addition to the obvious operational
questions of mul t
i—
I
ocat on
i
distribution systems) the basic logistics choices have important strategic
The strategic
implications.
implications of
logistics choices have been
examined by Shapira> [1] by ShapirO) Rosenfield) and Bohn; C23) Shycon and
Sprague and) with respect to facilities choices) by Hayes and Wheelwright
A
f
i
rm can ga n a competitive advantage using distribution and
i
facilities.
example)
in
operating a large number of distribution facilities and
A
service (large numbers of facilities) or
low cost
f
i
in
rm might compete by offering high
(smaller number of
By understanding the distribution and logistics options available
and the nature of the marketplace) a firm can better design
network
its network of
There are quite clearly significant strategic differences) for
operating a small number of facilities.
facilities.)
C4II.
its
distribution
-
-
1
multiple distribution facilities there are a number of important
In using
These include:
questions that must be answered.
- number and
- servy ce
i
- s ze of
i
location of facilities
eve
I
fac
i
I
I
t
i
i
es
- assignment of products and markets to facilities
- design of system during growth stage
- eche on des gn
i
I
-
inventory control and coordination
The number and locations and sizes of both manufacturing and distribution
f
ac
i
I
i
t
i
es have obvious
impacts on both cost and service)
Once a network
service are strategically important.
also complex issues of product and market assignment.
is
and the goals for
designed? there are
For an expanding firm)
Firms
there are the important issues of the growth of the logistics system.
can alternatively grow simultaneously in all
a
regions of the country) requiring
full-scale distribution network) or grow sequentially region by region;
requiring on y a staged growth of the distribution and manufacturing network.
I
issue for service and
The echelon design
is
firms have several
stages) or echelons; of
a key
inventory and distribution.
national plant or warehouse may supply a regional
warehouse which may
supply a local warehouse and possibly even a representatives' trunk!
these
is
an echelon.
In the
parts may be required only occass ona
i
one of several echelons.
I
I
y
)
in
turn
Each of
spare
individual parts may be stored at any
For these types of distribution systems)
of echelons can be a crucial
A
industry) where specific critical
computer
Many
inventory management.
design factor.
the number
- 2 -
The echelon design leads to the final
control) and coordination.
Uh
i
I
inventory allocation)
issues of
multiple echelons may not be common) most
e
plants and warehouses
large businesses maintain two echelons where central
+
ac
I
i
1
1
i
es may supply sate
I
I
i
How to distribute and control
te warehouses.
inventory among the locations are important design and management questions.
for addressing the design and
In order to provide a focus and framework
control of mu t -I ocat on distribution networks) we focus
i
I
i
in
this paper an what
we view as the four key questions:
- number of distribution facilities
-
location and size of distribution
f ac
i
I
i
t es
i
- deployment of inventory among distribution facilities
in a two stage (plant and distribution center) system
- control
of
inventory among
Number of facilities
is
f ac
i
I
i
t
i
es
clearly a key design issue.
Given the number of
facilities) sizing and location are dependent on many characteristics of the
business.
These factors include sourc ng factors)
i
economies of scale
in
locations of markets)
manufacturing and distribution) and locations and
capacities of existing facilities for an expanding firm.
Inventory deployment
and control are crucial because of the nature of manufacturing and
distribution.
For many nationally or regionally based bus nesses the number of
manufacturing facilities
II4I]
.
is
less than the number of distribution facilities
As a result) plants will generally serve as combination plants and
distribution centers) wh ch
i
centers.
w
i
M
in
turn supply the additional distribution
For firms with extensive distribution networks)
two stages or echelons.
of
)
i
The key
inventory management
inventory between the two echelons.
That
is)
there will hence be
issue
is
the a
I
location
should inventory be
concentrated at the first) or plant stage) of the system with modest stock
- 3 -
inventories be concentrated at the
levels at the second stage) or should be
staging stDci< at the
second) or warehouse) stage of the network) with minimal
plant stage a+ the system.
two stages* how should
addition) once inventory
In
be control
it
is
al
located among the
Standard methods for control
led'?'
I
i
ng
inventory at a single location) such as order point systems) may not be
sufficient for two-stage networks where there are complex interactions between
the two stages.
Methods such as Distribution Requirements Planning C5D have
been suggested for hand
I
i
ng these more complex systems.
different framework or approach
is
In any case)
a
required for a multi-stage network.
This paper presents an overview of these four key questions
in
the design
and control of multi-location distribution networks) and identifies the
different situations which will cause different firms to approach design
questions differently.
Number of Distribution Fac
There are several
i
I
i
t
i
es
factors that
distribution facilities.
impact the choice of the number of
These include
- distribution costs
- customer service
levels
- growth patterns of business
- number and
There
is
location of manufacturing facilities
an obvious relationship between the number of distribution
facilities and both distribution costs and customer service.
facilities) customer service improves.
facilities
investments
increase;
Uh
i
I
e
inventory investments and
transportation costs may decrease as described
as follows) due to the economies of scale
in
the costs of
transportation loads. Economies of scale dictate that full
unit than partial
loads.
If a
Uith additional
manufacturing firm
is
individual
loads cost
less per
paying for outbound
- 4 -
transportation costs (from distribution centers or warehouses to customers
ul-i
i
ch may be
small
in
loads))
transportation
in
consolidated loads to
warehouses or distribution centers will give more economic transportation to
the
inbound (to warehouses or distribution centers) portion of the delivery.
Dith additional distribution centers or warehouses^ facilities are> on average)
closer to the customer) the inbound portion of the delivery increases) and
In a
retailing business) where loads
loads and
loads from distribution centers
transportation costs can decrease.
total
from vendors are typical
to stares are
ly
in
consolidated
in
sma
I
I
I
oads
)
a distribution network with several
distribution centers will provide a similar economic advantage.
In both
situations) however) as the number of distribution centers substantially
increases)
may not be possible to del
it
i
I
i
ver ful
loads to distribution centers
I
(for a manufacturing firm) ar from distribution centers
or warehouses
reta
i
ng cha ns
i
)
(for
.
In the situation where the customer
distribution center or warehouse)
is
paying for transportation from the
facility and inventory costs quite clearly
increase as the number of facilities
increases.
Transportation costs may also
With an increase
increase) or they can stay approximately the same.
in
the
number of facilities) some distribution centers or warehouses may be closer to
plants (decreasing inbound costs) and some may be farther away (increasing
The overall effect
inbound costs).
is
in
general
not clear but costs should
not Kiary substantially with the number of facilities.
Some specific
quantitative results for these types of relationships are presented below.
Corporate growth
number of
f ac
i
I
i
t
i
es
is
.
another
important factor
in
the determination of the
Companies that are expanding geographical
distribution facilities for both economic and service reasons. A
need to add
ly
f
i
rm may
expand by slowly expanding its geographic base or by attempting to expand
simultaneously
in
several
locations on a small scale. The latter approach may
- 5 -
be problematic
in
terms of economies of scale of distribution costs.
For a
broad-scale geographic expansion) Hayes and Wheelwright discuss the requirement
of establishing "beachhead plants" for the associated manufacturing network.
growth strategy also critically affects
the topic
is
more extensively discussed
A
location and size of facilities) and
the next section.
in
A fourth factor that affects the number of distribution facilities
is
the
nature of the manufacturing network. Distribution facilities are often located
adjacent tO) or are designed as part of) a manufacturing plant.
a manufacturing network
is
not the focus of this paper) but
note that manufacturing facility location
labor and tax questions)
materials) and plant focus
in
is
important to
often based on a different type of
is
analysis than the analysis of the distribution.
economies of scale)
it
The design of
This may include manufacturing
location of key suppliers or raw
terms of products and process.
In any case)
the
design of the distribution network needs to take into account the design of the
manufacturing network.
For most nationally-based manufacturing
of distribution
locations exceeds the ideal
The distribution system design issue
is
f
i
rms
issues
In general)
the ideal
as noted)
number
number of manufacturing locations.
therefore to determine the best number
of warehouses or distribution centers given the
locations.
>
I
i
m ted
i
number of manufacturing
the two problems are related) but given the additional
inherent in the manufacturing network design) a decoup
I
i
ng
is
often
feasible) and we concentrate on the separate design of the distribution
network
To deal
with the various
of distribution facilities)
issues
inherent
in
the determination of the number
we consider the two primary questions concerning
the number of distribution facilities (distribution centers or warehouses):
- How do costs vary with number of distribution
-
tAJhat
is
f
ac
i
I
i
t
i
es?
the relationship between service and cost as the number
is varied?
of distribution facilities
- ^ -
The discourse that follauis
but sma
I
An analogous set of conclusions can be
number of plants.
I
reached for a retai
I
i
based an a manufacturing firm with a fixed
is
ng chain.
To answer these two questions; one can make some
s
i
mp
I
i
fy
i
ng
assumptions about the distribution of demand and the locations of
distribution facilities that) while not always validj should not
compromise the determination of the appropriate number of facilities.
Specifically)
one assumes that 1) demand
if
each distribution facility
is
located
uniformly distributed 2)
is
the center of a region that
in
supports and 3) the area of each distribution facility territory
then some general
it
equal)
is
results are obtainable.
Consider a network of an arbitrary number of distribution facilities
Each
N.
f ac
i
I
i
ty covers
I
/N of the total area of the business.
fol lows
It
that the outbound transportation time (from the distribution centers to
customers) will be proportional
the
to the square root of
l/N)
since this
is
linear dimension of area corresponding to each distribution center.
These outbound movements will general
ly
be LTL movements) and assuming LTL
costs are linear functions of distance) variable outbound costs will also
be proportional
substantially)
to the square root of l/N.
general
in
Uh
i
I
the linear assumption
e LTL costs often ^ary
is
reasonable Z61
noted) up to a certain number of distribution facilities
As
.
inbound costs
should not vary with the number of facilities) since the average distance
plant or plants
from the central
some
f ac
i
I
i
t
i
es w
farther away.)
a
f ac
I
I
I
I
(With more
not change.
be closer to a central
f
ac
plant) and some will
i
I
i
t
i
es
be
However) as the number of distribution facilities reaches
certain level)
How will
i
wi
it
i
I
i
is
not possible to obtain full
ty and
transit loads
inbound.
inventory costs vary as the number of
distribution facilities changes?
Certain costs
)
e.g. administrative
- 7 -
overhead) will be +ixed> regardless of the size of the facility.
costS) particularly those related to
For example)
scale.
the so-ca
inventories at warehouses
by the stocking
I
led
inventory)
uu
i
I
Other
exhibit economies of
I
square-root law hypothesizes that
increase as the square root of the sales covered
While there are economies of scale
location.
inventories) empirical studies
in
indicate that the precise relationship
varies with the business) and that)
general) that)
in
^sry w th a power of sales between .5 and 1.0 [73.
i
inventories will
A higher power
indicates a higher degree of correlation across geographic areas.
case the splitting of
In this
inventories across several distribution facilities
does not substantially increase total
inventories.
simply proportional to the total sales volume.
Other costs will be
Labor costs will
presumably be proportional to total sales volume) as each unit of
merchandise will require the same type of materials movement) regardless
of how
long
sits on the shelf.
it
inventory and other
In summary)
f ac
i
I
i
ty costs
(not
including those
costs that are proportional to sales volume) will be fixed for each
location or will
vary as a power of sales between .5 and l.D.
That
iS)
C = A + KS^
where
C =
inventory and
A =
f
i
f ac
i
I
i
ty costs
xed costs
K = constant
S = sa es
I
I
eve
I
B = constant
As the number of facilities
but the total
increases) the cost per facility decreases)
casts increase.
- 8 -
These types af general re iat onsh ps can be used to develop
i
i
cone us ons an the best number at distribution facilities and the
i
I
For example) with outbound costs
tradeoffs between costs and service.
paid by the manufacturer; transportation costs decrease but facility costs
increase as the number of
f ac
i
I
i
t
i
es
(This assumes
increases.
transportation costS) or those from plant to distribution
f ac
inbound
I
i
i
t es
i
remain approximately constant) while outbound transportation costs
decrease as customers are generally closer to the nearest distribution
With fixed-facility costs low (i.e. total costs are
facility).
proportional to a power of sales) a mathematical relationship can be
derived showing that the best number of distribution facilities
proportional
power
no premium for spl
is
power of .5 results when faci
I
.
I
i
i
(The
.5.
to sales volume)
when facility costs are proportional
is
case there
vo ume
sales volume between D and
to a power of total
is
tt ng volume among several
i
f ac
i
which
in
I
i
t es
i
.
ty costs vary as the square root of sales
)
If a
firm doubles
number of
its volume)
for example)
it
should increase the
distribution facilities between zero and 41%.
its
relating total costs and the number of facilities (see figure
The curve
1)
will
be
around the region of the optimum) but the approach
relatively flat
indicates the nature of the relationship between the number of faci
I
i
t es
i
and sales volume.
Perhaps a more important question than cost minimization
is
the
relationship between the distribution costs and customer service) defined
as del ivery time) as the number of faci
I
outbound costs are paid by the customer.
facilities
varies as N
increased) the costs
is
-k
.
i
t
i
es
is
varied.
Assume now that
Hence as the number of
increase) but outbound delivery time
Since both costs and outbound del ivery time can be
A
- ^ -
expressed
terms af N; N can be eliminated and distribution casts can
in
be related ta outbound del i'^ery time T.
Ue do not present this derivation but note that the term
this
in
relationship between the costs ai distribution and the del ivery time
proportional
exponent
in
to T
— 2+2B
where T
>
is
the del ivery time and B
the power relationship (1) between
facilities costs and sales volume.
prapartional
The result
proportional to deliver time.
the
is
inventory and other
For example;
to the square root of sales)
is
if
inventory costs are
then costs are inversely
is
a wide range of cost-delivery
time relationships on the efficient frontier) or the most cost-efficient
distribution system for a given level of service.
The general
this tradeoff relationship can have a significant impact on
logistics structure
C2I1
form of
industry
Industries with relatively flat curves may offer
.
more feasible alternatives for the various firms
industries with relatively sharp turns.
In the
in
the marketplace than
latter case firms not
locating at the point of curvative may offer significant premiums either
in
In the former
cost or del ivery time.
service levels for modest differences
in
case firms can offer alternative
cost.
(See figures 2 and 3).
The important issue for number of distribution facilities
impact of the
inventory-sales parameter B
tradeoff curve.
B.
in
(1)
is
the
on the cost-del ivery time
Figure 4 presents the curves for two different values of
For the higher B case of
.875)
there
is
higher correlation among
regions of the country) and splitting inventories among locations does not
significantly increase costs.
a wider
Indeed)
the B = .875 curve
range of delivery time valueS) until
low values of delivery time)
the nature of demand and
of the curve and)
in
f ac
turn)
it
I
i
ty economies of scale will
the structure of the
flatter over
becomes sharply kinked at
or very fast delivery time.
i
is
industry.
Consequently)
affect the shape
In
industries
- ID -
with higher B,
while
f ac
i
I
in
i
t
i
firms will
industries with
es
generally have many distribution facilities,
lower B,
there may be a wide range of number of
- 11
3
.
La catian and Size of Facilitie s
Sizing and
- How
I
ocat ans questions primarily consist n+ the fa lowing
i
I
large are appropriate facility territories?
- How sensitive
is
total
market share and costs to location and
size'7
- How are
locations
identified as the firm grows
Given a territory? a distribution facility location will be based on
transportation costs and customer proximity.
size required to service the territory.
The size will be
s
i
mp y the
I
The demand centra id of the
facility) the location that minimizes the weighted average distance to
demand po nts
i
j
minimize average customer proximity and> assuming
will
transportation costs are proportional to distance) the transportation
cost.
The centro d can be approximated either by weighted coordinate
i
average or a coordinate median.
Determination of facility territories can be salved on the basis of
minimizing average distance to the nearest distribution center or
warehouse.
Generally) this also minimizes transportation cost and
delivery time.
For areas of high cost (or delivery time) per mile?
distances should be mare heavily weighted.
Intuitively? where demand
is
denser facility territories should be
smaller) but total demand covered by the facility should be larger.
the size of the
f ac
i
I
density between D and
i
ty should vary
1.
inversely w th a power of demand
The precise power
i
is
2/3 [7].
territory sizes will decrease by a factor of 4 and total
will
double
Ta best
if
Hence
Hence facility
facility) demand
demand density increases by a factor of 8.
illustrate the sensitivities and growth questions) we present
a case study.
The study illustrates some conclusions that are applicable
- 12 -
involved was a major Eastern retailer
The company
ta many situations.
embarking on an ambitious growth program.
Service requirements and the
economics of transportation consolidation pointed out the need for
Three different scenarios for chain size
additional distribution centers.
were of concern:
i
the current chain;
the ful
expanded chain; and an
ly
nter m cha n
i
i
ConsD
I
i
dat on economics plays an important role for any logistics
i
system involving deliveries from many origins to many destinations.
large numbers of paths of small
loads?
it
is
With
economical to consoldiate
The automobile companies? who procure goods from hundreds of
loads.
vendors and deliver them to multiple assembly
pi
ants
>
and retailers? who
need to transport merchandise from hundreds of vendors to large numbers of
Perhaps the most striking example of
stores? are good examples of this.
this
is
Federal Express Corporation? who conso
deliveries at
i
ts ma n hub at Memphis?
i
The key questions for the reta
I
i
I
i
dates almost all of its
Tennessee.
er were
- The sensitivity of cost and service to the utilization of
its
existing facility? and
- The staging of expansion decisions within the firm-'s overall
growth strategy
The utilization of the existing facility was important
had a large facility
or
reduced
in
size.
in
that the company
the eastern part of the country that could be expanded
Hence
it
was
important to understand the sensitivity of
costs and service to utilization of this facility
the firm.
in
in
the
long-term strategy of
With respect to the second issue? the staging of decisions as part
of the growth strategy?
it
was
important to understand how the firm could
expand while at the same time controlling distribution costs and services.
- 13 -
Td analyze the
issues
>
the author develaped a computer model
to optimize
product flows within the distribution network given the utilization of each of
the distribution facilities.
and ut
i
I
i
Figure 5 presents the relationships between costs
zat an of the existing
i
distribution centers.
f ac
i
I
i
ty for alternative networks of two
The upper curve represents a network with the Eastern
location and a fixed midwestern location.
The
lower curve represents network
with the Eastern location and the best second location (which will
K^ary as
the
utilization of the Eastern facility changes).
As the ut
i
I
i
zat on of the existing
i
f ac
i
I
i
ty
increases
j
the best second
location moves further awayj and the cost of a network w th a fixed second
i
location can rise very sharply.
f
ac
fac
i
I
i
i
I
i
as we
t es
i
I
I
The analysis shows that locations of
as costs can be very sensitive to ut
i
I
i
zat ion of given
t ies.
The set of optimum distribution networks for different points
in
time
during the growth stage of the firm identified the best implementation strategy
for new distribution centers.
It turned out that best
second location for the
interim point of the rapid growth stage was 1) the best second
ful ly
location for the
expanded chain and> 2) a part of the best network with three distribution
centers.
Uh
i
I
e this
result was somewhat fortuitousj
supports the concept
it
that a firm should expand into new geographical areas sequentially (a fanning
out process) rather than expanding simultaneously to a
The
latter approach can
lead to disecanomies of scale
I
i
costs
II
y
in
distribution) as such
in
an approach will yield large geographical areas with sma
sequential expansion might be achieved econom ca
projected markets.
I
I
I
volumes) wh
i
I
e a
terms of distribution
- 14 -
4
.
D eployment of
Inve ntory
ui
i
th n a Mu 1 -ec h e o n
i
1
I
i
Inventory Sys tem
The third key issue
distribution network
is
in
the design and control
of a mu t -I ocat on
i
I
inventory deployment tor a mu
I
t
i
i
-eche on system.
While the five
echelon or stage feeds the succeeding stage within the network.
ar six stage systems
for
field service
in
many high-tech businesses are
minority? many firms operate a large number of distribution
the
limited number of manufacturing
locations
f ac
The situation
The deployment of
complex question.
is
depicted
in
I
i
t
i
es
Since
.
inventory
inventories between the two stages of the systems
in a
the
figure h.
Indeed; when one starts
deploying inventories
i
in
invariably act also as stocking
locations) these distribution systems are defacto two-echelon
systems.
Each
I
is
a
investigating alternative methods of
two— stage system? there are very different
implications for facility capacities and buffer stocks.
In general?
there are
two sensible methods for deploying inventories between the two echelons of the
system.
One method concentrates
locations (a central
.
location or
system)? while the second method concentrates
at the second stage? or the satel
system) CBD
inventories at the central
LJith a central
I
i
inventories
locations of the system (a satel
te
i
te
system? the satellite warehouses carry stocks to
protect against lead time only? wh
i
I
e the central
location or
locations carry
large buffer stocks to protect against the production of procurement
lead
With a satellite system? the satellite warehouses carry larger buffer
time.
stocks to protect against both transit and production lead time.
type of approach) the warehouses associated with the central
act mainly as a staging and marshal
satel
I
I
i
I
i
ng areas for conso
I
i
Under this
plant ar plants
dated shipments to the
te warehouses.
In a satel
I
i
te system) merchandise
is
satellite locations as much as possible.
pushed (ar pu led) out to the
I
In a central
system) some inventory
- 15 -
held back iar protect ion) thereby reducing requirements at the sate!
is
a significant degree.
The exact inventory
I
i
tes to
levels can then be based on standard
approaches for calculating buffer stocks given the appropriate lead times
(transit time for the sate
central
u)
i
I
I
location).
I
I
i
te
locations and the production time tor the
Obviously) the type of organization and information system
affect the relative desirabi
of deployment strategy will
discussed
in
I
i
ty of the two types of systems.
Each type
require a specific type of control system) which
is
the next section.
Theoreticians have not been able
in
general to characterize the best
inventory deployment strategies for these mu
1
1
i
-eche on systems.
However) the
I
only two reasonable options are the two deployment strategies outlined above.
The choice between the two options) moreover) can have an enormous
facility requirements.
study.
The author was
country.
involved
in a
is
also best illustrated by a case
location study for a major consumer goods
At the time of the study) the East coast factory and warehouse
manufacturer.
serviced
This latter point
impact on
SD7. of
the country) and the west coast sate
I
I
i
te serviced 20% of the
The purpose of the study was to evaluate and recommend additional
locations for warehouses.
One of the keys to the analysis was that the product was a high-value>
low-weight product for which inventory costs were dominant.
fairly early
in
became clear
It
the analysis that the distribution cost analysis would require
identification of the specific inventory deployment strategy.
Ue then
simulated the inventory levels of each and every product of the company for
both a central and satellite inventory deployment strategy.
The results of the simulation are presented
the net
in
Table
1.
Note that wh
i
I
inventories of the two approaches are not vastly different) there are
very different allocations of
inventory.
These allocations will
require
- 16 -
different facility capacities and are hence critical
in
the deve apment of a
I
strategic distribution plan.
Which of the two types of approaches should be adopted general y?
There
I
is
no direct answer and each of the two approaches must be evaluated separately.
Table 2 shows which system
the system C9]
general
.
favored for several different characteristics of
is
The analysis of many of these factors can be based on a very
principle of
inventory management: hold inventory before the high
That
value-added step.
isj
if
delivery to the final echelon
is
a high
value-added step
in
central system.
This principle can be illustrated by its application to the
terms of a
II
costs; hold the
inventory central
characteristic of the number of remote warehouses.
remote warehouses
>
through additional
this
the final
echelon
in
ly
in
the
Uith a large number of
aggregate adds a great deal of value)
inventory; to the product.
inventory before the high value-added step
It
is
in a
hence beneficial to store
central system.
number of remote warehouses hence favors a central system.
A large
- 17 -
5
.
Co ntrol of Inve n tory
Mu
in a
1
1
i
-E che o n System
I
Multi-stage distribution systems pose issues of
as deployment.
The dependencies of demand)
from satellite
for example^
require more sophisticated types of control
locations)
locations to central
inventory control as well
than the simpler types of approaches for single locations.
In the past several
yearS) Distribution Requirements Planning) or DRPj has been proposed as an
appropriate means of controlling inventory within a mu
I
t
i
-eche Ion environment.
DRP uses demands; either actual or forecasted) at the satellite locations to
determine replenishment requirements at the satellite
determine a requirements schedule at the central
approach)
MRP)
like
I
ocat ons
i
location or
>
and
in
turn to
locations.
The
manufacturing analog materials requirements planning) or
its
uses a requirements schedule to develop a precise schedule of production
and procurements at the central
DRP
central
is
designed to deal with some of the problems of coordination between
locations and sae
however)
is
location.
I
I
i
locations
te
not always the system
q-^
c! lU
in a
i
mu
1
ce for a
1
i
I
I
-eche on system.
DRP)
I
mu 1 -eche on systems.
1
i
I
For
two-stage systems) the most typical system for a manufacturing firm) there are
actually three different approaches for
inventory control:
Separate simple systems
DRP
Allocation control
Separate systems involve separate control systems for each location.
Order-point control
location controls
is
its
In this type of approach)
the most typical.
inventory independently
quantities characteristic of
s
i
ng e- ocat on
I
I
i
each
using order points and order
inventory systems.
When there are
significant interactions among locations) for example when several satellite
locations simultaneously make
large orders) an order-point system can
lead to
- la -
problems.
DRP
is
designed to deal with these problems through better
scheduling of requirements at the central
location.
Simple control systems such as order-point systems; however) can also be
tormulated
terms ot echelon
in
at the specific
I
I
location) which are referred to as
inventory at succeeding locations.
of the
I
I
as
in
terms of
inventories
installation inventories.
inventory consists of the inventory at a single installation as well
An echelon
as a
inventories as we
For a two-stage system w th a
i
single central warehouse) for example) the echelon inventory for the central
location consists of the entire inventory
at the central
in
the entire system.
location would therefore be based on total system
This type of approach when associated with perpetual
Replenishment
inventory.
target inventories)
is
also known as a base stock approach and can a lev late some of the problems of a
I
simple order-point systems.
The final type of control system) the allocation control system)
is
based
on the concept of simultaneously replenishing groups of satellite locations.
When such a joint order reaches the central warehouse stage of the network)
is
it
allocated and pushed out to the satellite locations as expeditiously as
The central
possible.
location acts as a staging area and hence the system
is
designed for a satellite inventory deployment strategy.
The best choice of
the means of
the control
inventory control
for a multi-stage system depends on
inventory deployment and other characteristics.
system appropriate for the three main scenarios of two-stage
inventory systems.
For a satellite
inventory deployment system)
locations are by definition staging areas and inventory
sate
I
I
i
te
Table 3 presents
locations.
An a
I
location system
is
is
the central
pushed out to the
appropriate here.
For a central
- 19 -
inventory deployment system w th a moderate number of satellite warehouses)
i
there are signi+ leant dependencies between the demands of the satellite
This requires a h gh level
warehouses.
Uh
i
I
e a
i
of coord nation
in
replenishment.
base stock system can be designed to deal with this; a DRP system
clearly the system of choice.
However; w th a central
i
system w th a large number of sate
i
I
1
i
is
inventory deployment
te warehouses or with sma
I
I
sate
I
I
i
te
warehouses) demand at the central warehouses achieves a certain level of
stab
i
I
ity.
For example? no single warehouse will make batch orders that will
dominate demand at the central
central
location
is
location or
locations.
Ulhen
demand at the
stable) the advantages of DRP are reduced) and a system
such as order-point control
is
sufficient.
Uith a hundred satellite locations with independent demands) for example;
it
is
is
not neccessary to tabulate detailed forecasts of satellite orders.
a certain statistical
but stable pattern of demand at the central
There
location)
and the control parameters of the inventory control system can be adjusted for
this pattern.
The important issue for
additional
facilities)
control of
inventories that
is
inventory control
improved)
is
there
required.
is
is
that as service) through
a certain
level
of coordinated
As a firm expands from a single
distribution facility or a small number of independently operated facilities)
simple control systems must evolve to more sophisticated ones.
- 2D -
^
•
Ca ne us o n
i
I
there are a
large number of
issues to address
of a manufacturing and distribution network.
some of the key
issues
in
in
the design and development
This article attempts to identify
the distribution part of the network.
no one prescribed method of system design and control)
aware of
- the tradeoff between cost and service and their
t es
sensitivity to the number of f ac
i
I
i
i
- the desire for smaller territories but higher
volume coverage
dens ty
in
areas with greater demand
i
- the sensitivity of costs and locations to
existing capacities during the firms growth
phase
- how inventories can be allocation between
echel ons
- the importance of more sophisticated control
an expanded network.
in
Uh
i
I
e
there
businesses should be
is
- 21 -
References
1.
ShapIrO) "Get Leverage from Logistics")
May-June 1984.
R.
i-iar'^'ard
B u sin e ss R e vieuj
)
)
ShapirQ) D. Rosenfield) and R. Bahnj "Imp cat ans at Cost-Service
Tradeoffs on Industry Logistics Structures"; to appear in Interfaces
2.
R.
3.
H.
i
i
i
Shycan and C. Bpraguej "Put a Price Tag on Your Customer Servicing
Levels") l-larvard B u sin e ss R e vie ui) 53 No. 4) p. 71-78.
)
Hayes and S. Wheelwright) Re s toring our Competitive E d ge
U ley)
1984.
4.
R.
5.
J. Magee) U). CopacinO) and D. Rosenfield) Mo dern L o gistics Managem ent)
Uiley) 1985) Chapter ID.
6.
.
)
)
i
Chapter 5.
Martin) Distributi o n Requirements Pla n nin g) Prentice-Hall)
1983.
7.
A.
a.
R.
9.
M. Haimovich and T. Magnant
"Extremum Properties of Hexagonal
Partitioning and the Uniform Distribution in Euclidean Location".
Paper OR 132-85) Operations Research Center, MIT, January) 1985.
G. Brown) S tatistical Forecasti n g for Inv e ntory Control
New York, 1959.
i
)
McGraw-Hi
I
I)
)
Working
Rosenfield and M. Pendrock "The Effects of Warehouse Configuration
Design on Inventory Levels and Holding Costs )" Sloan Manag em ent Revi ew,
Summer, 198D
ID.
D.
11.
See Rosenfield and Pendrock for an explanation of each.
>
- 22 -
Table
1
Simulation far Central and Satellite Inventory
Deployment Strategies
Centra
Central Strategy
Sate!
I
i
te Strategy
1
- 23 -
Table 2
Factors Favoring Central or Sate
Fac tor
I
I
i
System Favored as
Fa c tor Le v el Increa ses
Value Added
Central
Number of Remote Warehouses
Central
Trans
it T
i
me
te System
Sate Mite
Procurement Time
Central
Demand Correlation among Regions
Sate
Transshipment Costs
Central
Sales Level
Satellite
I
I
i
te
- 24 -
Table 3
Inventory Control Strategies Appropriate
far Different Scenarios
D eploym ent See nar o
i
Bes t C o ntrol Sy stem
— po
Central with numerous
sate
tes
ordei
Central w th limited
tes
number of sate
D.R.P.
Sate
A
I
I
I
I
nt
i
i
I
i
ite
I
i
I
I
ocat on
i
Figure
1
Distribution Costs
Versus
Number of Facilities
Cost
Number of Distribution Facilities
Figure
2
Relatively Flat Cost-Delivery
Time Tradeoff Curve
Cost
Delivery Time
Figure
3
Cost-Delivery Time Tradeoff
Curve with Sharp Curvature
Cost
Delivery Time
Figure
4
Distribution Cost-Delivery Time
Curves for Alternative B
Cost
Delivery Time
Figure
5
Cost versus Capacity Utilization
of Eastern Distribution Facility-
Variable
Cost
fixed
locations
Utilization of Eastern Facility
Best
two-location
strategy
Figure
6
Two-echelon Inventory Systems
Typical in many Businesses
Plants
Central
Warehouses
Satellite
Warehouses
(Customers)
625i*
086
(
3
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1991
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