Business Administration
Lecture No. 12: Delivery Improvement and
Inventory System
1．Reduction of Production Period
2．Variety and Function of Inventory
3．Fixed-Quantity Order and Fixed-Period Order
4．Kanban System
Takahiro Fujimoto
Department of Economics, University of Tokyo
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１．Reduction of Production Period
Competitive effect of reducing production period (Throughput Time)
Direct effect
(1) order production → delivery reduction
(2) stock production → demand projection accuracy
→ prevent out-of-stock
inventory cost
Indirect effect
elicitation of waste, production problem
→ increase in productivity, quality
What is Production Period (Throughput Time)?
Time required for material to absorb (receive)
product design information stocked within process,
and be transformed to a product
Production Period = time for receiving product design information
+ time for not receiving product design information
Actually, in general, "time for not receiving information" is
overwhelmingly large.
(typically, time to accumulate as an inventory）
→ Key to reduce a throughput time is in improving the
inventory system.
Production Lead-Time as Time to Receive (absorb) Information
(conceptual diagram)
transmit product design information from worker/machine
in-process products
materials receiving
receiving
second process
first process
inventory transpor
tation
time
time
inventory
time
final products
inven
tory
time
inventory
time
cycle time
cycle time
production lead-time
legends：
net working hours ( time for receiving information)
time for not receiving information
(inventory, transportation, etc.)
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp209 figure.6.13)
product design
(information M+A+B)
information A
design/worker
information stock B
design/worker
information stock A
information
customer
information
●●●●●
●●●●●
M+A
M+A+B
●●●●●
●●●●●
second
operation
●●●●●
●●●●●
M
●
●
finished-product
inventory
M
M+A
in-process
product
inventory
material
inventory
first
operation
supplying company
product design information A
product design information B
M+A+B
information M
information B
information flow
product (Mono) flow
●
work (in-process product)
Diagram 6 14 In-Process Product Inventory and Throughput Time
grinding process
cycle: 1 min.
in-process product inventory = zero
lathe process
cycle: 1 min
production period: 2 min.
grinding process
cycle: 1 min
in-process product inventory = 1
lathe process
cycle: 1 min
production period: 3 min.
grinding process
cycle: 1 min
in-process product inventory = 10 lathe process
(first-in, first-out)
cycle: 1 min
production period: 12 min
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp211 figure.6.14)
２．Variety and Function of Inventory
(1) Pipeline inventory (warehouse, inventory in transportation)
(2) Cycle inventory (to accrue depending on lot size)
(3) Buffer inventory
(to correspond to fluctuation of order volume)
(4) Inventory corresponding to seasonal variation
(gap between seasonal variation and leveled production)
(5) Decoupling in-process inventory
(to relieve interdependence among processes)
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp213 figure.6.15)
Types of Inventory System
(1) System corresponding to independent demand
fixed-quantity order system
fixed-time order system
IPS (Inventory Planning System: MRP's independent-demand version)
(skip)
(2) System corresponding to dependent demand
MRP, MRP Ⅱ
Kanban system
Types of Main Inventory System
system corresponding
to independent demand
fixed-quantity order model
(fixed-order quantity)
(independent demand)
fixed-time/period order model
(fixed-time period)
Material Requirement
Planning System (MRP)
system corresponding
to dependent demand
(dependent demand)
Kanban system
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp215 figure.6.16)
‡
３．Fixed-Quantity Order and Fixed-Period Order
（１） Fixed-Quantity Order
Order lot is constant.
Check inventory all the time.
Automatically place order when inventory reaches reorder point.
Order interval is elastic.
"2 bin system" is a typical case in point.
Fixed-Quantity Order System
Order volume is constant each time. Order cycle is elastic.
cycle
inventory
safety
inventory
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp216 figure.6.17)
① Case: Order cycle ≻ Lead-time
average production base
average parts consumption volume
order cycle
order lot
(slope)
lead-time
point of
order
cycle inventory
safety inventory = B
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp216 figure.6.17)
② Case: Lead-time ≻ Order cycle
lead-time
order cycle
point of
order
unfilled
order
order
lot
cycle
inventory
safety inventory = B
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp216 figure.6.17)
２-Bin System
container 1
container 2
capacity = P
Consume material from Container 1.
When Container 1 becomes empty, place a refill order.
Container 2 is firstly filled
with the arrived material.
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp217 figure.6.18)
Fixed-Quantity Order :
Level of Buffer Inventory (Safety Inventory)
Balance between inventory-holding cost and out-of-stock cost
(opportunity cost)
Assume a probability distribution of demand volume to accrue in
a given period.
Set "probability of desirable out-of-stock" (service level: 1 - s).
Set safety inventory at a level where out-of-stock probability
becomes "S" at the bottom of inventory.
for example, in Critical Fractile method,
s = L / (G + L) L = variable profit, G = inventory cost, etc.
Level of Safety Stock
lead-time = t
～
d
order lot ＝ Q
～
D’s distribution
～ ～
D = d・t
safety inventory＝B
σ
timing of order
S = 2.5%
（service level = 97.5%）
～
where σ is
B≒2σ D‘s standard
deviation
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp218 figure.6.19)
Fixed-Quantity Order: Setting Order Lot Size (EOQ)
When an order lot size = Q,
then, an average cycle inventory level = Q / 2.
EOQ (Economic Order Quantity)
an optimum lot size in short term,
on assumptions of fixed-quantity order,
without buffer inventory, with no uncertainty
static balance concept (⇔ Kanban system)
concept of EOQ
annual demand volume
(production volume in succeeding process)
annual
ordering cost
lot size
ordering cost per 1 time
cost per unit
annual
inventory cost
annual inventory interest rate
(borrowing interest + warehouse/マテハン)
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp220 figure.6.20)
Aggregate cost = Inventory cost + Ordering cost ---Minimization thereof
cost per period
aggregate
cost
ordering cost
Takahiro Fujimoto
'Introduction to Production Management'
Nihon Keizai Shimbun, Inc. 2001 (Ⅰp220 figure.6.20)
inventory cost
‡
（２）Fixed-Period Order System
Order periodically (Order interval is constant.).
Order quantity per one occasion is elastic (Qt).
Set an upper limit value (M) for unfilled order + inventory,
based on safety inventory, order interval, and delivery lead-time →
When unfilled order = Ot, inventory = It ,at ordering time-point = t,
an order volume at t time t is Qt = M - Ot - It.
Basic thought on setting a safety inventory level is the same
with one on the fixed-volume order.
Fixed-Period Order System
Order cycle is constant. Order volume is elastic each time.
cycle inventory
safety inventory
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp222 figure.6.21)
Case: Delivery Lead-time (t) ≺ Order Cycle (T)
order cycle
lead-time
order lot
cycle inventory
unfilled
order
unfilled
order
unfilled
order
cycle
inventory
unfilled
order
cycle
inventory
level point of inventory
replenishment = M
upper limit of "inventory
+ backlog“
= upper limit of B+d (T+t)
safety inventory = B
while,
M = inventory level point = upper limit of "safety inventory + cycle inventory + unfilled order"
Ii = inventory at ordering time-point of sequential order i
‡
Oi = unfilled order = 0 at ordering time-point of sequential order i
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp222 figure.6.21)
Case: Delivery Lead-time (t) > Order Cycle (T)
order cycle
lead-time
unfilled
order
unfilled
order
unfilled
order
unfilled
order
cycle
inventory
cycle inventory
cycle
inventory
level point of inventory
replenishment = M
upper limit of "inventory
+ backlog“
= upper limit of B+d (T+t)
unfilled order
cycle inventory
safety inventory = B
while,
M = inventory level point = upper limit of "safety inventory + cycle inventory + unfilled order"
Ii = inventory at ordering time-point of sequential order i
Oi = unfilled order = 0 at ordering time-point of sequential order i
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp222 figure.6.21)
４．Kanban System
One of representative "dependent demand corresponding systems",
along with MRP.
Which was established primarily by 耐一 Ono in Toyota Automobiles.
Kanban is--used for both delivery instruction (order) and production
instruction (order release)
the card (circulating invoice) which can be used repeatedly.
(1) take-back Kanban
(2) order release (in-process) Kanban
Take-back Kanban
parts delivery place
‡
supplier
product
content quantity per box
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp225 figure.6.22)
Variety of
Kanban
Basics of Kanban System
"Take back by succeeding process“
--- Process in a downstream goes to its upper stream
to take its required parts in a required quantity.
I.e., a "pull method".
Kanban moves together with a standardized container which
includes n units of in-process parts. (shadow of container)
number of containers (N) = number of Kanban pieces
speed of container's movement = speed of Kanban
(synchronization of Mono and information)
Flow of Kanban, Container, and Actual Items
acts as
acts as
an identification tag an identification tag
in- process Kanban
take-back Kanban
parts
consumption
smaller
parts
storage
site
smaller
parts
process
in- process Kanban
parts
line
side
acts as
an identification tag
in- process Kanban
finished
parts
storage
site
parts
process
parts
consumption
take-back Kanban
in- process Kanban
acts as
an identification tag
take-back Kanban
assembly
line
side
assembly
instruction
assembly
process
parts
consumption
assembly
completion
take-back Kanban
empty
empty
empty
empty
acts as
an order release
acts as
a delivery instruction
acts as
an order release
acts as
a delivery instruction
Reference: Drawn by the author in reference to Shgeo Shingo, previously stated book
Legends：
parts box
actual parts
flow of actual item
flow of information
Kanban
Kanban
Author making (reference: Shigeo Shingo 'IE consideration of the Toyota Production System')
Reference: Takahiro Fujimoto 'Introduction to Production Mmanagement' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp226)
‡
Function of Kanban changes depending on the container'
conditions.
(1)When it is with a container full of parts (outward):
---- Kanban is an "identification tag".
(2)When it is with an empty box (homeward):
--- Kanban is a "delivery instruction tag“ and an "order release".
Analogy of a ski lift
Consider the ski lift's chairs as containers, and persons as parts;
An equalized movement;
Number of people disembarked at the mountain peak accrues number of
empty seats ( accrual of empty boxes);
Number of seats (content quantity) is set (1 seat, 2 seats, 3 seats ---);
People get on the lift at the hillside when empty seats come around;
Departure time is not fixed. (fixed-quantity and irregular trip).
Kanban Test --- Design-Draw Product
＜parts＞
＜product assembly drawing＞
side view
front view
hollow triangle pole
Kanban Test --- Work Standardization of Upstream Process
＜Work Standard of the First Process＞
（１） Prepare
2 plates.
（２）Bring 2 sheets together as the following .
（３） Put the completed parts (sub assembly) into a container.
Kanban Test --- Work Standardization of Downstream Process
initial condition
(total number of parts: 75)
today's production:25units
25 parts
first process
second process
40 parts
order-release
Kanban
take-back
Kanban
take-back
Kanban
container
22 parts
in-transit condition
first process
second process
30 parts
5 units
finished
order-release
Kanban
take-back
Kanban
3 units
finished
take-back
Kanban
Take-back Kanban
name of parts: subassembly (pair of 2 sheets)
preceding process = first process
succeeding process = 2nd process
container content quantity = 5
Take-back Kanban
name of parts: subassembly (pair of 2 sheets)
preceding process = first process
succeeding process = 2nd process
container content quantity = 5
Order-release Kanban
name of parts: subassembly (pair of 2 sheets)
preceding process = first process
production quantity = 5
Decision on Pieces of Kanban (= Quantity of Containers)
Ｎ ＝ （Ｑ + Ｂ）／ｎ
Demand speed of a succeeding process (constant, assured) = d
When a delivery equals a re-order (zero lead-time),
Ｎ ＝ （ｄ ・ ｔ + Ｂ）／ｎ
While t = delivery lead-time of preceding process,
= time for container to make one cycle of trip
between preceding and succeeding processes
= cycle time of take-back K + cycle time of order- release K
Case of Kanban System
inventory
preceding
process
on
passage
succeeding
process
Takahiro Fujimoto
'Introduction to Production Management'
Nihon Keizai Shimbun, Inc. 2001
(Ⅰp230 figure.6.24)
inventory
total
‡
(continued from previous slide)
Number of Kanban Pieces
order-release Kanban's
take-back Kanban's
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp231 figure.6.24)
‡
Number of Containers
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp231 figure.6.24)
(a) Snapshot of Kanban System (time point AA)
succeeding
process
preceding
process
shipping area at
succeeding
process
post for receiving
Kanban's
receiving area at
succeeding process
empty containers
at preceding
process
empty containers
at succeeding
process
container
parts
(containing 10 pieces)
take-back Kanban
production in
succeeding
process
post for receiving
take-back
Kanban's
order-release
Kanban
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp232 figure.6.25)
(b) Snapshot of Kanban System (time point BB)
succeeding
process
preceding
process
shipping area at
succeeding
process
receiving area at
succeeding process
post for receiving
Kanban's
empty containers
at succeeding
process
container
parts
(containing 10 pieces)
take-back Kanban
production in
succeeding
process
post for receiving
take-back
Kanban's
order-release
Kanban
‡
Takahiro Fujimoto 'Introduction to Production Management' Nihon Keizai Shimbun, Inc. 2001 (Ⅰp232 figure.6.25)
Improvement of Production by Reducing Quantity of Kanban's
Calculate an optimum number of Kanban pieces by EOQ
(Economic Order Quantity)?
N = (EOQ + B ) / n
(right side → left side)
but, this is a static balance concept. No idea on improvement.
Rather, improve production through an effort to reduce number
of Kanban pieces. (left side → right side)
(1) improvement on production and distribution
→ cutting down of lead-time (t)
(2) deduction of reserved-capability time
(3) equalization and stabilization of production
→ reduction of safety inventory (B)
Kanban System Contrasted to MRP
Both are based on Master Schedule
→ Calculate requirements by parts explosion.
Premises for Kanban are an equalization and a consistent cycle time.
Instead, no "lead-time compensation".
Kanban is a "pull method", while MRP is a "push method“
MRP does not have a means of an order release contained in Kanban.
MRP does not contain a fine-tuning means and an improvement
mechanism when deviations from plans incur.
MRP (planning) and Kanban (execution/fine-tuning) can be used together
complementarily.
① Kanban System
market D
Ď t; t + i
B0
1
I2
B1
information
inventory waiting
for process
I
inventory waiting
for transportation
feedback
transportation
flow of Mono
(product)
I3
B3
3
P volume for order release
T instructed volume for transportation
process
② MRP
Ďkt; t+1
B2
2
B
P3
T2
P2
T1
P1
central control
Ďkt; t+2
market D
P1
Ďkt; t+3
I0
I1
1
2
L1
information
feedback
flow of Mono
(product)
P3
P2
I2
3
I3
L3
L2
order- release volume
inventory
Pn
Ln
process
Ď t; t + I
instructed volume for transportation
important demand forecast for i period ahead
made at the end of t period
For Reference: Comparison Between Waiting-in-Procession Problem and Inventory Problem
1 input (arrival)
production lot = Q
Q
t
pace of arrivals as
per probability distribution
t
to reduce
cumulative number of
processed persons
～
A(t)
t
safety inventory level = B
waiting in procession,
(arrival)
B
fixed volume of inventory consumption
cumulative output
fixed volume of arriving inventory
inventory
cumulative number of
arrived persons
Waiting-in-procession
problem
t
t
t
（case of order lot problem）
4
t
t
inventory
Safety inventory
decision problem
Q
fixed volume of inventory consumption
cumulative output
Q
3 output (process)
cumulative output
order lot = Q
inventory
EOQ
(decision on
product lot)
cumulative input
3
fixed volume of arriving inventory
fixed volume of arriving inventory
cumulative input
2
EOQ
(decision on
order lot)
cumulative input
１
2 waiting, stagnation, inventory
t
t
inventory consumption volume
as per probability distribution
t
〈service ratio〉
t
pace of process as
per probability distribution