Chapter 3
Network Planning
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
3.1 Why Network Planning?
Find the right balance between inventory,
transportation and manufacturing costs,
 Match supply and demand under
uncertainty by positioning and managing
inventory effectively,
 Utilize resources effectively by sourcing
products from the most appropriate
manufacturing facility

1-2
Three Hierarchical Steps

Network design





Inventory positioning:





Number, locations and size of manufacturing plants and
warehouses
Assignment of retail outlets to warehouses
Major sourcing decisions
Typical planning horizon is a few years.
Identifying stocking points
Selecting facilities that will produce to stock and thus keep
inventory
Facilities that will produce to order and hence keep no inventory
Related to the inventory management strategies
Resource allocation:



Determine whether production and packaging of different
products is done at the right facility
What should be the plants sourcing strategies?
How much capacity each plant should have to meet seasonal
demand?
1-3
3.2 Network Design
Physical configuration and infrastructure of
the supply chain.
 A strategic decision with long-lasting
effects on the firm.
 Decisions relating to plant and warehouse
location as well as distribution and
sourcing

1-4
Reevaluation of Infrastructure

Changes in:
demand patterns
 product mix
 production processes
 sourcing strategies
 cost of running facilities.


Mergers and acquisitions may mandate
the integration of different logistics
networks
1-5
Key Strategic Decisions
Determining the appropriate number of
facilities such as plants and warehouses.
 Determining the location of each facility.
 Determining the size of each facility.
 Allocating space for products in each
facility.
 Determining sourcing requirements.
 Determining distribution strategies, i.e., the
allocation of customers to warehouse

1-6
Objective and Trade-Offs

Objective: Design or reconfigure the logistics network in
order to minimize annual system-wide cost subject to a
variety of service level requirements

Increasing the number of warehouses typically yields:





An improvement in service level due to the reduction in average
travel time to the customers
An increase in inventory costs due to increased safety stocks
required to protect each warehouse against uncertainties in
customer demands.
An increase in overhead and setup costs
A reduction in outbound transportation costs: transportation
costs from the warehouses to the customers
An increase in inbound transportation costs: transportation costs
from the suppliers and/or manufacturers to the warehouses.
1-7
Data Collection









Locations of customers, retailers, existing warehouses
and distribution centers, manufacturing facilities, and
suppliers.
All products, including volumes, and special transport
modes (e.g., refrigerated).
Annual demand for each product by customer location.
Transportation rates by mode.
Warehousing costs, including labor, inventory carrying
charges, and fixed operating costs.
Shipment sizes and frequencies for customer delivery.
Order processing costs.
Customer service requirements and goals.
Production and sourcing costs and capacities
1-8
Data Aggregation

Customer Zone




Aggregate using a grid network or other clustering technique for
those in close proximity.
Replace all customers within a single cluster by a single
customer located at the center of the cluster
Five-digit or three-digit zip code based clustering.
Product Groups

Distribution pattern



Products picked up at the same source and destined to the same
customers
Logistics characteristics like weight and volume.
Product type

product models or style differing only in the type of packaging.
1-9
Replacing Original Detailed Data
with Aggregated Data
Technology exists to solve the logistics
network design problem with the original
data
 Data aggregation still useful because
forecast demand is significantly more
accurate at the aggregated level
 Aggregating customers into about 150-200
zones usually results in no more than a 1
percent error in the estimation of total
transportation costs

1-10
General Rules for Aggregation

Aggregate demand points into at least 200
zones


Make sure each zone has approximately an
equal amount of total demand



Holds for cases where customers are classified into
classes according to their service levels or frequency
of delivery
Zones may be of different geographic sizes.
Place aggregated points at the center of the
zone
Aggregate products into 20 to 50 product groups
1-11
Customer Aggregation
Based on 3-Digit Zip Codes
Total Cost:$5,796,000
Total Customers: 18,000
Total Cost:$5,793,000
Total Customers: 800
Cost Difference < 0.05%
1-12
Product Aggregation
Total Cost:$104,564,000
Total Products: 46
Total Cost:$104,599,000
Total Products: 4
Cost Difference: 0.03%
1-13
Transportation Rates
Rates are almost linear with distance but
not with volume
 Differences between internal rate and
external rate

1-14
Internal Transportation Rate
For company-owned trucks
 Data Required:

Annual costs per truck
 Annual mileage per truck
 Annual amount delivered
 Truck’s effective capacity


Calculate cost per mile per SKU.
1-15
External Transportation Rate
Two Modes of Transportation


Truckload, TL
Country sub-divided into zones. One zone/state
except for:


Zone-to-zone costs provides cost per mile per
truckload between any two zones.


Big states, such as Florida or New York (two zones)
TL cost from Chicago to Boston =
Illinois-Massachusetts cost per mile X ChicagoBoston distance
TL cost structure is not symmetric
1-16
External Transportation Rate
Two Modes of Transportation


Less-Than-Truckload, LTL
Class rates



standard rates for almost all products or commodities shipped.
Classification tariff system that gives each shipment a rating or a
class.
Factors involved in determining a product’s specific class
include:


After establishing rating, identify rate basis number.




product density, ease or difficulty of handling and transporting, and
liability for damage.
Approximate distance between the load’s origin and destination.
With the two, determine the specific rate per hundred pounds
(hundred weight, or cwt) from a carrier tariff table (i.e., a freight
rate table).
Exception rates provides less expensive rates
Commodity rates are specialized commodity-specific
rates
1-17
SMC3’s CzarLite





Engine to find rates in fragmented LTL industry
Nationwide LTL zip code-based rate system.
Offers a market-based price list derived from
studies of LTL pricing on a regional,
interregional, and national basis.
A fair pricing system
Often used as a base for negotiating LTL
contracts between shippers, carriers, and thirdparty logistics providers
1-18
Transportation Rate for Shipping
4,000 lbs.
FIGURE 3-7: Transportation rates for shipping 4,000 lb
1-19
Mileage Estimation
Estimate lona and lata, the longitude and
latitude of point a (and similarly for point b)
 Distance between a and b


For short distances
Dab  69 (lona  lonb ) 2  (lata  latb) 2

For large distances
Dab  2(69) sin 1 (sin(
lata  latb 2
lona  lonb 2
))  cos(lata ) X cos(latb ) X (sin(
))
2
2
1-20
Circuity Factor, ρ
Equations underestimate the actual road
distance.
 Multiply Dab by ρ.
 Typical values:

ρ = 1.3 in metropolitan areas
 ρ = 1.14 for the continental United States

1-21
Chicago-Boston Distance











lonChicago = -87.65
latChicago = 41.85
lonBoston = -71.06
lonBoston = 42.36
DChicago, Boston = 855 miles
Multiply by circuity factor = 1.14
Estimated road distance = 974 miles
Actual road distance = 965 miles
GIS systems provide more accuracy
Slows down systems
Above approximation good enough!
1-22
Warehouse Costs

Handling costs



Fixed costs



Labor and utility costs
Proportional to annual flow through the warehouse.
All cost components not proportional to the amount of
flow
Typically proportional to warehouse size (capacity)
but in a nonlinear way.
Storage costs


Inventory holding costs
Proportional to average positive inventory levels.
1-23
Determining Fixed Costs
FIGURE 3-8: Warehouse fixed costs as a function of the
warehouse capacity
1-24
Determining Storage Costs
Multiply inventory turnover by holding cost
 Inventory Turnover =

Annual Sales / Average Inventory Level
1-25
Warehouse Capacity




Estimation of actual space required
Average inventory level =
Annual flow through warehouse/Inventory turnover ratio
Space requirement for item = 2*Average Inventory Level
Multiply by factor to account for





access and handling
aisles,
picking, sorting and processing facilities
AGVs
Typical factor value = 3
1-26
Warehouse Capacity Example
Annual flow = 1,000 units
 Inventory turnover ratio = 10.0
 Average inventory level = 100 units
 Assume each unit takes 10 sqft. of space
 Required space for products = 2,000 sqft.
 Total space required for the warehouse is
about 6,000 square feet

1-27
Potential Locations
Geographical and infrastructure
conditions.
 Natural resources and labor availability.
 Local industry and tax regulations.
 Public interest.


Not many will qualify based on all the
above conditions
1-28
Service Level Requirements
Specify a maximum distance between each
customer and the warehouse serving it
 Proportion of customers whose distance to
their assigned warehouse is no more than
a given distance

95% of customers be situated within 200 miles
of the warehouses serving them
 Appropriate for rural or isolated areas

1-29
Future Demand
Strategic decisions have to be valid for 3-5
years
 Consider scenario approach and net
present values to factor in expected future
demand over planning horizon

1-30
Number of Warehouses
Optimal
Number
of Warehouses
$90
Cost (millions $)
$80
$70
$60
Total Cost
Transportation Cost
Fixed Cost
Inventory Cost
$50
$40
$30
$20
$10
$-
0
2
4
6
8
10
Number of Warehouses
1-31
Industry Benchmarks:
Number of Distribution Centers
Pharmaceuticals
Avg.
# of
WH
3
- High margin product
- Service not important (or
easy to ship express)
- Inventory expensive
relative to transportation
Food Companies
14
Chemicals
25
- Low margin product
- Service very important
- Outbound transportation
expensive relative to inbound
1-32
Model Validation



Reconstruct the existing network configuration using the
model and collected data
Compare the output of the model to existing data
Compare to the company’s accounting information


Make local or small changes in the network configuration
to see how the system estimates impact on costs and
service levels.


Often the best way to identify errors in the data, problematic
assumptions, modeling flaws.
Positing a variety of what-if questions.
Answer the following questions:




Does the model make sense?
Are the data consistent?
Can the model results be fully explained?
Did you perform sensitivity analysis?
1-33
Solution Techniques

Mathematical optimization techniques:
1. Exact algorithms: find optimal solutions
2. Heuristics: find “good” solutions, not
necessarily optimal

Simulation models: provide a mechanism to
evaluate specified design alternatives created by
the designer.
1-34
Example

Single product

Two plants p1 and p2

Plant p2 has an annual capacity of 60,000 units.

The two plants have the same production costs.

There are two warehouses w1 and w2 with
identical warehouse handling costs.

There are three markets areas c1,c2 and c3 with
demands of 50,000, 100,000 and 50,000,
respectively.
1-35
Unit Distribution Costs
Facility
warehouse
p1
p2
c1
c2
c3
w1
0
4
3
4
5
w2
5
2
2
1
2
1-36
Heuristic #1:
Choose the Cheapest Warehouse to Source
Demand
D = 50,000
$2 x 50,000
$5 x 140,000
Cap = 60,000
$2 x 60,000
D = 100,000
$1 x 100,000
$2 x 50,000
D = 50,000
Total Costs = $1,120,000
1-37
Heuristic #2:
Choose the warehouse where the total delivery
costs to and from the warehouse are the lowest
[Consider inbound and outbound distribution costs]
$0
D = 50,000
$3
$5
$4
$2
$5
$3
$7
$7
$4
D = 100,000
$4
Cap = 60,000
P1 to WH1
P1 to WH2
P2 to WH1
P2 to WH 2
P1 to WH1
P1 to WH2
P2 to WH1
P2 to WH 2
$1
$2
$2
$4
$6
$8
$3
D = 50,000
P1 to WH1
P1 to WH2
P2 to WH1
P2 to WH 2
$5
$7
$9
$4
Market #1 is served by WH1, Markets 2 and 3
are served by WH2
1-38
Heuristic #2:
Choose the warehouse where the total delivery
costs to and from the warehouse are the lowest
[Consider inbound and outbound distribution
costs]
$0 x 50,000
D = 50,000
$3 x 50,000
Cap = 200,000
P1 to WH1
P1 to WH2
P2 to WH1
P2 to WH 2
$5 x 90,000
D = 100,000
$1 x 100,000
Cap = 60,000
$3
$7
$7
$4
$2 x 60,000
$2 x 50,000
P1 to WH1
P1 to WH2
P2 to WH1
P2 to WH 2
$4
$6
$8
$3
D = 50,000
P1 to WH1
P1 to WH2
P2 to WH1
P2 to WH 2
$5
$7
$9
$4
Total Cost = $920,000
1-39
The Optimization Model



The problem described earlier can be framed as the
following linear programming problem.
Let
x(p1,w1), x(p1,w2), x(p2,w1) and x(p2,w2) be the flows
from the plants to the warehouses.
x(w1,c1), x(w1,c2), x(w1,c3) be the flows from the
warehouse w1 to customer zones c1, c2 and c3.
x(w2,c1), x(w2,c2), x(w2,c3) be the flows from
warehouse w2 to customer zones c1, c2 and c3
1-40
The Optimization Model
The problem we want to solve is:
min 0x(p1,w1) + 5x(p1,w2) + 4x(p2,w1)
+ 2x(p2,w2) + 3x(w1,c1) + 4x(w1,c2)
+ 5x(w1,c3) + 2x(w2,c1) + 2x(w2,c3)
subject to the following constraints:
x(p2,w1) + x(p2,w2)  60000
x(p1,w1) + x(p2,w1) = x(w1,c1) + x(w1,c2) + x(w1,c3)
x(p1,w2) + x(p2,w2) = x(w2,c1) + x(w2,c2) + x(w2,c3)
x(w1,c1) + x(w2,c1) = 50000
x(w1,c2) + x(w2,c2) = 100000
x(w1,c3) + x(w2,c3) = 50000
all flows greater than or equal to zero.
1-41
Optimal Solution
Facility
warehouse
p1
p2
c1
c2
c3
w1
140,000
0
50,000
40,000
50,000
w2
0
60,000
0
60,000
0
Total cost for the optimal strategy is $740,000
1-42
Simulation Models

Useful for a given design and a micro-level
analysis. Examine:
Individual ordering pattern.
 Specific inventory policies.
 Inventory movements inside the warehouse.

Not an optimization model
 Can only consider very few alternate
models

1-43
Which One to Use?
Use mathematical optimization for static
analysis
 Use a 2-step approach when dynamics in
system has to be analyzed:

Use an optimization model to generate a
number of least-cost solutions at the macro
level, taking into account the most important
cost components.
 Use a simulation model to evaluate the
solutions generated in the first phase.

1-44
DSS for Network Design


Flexibility to incorporate a large set of preexisting
network characteristics
Other Factors:







Customer-specific service level requirements.
Existing warehouses kept open
Expansion of existing warehouses.
Specific flow patterns maintained
Warehouse-to-warehouse flow possible
Production and Bill of materials details may be important
Robustness

Relative quality of the solution independent of specific
environment, data variability or specific settings
1-45
3.3 Inventory Positioning and
Logistics Coordination




Multi-facility supply chain that belongs to a single firm
Manage inventory so as to reduce system wide cost
Consider the interaction of the various facilities and the
impact of this interaction on the inventory policy of each
facility
Ways to manage:



Wait for specific orders to arrive before starting to manufacture
them [make-to-order facility]
Otherwise, decide on where to keep safety stock?
Which facilities should produce to stock and which should
produce to order?
1-46
Single Product, Single Facility
Periodic Review Inventory Model

Assume 





SI: amount of time between when an order is placed
until the facility receives a shipment (Incoming
Service Time)
S: Committed Service Time made by the facility to its
own customers.
T: Processing Time at the facility.
SI  T  S
Net Lead Time = SI + T - S
Safety stock at the facility:zh
SI  T  S
1-47
2-Stage System

Reducing committed service time from facility 2
to facility 1 impacts required inventory at both
facilities



Inventory at facility 1 is reduced
Inventory at facility 2 is increased
Overall objective is to choose:



the committed service time at each facility
the location and amount of inventory
minimize total or system wide safety stock cost.
1-48
ElecComp Case




Large contract manufacturer of circuit boards and other
high tech parts.
About 27,000 high value products with short life cycles
Fierce competition => Low customer promise times
< Manufacturing Lead Times
High inventory of SKUs based on long-term forecasts =>
Classic PUSH STRATEGY



High shortages
Huge risk
PULL STRATEGY not feasible because of long lead
times
1-49
New Supply Chain Strategy

OBJECTIVES:



ACHIEVE THE FOLLOWING:




Push Stages produce to stock where the company keeps safety stock
Pull stages keep no stock at all.
Challenge:



Determining the optimal location of inventory across the various
stages
Calculating the optimal quantity of safety stock for each component at
each stage
Hybrid strategy of Push and Pull


Reduce inventory and financial risks
Provide customers with competitive response times.
Identify the location where the strategy switched from Push-based to
Pull-based
Identify the Push-Pull boundary
Benefits:


For same lead times, safety stock reduced by 40 to 60%
Company could cut lead times to customers by 50% and still reduce
safety stocks by 30%
1-50
Notations Used
FIGURE 3-11: How to read the diagrams
1-51
Trade-Offs

If Montgomery facility reduces committed lead time to 13
days


assembly facility does not need any inventory of finished goods
Any customer order will trigger an order for parts 2 and 3.


Part 2 will be available immediately, since it is held in inventory
Part 3 will be available in 15 days






13 days committed response time by the manufacturing facility
2 days transportation lead time.
Another 15 days to process the order at the assembly facility
Order is delivered within the committed service time.
Assembly facility produces to order, i.e., a Pull based
strategy
Montgomery facility keeps inventory and hence is
managed with a Push or Make-to-Stock strategy.
1-52
Current Safety Stock Location
FIGURE 3-12: Current safety stock location
1-53
Optimized Safety Stock
Location
FIGURE 3-13: Optimized safety stock
1-54
Current Safety Stock with Lesser
Lead Time
FIGURE 3-14: Optimized safety stock with reduced lead time
1-55
Supply Chain with
More Complex Product Structure
FIGURE 3-15: Current supply chain
1-56
Optimized Supply Chain with
More Complex Product Structure
FIGURE 3-16: Optimized supply chain
1-57
Key Points


Identifying the Push-Pull boundary
Taking advantage of the risk pooling concept


Demand for components used by a number of
finished products has smaller variability and
uncertainty than that of the finished goods.
Replacing traditional supply chain strategies
that are typically referred to as sequential, or
local, optimization by a globally optimized
supply chain strategy.
1-58
Local vs. Global Optimization
FIGURE 3-17: Trade-off between quoted lead time and safety stock
1-59
Global Optimization



For the same lead time, cost is reduced
significantly
For the same cost, lead time is reduced
significantly
Trade-off curve has jumps in various
places


Represents situations in which the location of
the Push-Pull boundary changes
Significant cost savings are achieved.
1-60
Problems with Local Optimization

Prevalent strategy for many companies:




try to keep as much inventory close to the customers
hold some inventory at every location
hold as much raw material as possible.
This typically yields leads to:



Low inventory turns
Inconsistent service levels across locations and
products, and
The need to expedite shipments, with resulting
increased transportation costs
1-61
Integrating Inventory Positioning
and Network Design

Consider a two-tier supply chain



Items shipped from manufacturing facilities to primary
warehouses
From there, they are shipped to secondary
warehouses and finally to retail outlets
How to optimally position inventory in the supply
chain?


Should every SKU be positioned both at the primary
and secondary warehouses?, OR
Some SKU be positioned only at the primary while
others only at the secondary?
1-62
Integrating Inventory Positioning
and Network Design
FIGURE 3-18: Sample plot of each SKU by volume and demand
1-63
Three Different Product
Categories
High variability - low volume products
 Low variability - high volume products, and
 Low variability - low volume products.

1-64
Supply Chain Strategy Different for
the Different Categories

High variability low volume products


Inventory risk the main challenge for
Position them mainly at the primary warehouses


Low variability high volume products



demand from many retail outlets can be aggregated
reducing inventory costs.
Position close to the retail outlets at the secondary
warehouses
Ship fully loaded tracks as close as possible to the
customers reducing transportation costs.
Low variability low volume products

Require more analysis since other characteristics are
important, such as profit margins, etc.
1-65
3.4 Resource Allocation

Supply chain master planning
The process of coordinating and allocating
production, and distribution strategies and
resources to maximize profit or minimize
system-wide cost

Process takes into account:


interaction between the various levels of the supply
chain
identifies a strategy that maximizes supply chain
performance
1-66
Global Optimization and DSS
FACTORS TO CONSIDER






Facility locations: plants, distribution centers and
demand points
Transportation resources including internal fleet and
common carriers
Products and product information
Production line information such as min lot size,
capacity, costs, etc.
Warehouse capacities and other information such as
certain technology (refrigerators) that a specific
warehouse has and hence can store certain products
Demand forecast by location, product and time.
1-67
Focus of the Output

Sourcing Strategies:


where should each product be produced
during the planning horizon, OR
Supply Chain Master Plan:

production quantities, shipment size and
storage requirements by product, location and
time period.
1-68
The Extended Supply Chain: From
Manufacturing to Order Fulfillment
FIGURE 3-19: The extended supply chain: from manufacturing to order fulfillment
1-69
Questions to Ask During the
Planning Process








Will leased warehouse space alleviate capacity problems?
When and where should the inventory for seasonal or
promotional demand be built and stored?
Can capacity problems be alleviated by re-arranging
warehouse territories?
What impact do changes in the forecast have on the supply
chain?
What will be the impact of running overtime at the plants or
out-sourcing production?
What plant should replenish each warehouse?
Should the firm ship by sea or by air. Shipping by sea implies
long lead times and therefore requires high inventory levels.
On the other hand, using air carriers reduces lead times and
hence inventory levels but significantly increases
transportation cost.
Should we rebalance inventory between warehouses or
replenish from the plants to meet unexpected regional
changes in demand?
1-70
SUMMARY
Network Planning Characteristics
Network Design
Inventory Positioning
and Management
Resource Allocation
Decision focus
Infrastructure
Safety stock
Production Distribution
Planning Horizon
Years
Months
Months
Aggregation Level
Family
Item
Classes
Frequency
Yearly
Monthly/Weekly
Monthly/Weekly
ROI
High
Medium
Medium
Implementation
Very Short
Short
Short
Users
Very Few
Few
Few
1-71
SUMMARY

Optimizing supply chain performance is difficult




conflicting objectives
demand and supply uncertainties
supply chain dynamics.
Through network planning, firms can globally
optimize supply chain performance


Combines network design, inventory positioning and
resource allocation
Consider the entire network




account production
Warehousing
transportation inventory costs
service level requirements.
1-72
SUMMARY
Demonstrate applicability of risk pooling
and postponement, EOQ modeling, and
inventory sizing to improve customer
service in make-to-order job shop setting
 Demonstrates value from getting and
looking at data

1-73
Case: H. C. Starck, Inc.
Background and context
 Why are lead times long?
 How might they be reduced?
 What are the costs? benefits?

Stephen C. Graves Copyright 2003
All Rights Reserved
1-74
Metallurgical Products







Make-to-order job shop operation
600 SKU’s made from 4” sheet bar (4 alloys)
Goal to reduce 7-week customer lead times
Expediting is ad hoc scheduling rule
Six months of inventory
Manufacturing cycle time is 2 – 3 weeks
Limited data
Stephen C. Graves Copyright 2003
All Rights Reserved
1-75
Sheet Bar
(forged ingot)
Roll
Clean
Anneal
Finish
(cut, weld, etc.)
Repeat
0n3
4” Bar
1/4” Plate
Production Order #1
1/8” Plate
0.015” Sheet
Production Order #2
Tubing
Production Order #3
Production Orders
Stephen C. Graves Copyright 2003
All Rights Reserved
1-76
Why Is Customer Lead Time 7
Weeks?
From sales order to process order takes 2
weeks
 Typical order requires multiple process
orders, each 2 – 3 weeks
 Expediting as scheduling rule
 Self fulfilling prophecy?

Stephen C. Graves Copyright 2003
All Rights Reserved
1-77
What Are Benefits From
Reducing Lead Time?
New accounts and new business
 Protect current business from switching to
substitutes or Chinese competitor
 Possibly less inventory
 Better planning and better customer
service
 Savings captured by customers?

Stephen C. Graves Copyright 2003
All Rights Reserved
1-78
How Might Starck Reduce
Customer Lead Times?

Hold intermediate inventory
How would this help?
 How much? Where?

Eliminate paper-work delays
 Reduce cycle time for each process order


How? What cost?
Stephen C. Graves Copyright 2003
All Rights Reserved
1-79
Two-Product Optimal Cycle Time
KB  KF
 hB DB hF DF 
Cost T  
T 


T
2
2


*
T 
*
T 
2 KB  KF 
hB DB  hF DF
2  400  400 
.06 100  526000  .06 125 183000
Stephen C. Graves Copyright 2003
All Rights Reserved
 0.02 years
1-80
Intermediate Inventory
Characterize demand by possible
intermediate for each of two alloys
 Pick stocking points based on risk pooling
benefits, lead time reduction, volume
 Determine inventory requirements based
on inventory model, e. g. base stock

Stephen C. Graves Copyright 2003
All Rights Reserved
1-81
Popularity Material Gauge - Description
1
1011 0.002 Foil
2
1004 0.015 Sheet
3
1003 0.005 Sheet
4
1029 0.500 Disk - 10" dia
5
1009 0.030 Sheet
6
1008 0.040 Sheet
7
1002 0.010 Sheet
8
1014 0.250 Plate
9
1007 0.060 Plate
10
1012 0.125 Plate
11
1013 0.150 Plate
12
1028 0.500 Ring - 10" OD x 8.5" ID
13
1010 0.020 Sheet
14
1017 0.750 Tube - 3/4"
15
1015 0.375 Plate
16
1018 0.015 Tube - 1.0" OD
17
1001 0.005 Sheet - 1.0" x 23.75"
18
1016 0.500 Tube - 0.50" OD
19
1023 0.010 Sheet - 1.0" x 23.75"
20
1027 0.015 Sputter Target - 2.0" x 5.0"
Other
17 Other Items
Jan
Feb
618 1,079
68
611
263
576
275
0
0
122
321
101
20
56
6
12
0
146
228
8
1,100
0
0
189
0
54
0
0
0
0
8
0
171
0
3
0
0
99
0
105
217
36
1999 Invoiced Sales - Pounds per month
Mar
Apr
May
Jun
Jul
Aug
Sep
1,215 1,188 1,020
290 1,590
849 1,017
1,263
167 1,917
803
321
377
404
584
812
617
969
572
359
909
353
0
581
0
530
414 1,017
614
275
422
360
686
246
177
191
486
8
98
263
176
690
287
179
41
204
560
143
276
0
770
0
752
0
0
174
32
117
129
414
581
26
191
32
90
432
17
8
0
450
0
0
0
35
0
0
0
0
48
293
93
0
0
174
102
183
45
54
126
92
119
0
8
12
558
0
0
12
0
0
0
0
375
0
0
0
0
0
230
0
41
0
0
20
0
0
0
17
0
0
51
6
54
33
27
33
14
18
0
0
0
0
0
0
0
0
0
0
0
0
57
86
100
40
52
43
35
Total Cum %
8,866
22%
5,931
37%
5,661
50%
3,170
58%
2,902
65%
2,334
71%
1,766
76%
1,714
80%
1,636
84%
1,265
87%
1,135
90%
797
92%
775
94%
590
95%
375
96%
279
97%
208
97%
207
98%
131
98%
105
98%
666
100%
40,513
Alloy 1
Stephen C. Graves Copyright 2003
All Rights Reserved
1-82
Sales
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Other
Material Gauge 2040
0.015
2031
0.020
2035
0.030
2041
0.020
2043
0.015
2027
0.060
2050
0.015
2029
0.045
2026
0.010
2051
0.022
2025
0.002
2034
0.125
2045
0.030
2044
0.020
2047
0.030
2039
0.020
2052
0.035
2036
0.015
2046
0.015
2012
0.045
-
Description
Welded Tube .75" OD
Sheet Annealed
Sheet Annealed
Welded Tube .75" OD
Welded Tube 1.0" OD
Plate Annealed
Welded Tube 1" OD With Cap
Sheet Annealed
Sheet Annealed
Welded Tube 1.25" OD
Foil Annealed
Plate Annealed
Welded Tube 1.0" OD
Welded Tube 1.0" OD
Welded Tube 1.5O" OD
Welded Tube .50" OD
Tube 1.25" OD
Sheet Annealed
Welded Tube 1.5" OD
4" Repair Disk
35 Other Items
Jan
296
761
1,638
0
0
0
0
137
0
0
551
0
0
0
0
0
0
108
0
0
77
1999 Invoiced Sales - Pounds per Month
Feb Mar Apr May Jun
Jul Aug Sep
936 2,989 1,366 2,468 989 657 528 1,392
521 826 671 889 1,004 3,975
27
7
116 1,138 634 524 579 1,672 703 517
50 316
3 379
0 2,856
0
0
0 480 444
0
77 118 343
0
0 277 323
60
0 504
12 205
0
0 1,003
0
0 176
0
0
122 430
18
37
16
0 368
5
0 435
0 251 412
0
0
0
0
0 1,014
0
0
0
0
0
0
0
0
0
0
0
0
0
35
78
63
34
0
0 208
0
0 370
0
0
1
0
0
41
0
0
32 241 108
4
0
0
255 100
0
0
0
0
0
0
0 181 142
0
0
0
0
0
0 302
0
0
0
0
0
0
0
13
56
0
27
0
0
1
0
0
0
40
0 133
0
0
8
6
15
0
84
7
9
8
118
64
67 113 133
44
24 112
Total Cum %
11,623
27%
8,681
48%
7,520
65%
3,604
74%
1,462
77%
1,382
80%
1,179
83%
1,133
86%
1,098
88%
1,014
91%
551
92%
418
93%
412
94%
386
95%
355
96%
323
96%
302
97%
205
98%
173
98%
137
98%
753
100%
42,709
Alloy 2
Stephen C. Graves Copyright 2003
All Rights Reserved
1-83
Alloy #1 Product Heirarchy
(Top 20 Items - 98% of Sales)
4" Bar
6,817 lbs/mo
25% RSD
4
8
12
15
1/4" Plate
5,463 lbs/mo
23% RSD
10
11
1/8" Plate
4,104 lbs/mo
30% RSD
2
5
6
9
13
14
16
18
20
0.030" Sheet
2,053 lbs/mo
28% RSD
1
3
7
17
19
Stephen C. Graves Copyright 2003
All Rights Reserved
1-84
Alloy #2 Product Heirarchy
(Top 20 Items - 98% of Sales)
4" Bar
7,474 lbs/mo
59% RSD
1/4" Plate
6,726 lbs/mo
59% RSD
6
12
1/8" Plate
5,181 lbs/mo
59% RSD
2
3
4
8
10
13
14
15
16
17
20
0.015" Sheet
1,808 lbs/mo
65% RSD
1
5
7
18
19
Stephen C. Graves Copyright 2003
All Rights Reserved
0.030" Sheet
204 lbs/mo
126% RSD
11
9
1-85
Sales
Rank Material Gauge From 0.030" Sheet
1
1011
0.002
3
1003
0.005
7
1002
0.010
19
1023
0.010
17
1001
0.005
Description
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Foil
Sheet
Sheet
Sheet - 1.0" x 23.75"
Sheet - 1.0" x 23.75"
Monthly Subtotal
Input required at yield
618
263
20
0
171
1,072
1,191
1,079
576
56
99
0
1,810
2,011
1,215
584
287
14
0
2,100
2,333
1,188
812
179
18
20
2,217
2,463
1,020
617
41
0
0
1,678
1,864
290
969
204
0
0
1,463
1,626
1,590
572
560
0
0
2,722
3,024
849
359
143
0
17
1,368
1,520
1,017
909
276
0
0
2,202
2,447
From 0.125" Plate
0.030" Sheet to Supply Above
2
1004
0.015 Sheet
16
1018
0.015 Tube - 1.0" OD
20
1027
0.015 Sputter Target - 2.0" x 5.0"
18
1016
0.015 Tube - 0.50" OD
14
1017
0.015 Tube - 3/4"
13
1010
0.020 Sheet
5
1009
0.030 Sheet
6
1008
0.040 Sheet
9
1007
0.060 Plate
Monthly Subtotal
90% Input Required at Yield
1,191
68
8
0
3
0
0
0
321
0
1,591
1,768
2,011
611
0
105
0
0
54
122
101
146
3,150
3,500
2,333
1,263
0
0
0
0
102
614
191
32
4,535
5,039
2,463
167
0
0
51
8
183
275
486
117
3,750
4,167
1,864
1,917
0
0
6
12
45
422
8
129
4,403
4,893
1,626
803
230
0
54
558
54
360
98
414
4,197
4,663
3,024
321
0
0
33
0
126
686
263
581
5,034
5,594
1,520
377
41
0
27
0
92
246
176
26
2,505
2,783
From 0.250" Plate
0.125" Plate to Supply Above
10
1012
0.125 Plate
11
1013
0.150 Plate
Monthly Subtotal
80% Input Required at Yield
1,768
228
1,100
3,096
3,870
3,500
8
0
3,508
4,385
5,039
32
0
5,071
6,339
4,167
90
0
4,257
5,321
4,893
432
0
5,325
6,656
4,663
17
35
4,715
5,894
5,594
8
0
5,602
7,002
From 4.0" Sheet Bar
0.250" Plate to Supply Above
8
1014
0.250 Plate
15
1015
0.375 Plate
4
1029
0.500 Disk - 10" dia
12
1028
0.500 Ring - 10" OD x 8.5" ID
Monthly Subtotal
90% Input Required at Yield
3,870
6
0
275
0
4,151
4,612
4,385
12
0
0
189
4,586
5,096
6,339
0
0
353
0
6,692
7,436
5,321
770
0
0
48
6,139
6,821
6,656
0
0
581
293
7,530
8,367
5,894
752
0
0
93
6,739
7,487
7,002
0
375
530
0
7,907
8,786
90%
Stephen C. Graves Copyright 2003
All Rights Reserved
Alloy 1
Total
(Pounds)
Monthly Standard
Average Deviation
% RSD
8,866
5,661
1,766
131
208
985
629
196
15
23
372
235
168
32
56
38%
37%
85%
223%
242%
18,480
2,053
569
28%
2,447
404
0
0
33
12
119
177
690
191
4,073
4,525
18,480
5,931
279
105
207
590
775
2,902
2,334
1,636
2,053
659
31
12
23
66
86
322
259
182
569
594
76
35
22
185
54
224
214
194
28%
90%
245%
300%
94%
282%
63%
70%
83%
107%
36,932
4,104
1213
30%
2,783
0
0
2,783
3,479
4,525
450
0
4,975
6,219
36,932
1,265
1,135
4,104
141
126
1213
185
365
30%
131%
290%
49,165
5,463
1273
23%
3,479
0
0
414
0
3,893
4,326
6,219
174
0
1,017
174
7,584
8,427
49,165
1,714
375
3,170
797
5,463
190
42
352
89
1273
328
125
337
107
23%
172%
300%
96%
121%
61,357
6,817
1722
25%
1-86
Sales
Rank
Material Gauge - Description
From 0.030" Sheet
11
2025
0.002 Foil Annealed
9
2026
0.010 Sheet Annealed
Monthly Subtotal
90% Input required at yield
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Total
Monthly Standard
(Pounds) Average Deviation
Sep
551
0
551
612
0
0
0
0
0
435
435
484
0
0
0
0
0
251
251
279
0
412
412
458
0
0
0
0
0
0
0
0
0
0
0
0
551
1,098
61
122
1,833
204
296
0
0
108
0
404
449
936
0
0
0
0
936
1,040
2,989
480
0
13
0
3,483
3,870
1,366
444
1,003
56
0
2,869
3,188
2,468
0
0
0
40
2,508
2,787
989
77
0
27
0
1,093
1,215
657
118
176
0
133
1,084
1,205
528
343
0
0
0
871
967
1,392
0
0
1
0
1,393
1,548
11,623
1,462
1,179
205
173
1291
162
131
23
19
16,269
1,808
From 0.125" Sheet
0.030" Sheet to Supply Above
0.015" Sheet to Supply Above
2
2031
0.020 Sheet Annealed
4
2041
0.020 Welded Tube .75" OD
14
2044
0.020 Welded Tube 1.0" OD
16
2039
0.020 Welded Tube .50" OD
10
2051
0.022 Welded Tube 1.25" OD
3
2035
0.030 Sheet Annealed
13
2045
0.030 Welded Tube 1.0" OD
15
2047
0.030 WELDED TUBE 1.5O" OD
17
2052
0.035
Tube 1.25" OD
8
2029
0.045 Sheet Annealed
20
2012
0.045 4" Repair Disk
Monthly Subtotal
90% Input required at yield
612
449
761
0
0
0
0
1,638
0
0
0
137
0
3,597
3,997
0
1,040
521
50
0
0
0
116
0
255
0
122
8
2,113
2,347
484
3,870
826
316
0
181
0
1,138
370
100
302
430
6
8,022
8,913
0
3,188
671
3
32
142
1,014
634
0
0
0
18
15
5,717
6,352
279
2,787
889
379
241
0
0
524
0
0
0
37
0
5,136
5,706
458
1,215
1,004
0
108
0
0
579
1
0
0
16
84
3,464
3,849
0
1,205
3,975
2,856
4
0
0
1,672
0
0
0
0
7
9,718
10,798
0
967
27
0
0
0
0
703
0
0
0
368
9
2,074
2,305
0
1,548
7
0
0
0
0
517
41
0
0
5
8
2,127
2,363
1,833
16,269
8,681
3,604
386
323
1,014
7,520
412
355
302
1,133
137
204
1808
965
400
43
36
113
836
46
39
34
126
15
46,630
5,181
From 0.250" Plate
0.125" Sheet to Supply Above
6
2027
0.060 Plate Annealed
12
2034
0.125 Plate Annealed
Monthly Subtotal
80% Input required at yield
3,997
0
0
3,997
4,996
2,347
0
35
2,382
2,978
8,913
277
78
9,268
11,585
6,352
323
63
6,738
8,423
5,706
60
34
5,801
7,251
3,849
0
0
3,849
4,811
10,798
504
0
11,302
14,128
2,305
12
208
2,524
3,156
2,363
205
0
2,568
3,210
46,630
1,382
418
5181
154
46
60,538
6,726
3990
59%
From 4.0" Sheet Bar
0.250" Plate to Supply Above
90% Input Required at Yield
4,996
5,551
2,978
3,309
11,585
12,872
8,423
9,359
7,251
8,057
4,811
5,346
14,128
15,698
3,156
3,506
3,210
3,567
67,264
7,474
4433
59%
From 0.015" Sheet
1
2040
5
2043
7
2050
18
2036
19
2046
0.015
0.015
0.015
0.015
0.015
90%
Welded Tube .75" OD
Welded Tube 1" OD
Welded Tube 1" OD With Cap
Sheet Annealed
Welded Tube 1.5" OD
Monthly Subtotal
Input required at yield
Stephen C. Graves Copyright 2003
All Rights Reserved
184
190
% RSD
256
900
202
332
37
45
1175
256
1175
1184
933
83
72
338
533
122
87
101
163
26
3053
3053
183
67
300%
156%
126%
70%
125%
254%
163%
232%
65%
126%
65%
123%
233%
193%
200%
300%
64%
268%
221%
300%
130%
171%
59%
59%
119%
145%
Alloy 2
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Material
Monthly Monthly
Demand Sigma
Period Average
(Weeks) (Pipeline)
Period
Sigma
Service
Level
Reliability
Factor
Buffer
Safety
Total
Alloy #1
0.125" Plate
0.030" Sheet
4,104
2,053
1,213
569
1
1
947
474
583
273
95%
95%
90%
90%
958
450
191
92
2,100
1,020
Alloy #2
0.125" Plate
0.015" Sheet
5,181
1,808
3,053
1,175
1
1
1,196
417
1,467
564
95%
95%
90%
90%
2,412
928
361
135
3,970
1,480
Estimated Inventory Requirements
Stephen C. Graves Copyright 2003
All Rights Reserved
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