Productivity improvement solutions for manufacturing systems with highly variable inputs

Productivity Improvement
Solutions for Manufacturing
Systems with Highly Variable
Inputs
Sudhendu Rai
Xerox Corporation

IIE Annual Conference and Expo 2008, Vancouver, BC (May 17-21)
Abstract
In many industries, the need for increased personalization and customization is introducing high
product variety and variability levels in manufacturing environments. What impact does it have
on the operations of such manufacturing environments in terms of productivity, quality and
expected cycle times? How can a manufacturer faced with such high levels of variability and/or
product variety improve their productivity levels and quality? Are there new operational
frameworks (factory design and scheduling policy structures) that might be more efficient in
such situations? This talk will discuss these questions and provide some practical solutions to
these problems.
The talk will describe how to detect and analyze very high levels of variability using fat-tailed
distributions. A special class of document manufacturing system will be described where such
high level of variability has been observed. A solution methodology to improve the productivity
in the presence of fat-tailed inputs will be presented. Specific equipment layout, process design
and scheduling strategies will be discussed that have shown to improve the productivity of such
environments. While the case study will be specific to document production, insights will be
generalized for application to other manufacturing systems that might be faced with similar
challenges.

Author Bio
Dr. Rai is a Principal Scientist, Project Leader and a certified Lean Six Sigma Black Belt at the
Xerox Research Center in Webster, N.Y. He received his PhD. from MIT in 1993, MS from Caltech
in 1989, and BTech from IIT, Kanpur (India) in 1988 – all in Mechanical Engineering. Dr. Rai
joined Xerox in 1995 as a Member of Research & Technology staff. He was promoted to
Principal Scientist in 2001. During 1996-97 he demonstrated the feasibility of virtual
prototyping of xerographic components. He created, validated and implemented a new
methodology for performing quantitative trade-offs in large-system design. Between 1997 and
1998 he developed and implemented a novel distributed control architecture for moving paper
across multiple paper handling modules. He is the lead inventor of the LDP Lean Document
Production® Solution . Starting in 1998 he led a team that developed the algorithms, software
toolkit to support the initial offering and a training curriculum to train Xerox Global Services
consultants. He has personally led and implemented process improvement initiatives in dozens
of small and large print shops spanning multiple industry segments. He holds 15 patents (with
35 additional pending) and has published more than 20 technical papers in conference
proceedings and technical journals. The Xerox entry “LDP Lean Document Production® -
Dramatic Productivity Improvements for the Printing Industry” is a finalist in the 2008 Franz
Edelman Award competition (sponsored by INFORMS). He is a member of IIE, ASME, Sigma Xi
and a senior member of IEEE. He is a recipient of the Xerox Excellence in Science and
Technology Award and was selected as a finalist for the Rochester Engineer of the Year award in
2007.

Print shops are document manufacturing systems
Collater
Cutter
Binder
Postage
Meter
Shipping
Paper
cart
Paper
cart
Paper
cart
Failure Repair
Failure Repair
Failure Repair
Labor
Labor
variability
WIP
WIP
WIP
Finishing Mailing
Customer
Electronic
Submission
Job Variability
•Demand
•Size
•Routing
Graphics design Pre-pressCustomer service
Failure Repair
Color Printer
BW Printer
CF Printer
Paper
cart
Failure Repair
Failure Repair
WIP
Paper
cart
WIP
Paper
cart
WIP
Printing
Failure Repair
Failure Repair
Failure Repair
WIP
Failure Repair
Failure Repair
WIP
Failure Repair
Failure Repair
Failure Repair
Failure Repair

Diverse Types of Print Shops
BellandHowell
Inserter
Inserter
Inserter
PB 8 Series
PB 8 Series
PB 8 Series
Inserter
Cage
Inserter Room
Desk
Desk
Desk
Desk
Desk
Desk
LOADING
Server Room
Mailing
Area
Input
Desk
P
r
i
n
t
e
r
1
Cutter
P
r
i
n
t
e
r
2
P
r
i
n
t
e
r
4
P
r
i
n
t
e
r
3
Desk
SQA
DESK
Moore
Sealer
Desk
Roll System
Printer
Desk
H
I
L
I
T
E
P
R
I
T
E
R
Desk
ShrinkWrapper
Pillar
DeskDesk
Desk
Desk
P
r
i
n
t
e
r
3
Desk
ShrinkWrapper
Roll System
Printer
Transaction Print Shop
55' - 4 1/4"
2' - 4 7/8"
18'-12"
62' - 1 1/8"
12'-0"
PAPER
PAPER
SKRINK
WRAP CUTTER DRILL
DOCUTECH # 2DOCUTECH # 1
D
O
C
U
T
EC
H
#
3
53905
1
0
0
D
O
C
4
0
B
DOC 40 A
DC
265 A
DC
265B
FAX
55' - 4 1/4"
Copy Shop
Combination of Transaction & Publishing Offset Print Shop

Print shop classification by complexity & utilization
Complexity
Utilization
II. FM business,
commercial
printers, CRDs
IV. Large complex
operations
III. Document factories
or book printers
I. Mom and pop
shops
Complexity
Utilization
II. FM business,
commercial
printers, CRDs
IV. Large complex
operations
III. Document factories
or book printers
I. Mom and pop
shops
CRD: Corporate Reprographics Department
FM: Facility Management

Optimization goals for document production
processes
• Improve profitability and customer satisfaction
• Cost containment
• Cycle time reduction
• Adapt to changing conditions

360003000024000180001200060000
Median
Mean
4003002001000
A nderson-Darling Normality Test
V ariance 2034062.0
Skew ness 16.142
Kurtosis 383.015
N 1692
Minimum 1.0
A -Squared
1st Q uartile 6.0
Median 28.0
3rd Q uartile 152.0
Maximum 39802.0
95% C onfidence Interv al for Mean
267.4
425.32
403.4
95% C onfidence Interv al for Median
25.0 33.0
95% C onfidence Interv al for StDev
1379.7 1476.0
P-V alue < 0.005
Mean 335.4
StDev 1426.2
95% Confidence Intervals
Job Size (Page Count) distribution
Challenges in optimizing production processes
Reducing the impact of multiple sources of variability
• Job arrival and due dates
• Job size
• Job types (routings)
• Random machine failure and repair
• Labor skill differences
• Flexible work schedule
• Processing rate variability for equipment
• Volume fluctuation
Day
Volume
39035131227323419515611778391
6000000
5000000
4000000
3000000
2000000
1000000
0
_
X=2220922
UCL=5074045
LB=0
3_5 4_5 5_5 6_5 7_5 8_5 9_5 10_511_512_51_6 2_6 3_6
111
Daily Production Volume

A schematic view of a large transaction production
environment
Inventory 1
Process 1
(30 machines)
Process 4
(Manual)
Process2
(10 machines)
Process3
(10 machines)
Process 5
(15 machines)
Inventory 2
240 operators

Challenges in Optimizing Large Operations
•High job size variability (fat-tailed distribution)
•Sequence-dependent setup variability with significant setup time
•Size related challenges
– High volume (~1 billion documents annually)
– Large number of operators (~300)
– Large number of machines
•Data collection issues
– Data comes from multiple sources and resides in multiple databases and getting sufficient and
reliable data is difficult
•Implementation issues
– Cultural issues: People skill, shop mindset
– Sustaining the improvements
– Cost of re-designing print shop
– Disruption in operations

Varying Customer Requested Job Turnaround Time
Turnaround Time Requirements (2002 Data)
0%
5%
10%
15%
20%
25%
30%
35%
D1 D2 D3 DR DS HE MA MN RD RN RS W1 WR
Turnaround Time Codes
%ofeachtype
1Day TAT
2 Day TAT
3 Day TAT
30 Day TAT
90 Day TAT
7-10 Day TAT
Product Types

High Product Variety
Contribution by formtype
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
0 20 40 60 80 100 120 140 160
FormType
%volumecontribution
Formtype
Contribution by Product Type
Product Type

High variation in size of incoming jobs

High WIP adversely affects Process Cycle Time
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
12/10/2002 1/29/2003 3/20/2003 5/9/2003 6/28/2003 8/17/2003
Cards Input Cards Shipped WIP Masses Input
Average WIP
~3 Million
Time (Days)

Fluctuating Demand Creates Scheduling Challenges
Day
Volume
39035131227323419515611778391
6000000
5000000
4000000
3000000
2000000
1000000
0
_
X=2220922
UCL=5074045
LB=0
3_5 4_5 5_5 6_5 7_5 8_5 9_5 10_511_512_51_6 2_6 3_6
111
Daily Production Volume

Special Business Process Constraints
•Hold jobs until customer calls to make last-minute
changes
•High security
•Customer owned inventory (missing parts)
•…

Production data resides in multiple forms and multiple
databases
•Oracle databases store transaction data
•Scheduling tools store production timing data
•Inventory databases store inventory data
•Manual logs (paper, spreadsheets)

Characterizing and analyzing very high variability using
fat-tailed distributions
Let X be a random variable with cdf F(x) = P[X≤ x] and complementary cdf (ccdf) Fc(x) =
P[X>x]. We say here that a distribution F(x) is fat-tailed if
Fc (x) ~ cx-a 0<a<2 (1)
In the limit of x->∞ (2)
α
dlogx
(x)dLogF
lim
x
c
−=
→
Heavy-tailed distribution determination
-6
-5
-4
-3
-2
-1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ln(JobSize)
Ln(CCDF)
Heavy-tailed distribution
determination
Fat-tailed distribution determination

Characteristics of fat-tailed distributions
Steady-state is not achieved quickly for fat-tailed data inputs
)/1(1 −
nConvergence rate proportional to 1/ where n is the size of the sample :
Mean Value as a Function of Sample Size for a fat-tailed vs. normally distributed job size
0
5000
10000
15000
20000
25000
0 500 1000 1500 2000 2500
Sample Size
MeanValue
Avg_Formtype 1 (a = 0.6)
Avg_Formtype 1 (a = 2.0)
 = 0.6
 = 2.0

A new way to look at designing and operating large
printshops
•Traditional shops handle job variability via scheduling
policies that are implemented by experienced shop-floor
managers
•We propose to invert the problem and look at it differently:
• First determine an efficient scheduling policy and use that
to drive the optimization of the shop and process
configurations

Scheduling Architecture and Policy Drives Shop and Process
Optimization
Job arrival
Job classifier by size
Big job pool classifier Small job pool scheduler
Insertstrategy variety threshold parameter
Formtype variety threshold parameter
High setup job
router
Low setup job
router
Cell1
Queue
sequencing
Batch Splitting, Sorting,
Machine assignment
Cell1
Queue
sequencing
Batch Splitting, Sorting
Machine assignment
Cell1
Queue
sequencing
Machine assignment
Cell1
Queue
sequencing
Machine assignment
Job size threshold parameter
Cell1
Queue
sequencing
Machine assignment
Cell1
Queue
sequencing
Machine assignment

The Notion of Autonomous Cells
BellandHowell Inserter
Inserter
Inserter
PB 8 Series
PB 8 Series
PB 8 Series
Inserter
Cage
Inserter Room
Desk
Desk
Desk
Desk
Desk
Desk
LOADING
Server Room
Mailing
Area
Input
Desk
P
r
i
n
t
e
r
1
Cutter
P
r
i
n
t
e
r
2
P
r
i
n
t
e
r
4
P
r
i
n
t
e
r
3
Desk
SQA
DESK
Moore
Sealer
Desk
Roll System
Printer
Desk
H
I
L
I
T
E
P
R
I
T
E
R
Desk
ShrinkWrapper
Pillar
DeskDesk
Desk
Desk
P
r
i
n
t
e
r
3
Desk
ShrinkWrapper
Roll System
Printer
LOADING
Server Room
Mailing
Area
Input
Desk
P
r
i
n
t
e
r
1
Cutter
Inserter
PB8
Series
Inserter
PB8
Series
P
r
i
n
t
e
r
2
P
r
i
n
t
e
r
4
P
r
i
n
t
e
r
3
Desk
Desk
Desk
SQA
DESK
Inserter
PB8
Series
Moore
Sealer
Desk
Cell 4
Roll System
Printer
Desk
Desk
Cell 2
H
I
L
I
T
E
P
R
I
T
E
R
Desk
Shrink Wrapper
Pillar
Cell 3
Cell 1
An autonomous cell has all the resources (equipment and labor) to
create a few different types of finished products

Traditional Production Frameworks
BellandHowell
Inserter
Inserter
Inserter
PB 8 Series
PB 8 Series
PB 8 Series
Inserter
Cage
Inserter Room
Desk
Desk
Desk
Desk
Desk
Desk
LOADING
Server Room
Mailing
Area
Input
Desk
P
r
i
n
t
e
r
1
Cutter
P
r
i
n
t
e
r
2
P
r
i
n
t
e
r
4
P
r
i
n
t
e
r
3
Desk
SQA
DESK
Moore
Sealer
Desk
Roll System
Printer
Desk
H
I
L
I
T
E
P
R
I
T
E
R
Desk
ShrinkWrapper
Pillar
DeskDesk
Desk
Desk
P
r
i
n
t
e
r
3
Desk
ShrinkWrapper
Roll System
Printer
•Functional/Departmental layout
•Specialized labor skills
•Classical job-shop scheduling
Job Shops Inline or FlowShops
Print Shrinkwrap
•Automated inline systems
•Single-piece flow
Print Insert Ship
PressureSeal
Shrinkwrap
Mail
Fulfillment

Current State Analysis
Job Types Capacity Analysis
Implementation
Bar-coded
Job Ticket
Control Logic
Tracking Database Internet
Server
Site Survey & Data Collection
Finishing Room
Print Room
Cell Design & Floor Plan Studies
Autonomous
Cells
Simulation results
The Print Shop Engagement & Assessment Process

Fat-tailed job stream splitting by job size
x0 Threshold = x1
Small jobs Big jobs
Threshold determined via a mixed integer programming optimization of a
simulation model of the shop

Job Routing Heuristics For Autonomous Cells
h
xxdF
h
M
xxdFxxdFxxdF
p
k
px
x
x
x
x
kx
h
h

 =====
=
= −
)(
)(...)()(
1
2
1
1
0
Routing policies
1.Random
2.Round-Robin
3.LeastWIP (Dynamic)
4.SITA-E: Size Interval Task Assignment with Equal Load1
x0=k xh=px1 x2 xi
1.0
F(x) = Pr{ X ≤ x }
Job
Arrival
S1
S2
Sh
1
1
)( 1
1
11
=



























+
−
=
−
−−




if
if
k
p
k
p
h
i
k
h
ih
x
h
ii
k: smallest job size
p: largets job size
: Exponent in the Bounded Pareto distribution
M: Mean
h: Number of cutoff points
Bounded Pareto Distribution f(x) = (kx--1)/(1-(k/p)) pxk 
1On Choosing a Task Assignment policy for a distributed server system: M. Harchol-Balter, M.E. Crovella, C.D Murta,
Lecture Notes in Computer Science, Springer Berlin/Heidelberg, ISBN 0302-9743 (2004)

Runtime Tail Reduction
•Determine the smallest and largest job size (k, p and a mean = m)
•For the jobs with size x > m; split the jobs using the following rule :
xf
p
x
x 





−
−
−=
m
m
1mod
f is a pre-specified factor
mJob
size
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

Process modeling and discrete-event simulation
Nested discrete-event simulation models
for performance evaluation and
optimization

Optimized Cell Structure
•3 autonomous cells for small jobs
with high average setup per job
•3 autonomous cells for large jobs
with low average setup per job

Inventory 1
Process 1
(30 machines)
Process 4
(Manual)
Process2
(10 machines)
Process3
(10 machines)
Process 5
(15 machines)
Inventory 2
BEFORE
New Production Environment Configuration
AC1AC2
AC3AC4
AC5AC6 AFTER
Inventory 2
Inventory 1
AC: Autonomous Cells

Impact
ROI (one year) 178%
IRR- Internal Rate of Return 186%
Payback Period 11 months
Space Savings 15%
Product Travel Distance Reduction 75%
Throughput Time Savings 31%
Defects Per Million Reduction 55%
Productivity Improvement 12%
Sigma Metric Improvement 4.8 to 5.0
Yield Improvement 99.941 to 99.973

Conclusions
•Manufacturing systems are experiencing higher product variety
•This is introducing higher levels and different types of variability in the
production environment
– Fat-tail behaviors
– Sequence dependent setups
– Interaction between different product types
• This paper proposes a solution using the concept of autonomous cells and
hierarchical scheduling to improve system performance
– Exploits fat-tail inputs and setup variability to create autonomous cells
• Results from a case study demonstrate the effectiveness of this approach
• Salient features of the methodology were abstracted so that they can be
generalized to similar large high variety/ high variability manufacturing
environments

Productivity improvement solutions for manufacturing systems with highly variable inputs

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