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McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 3

Network Planning

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3.1 Why Network Planning?

Find the right balance between inventory,transportation and manufacturing costs,

Match supply and demand underuncertainty by positioning and managinginventory effectively,

Utilize resources effectively by sourcingproducts from the most appropriatemanufacturing facility

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Three Hierarchical Steps Network design

Number, locations and size of manufacturing plants andwarehouses Assignment of retail outlets to warehouses Major sourcing decisions Typical planning horizon is a few years.

Inventory positioning: 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?

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3.2 Network Design

Physical configuration and infrastructure ofthe supply chain.

A strategic decision with long-lastingeffects on the firm.

Decisions relating to plant and warehouselocation as well as distribution andsourcing

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Reevaluation of Infrastructure

Changes in: demand patterns

product mix

production processes sourcing strategies

cost of running facilities.

Mergers and acquisitions may mandatethe integration of different logisticsnetworks

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Key Strategic Decisions

Determining the appropriate number offacilities such as plants and warehouses.

Determining the location of each facility.

Determining the size of each facility.

Allocating space for products in eachfacility.

Determining sourcing requirements. Determining distribution strategies, i.e., the

allocation of customers to warehouse

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Objective and Trade-Offs

Objective: Design or reconfigure the logistics network inorder to minimize annual system-wide cost subject to avariety of service level requirements

Increasing the number of warehouses typically yields: An improvement in service level due to the reduction in averagetravel time to the customers

An increase in inventory costs due to increased safety stocksrequired to protect each warehouse against uncertainties incustomer 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.

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Data Collection

Locations of customers, retailers, existing warehousesand distribution centers, manufacturing facilities, andsuppliers.

All products, including volumes, and special transportmodes (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

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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 samecustomers

Logistics characteristics like weight and volume.

Product type product models or style differing only in the type of packaging.

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Replacing Original Detailed Datawith Aggregated Data

Technology exists to solve the logisticsnetwork design problem with the originaldata

Data aggregation still useful becauseforecast demand is significantly moreaccurate at the aggregated level

Aggregating customers into about 150-200zones usually results in no more than a 1percent error in the estimation of totaltransportation costs

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General Rules for Aggregation

Aggregate demand points into at least 200zones

Holds for cases where customers are classified intoclasses according to their service levels or frequency

of delivery Make sure each zone has approximately an

equal amount of total demand

Zones may be of different geographic sizes.

Place aggregated points at the center of thezone

Aggregate products into 20 to 50 product groups

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Customer AggregationBased 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%

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Product Aggregation

Total Cost:$104,564,000Total Products: 46

Total Cost:$104,599,000Total Products: 4

Cost Difference: 0.03%

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Transportation Rates

Rates are almost linear with distance butnot with volume

Differences between internal rate andexternal rate

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Internal Transportation Rate

For company-owned trucks

Data Required:

Annual costs per truck

Annual mileage per truck

Annual amount delivered

Trucks effective capacity

Calculate cost per mile per SKU.

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External Transportation RateTwo Modes of Transportation

Truckload, TL Country sub-divided into zones. One zone/state

except for: Big states, such as Florida or New York (two zones)

Zone-to-zone costs provides cost per mile pertruckload between any two zones.

TL cost from Chicago to Boston =

Illinois-Massachusetts cost per mile X Chicago-Boston distance

TL cost structure is not symmetric

E t l T t ti R t

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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 products specific class

include: product density, ease or difficulty of handling and transporting, and liability

for damage.

After establishing rating, identify rate basis number. Approximate distance between the loads 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 freightrate table).

Exception rates providesless expensive rates Commodity rates are specialized commodity-specific

rates

External Transportation RateTwo Modes of Transportation

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SMC3s 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 LTLcontracts between shippers, carriers, and third-party logistics providers

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Transportation Rate for Shipping4,000 lbs.

FIGURE 3-7: Transportation rates for shipping 4,000 lb

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Mileage Estimation

Estimatelonaand lata, the longitude andlatitude of point a (and similarly for point b)

Distance between a and b

For short distances

For large distances

2 2)69 ( ( )ab a b a blonD lon lat lat

1 2 2) ))) ))2(69) sin (sin( cos( cos( (sin(

2 2

a b a b

ab a X b X

lat lat lon lonD lat lat

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CircuityFactor,

Equations underestimate the actual roaddistance.

Multiply Dab

by .

Typical values:

= 1.3 in metropolitan areas

= 1.14 for the continental United States

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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!

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Warehouse Costs Handling costs

Labor and utility costs

Proportional to annual flow through the warehouse.

Fixed costs

All cost components not proportional to the amount offlow

Typically proportional to warehouse size (capacity)but in a nonlinear way.

Storage costs Inventory holding costs

Proportional to average positive inventory levels.

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Determining Fixed Costs

FIGURE 3-8: Warehouse fixed costs as a function of the

warehouse capacity

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Determining Storage Costs

Multiply inventory turnover by holding cost

Inventory Turnover =

Annual Sales / Average Inventory Level

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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

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Warehouse Capacity Example

Annual flow = 1,000 units

Inventory turnover ratio = 10.0

Average inventory level = 100 unitsAssume each unit takes 10 sqft. of space

Required space for products = 2,000 sqft.

Total space required for the warehouse isabout 6,000 square feet

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Potential Locations

Geographical and infrastructureconditions.

Natural resources and labor availability.

Local industry and tax regulations.

Public interest.

Not many will qualify based on all theabove conditions

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Service Level Requirements

Specify a maximum distance between eachcustomer and the warehouse serving it

Proportion of customers whose distance totheir assigned warehouse is no more thana given distance

95% of customers be situated within 200 miles

of the warehouses serving themAppropriate for rural or isolated areas

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Future Demand

Strategic decisions have to be valid for 3-5years

Consider scenario approach and netpresent values to factor in expected futuredemand over planning horizon

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$-

$10

$20

$30

$40$50

$60

$70

$80

$90

0 2 4 6 8 10

Number of Warehouses

Cost(millions$)

Total Cost

Transportation CostFixed Cost

Inventory Cost

Number of Warehouses

OptimalNumberof Warehouses

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Industry Benchmarks:Number of Distribution Centers

Avg.# ofWH 3 14 25

Pharmaceuticals Food Companies Chemicals

- High margin product- Service not important (oreasy to ship express)- Inventory expensiverelative to transportation

- Low margin product- Service very important- Outbound transportationexpensive relative to inbound

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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 companys accounting information

Often the best way to identify errors in the data, problematicassumptions, modeling flaws.

Make local or small changes in the network configurationto see how the system estimates impact on costs andservice levels. 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?

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Solution Techniques

Mathematical optimization techniques:

1. Exact algorithms: find optimal solutions

2. Heuristics: find good solutions, notnecessarily optimal

Simulation models: provide a mechanism to

evaluate specified design alternatives created bythe designer.

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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 withidentical warehouse handling costs.

There are three markets areas c1,c2 and c3 withdemands of 50,000, 100,000 and 50,000,respectively.

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Unit Distribution Costs

Facilitywarehouse

p1 p2 c1 c2 c3

w1 0 4 3 4 5

w2 5 2 2 1 2

H i ti #1

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Heuristic #1:Choose the Cheapest Warehouse to Source

Demand

D = 50,000

D = 100,000

D = 50,000

Cap = 60,000

$5 x 140,000

$2 x 60,000

$2 x 50,000

$1 x 100,000

$2 x 50,000

Total Costs = $1,120,000

Heuristic #2:

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Heuristic #2:Choose the warehouse where the total deliverycosts to and from the warehouse are the lowest

[Consider inbound and outbound distribution costs]

D = 50,000

D = 100,000

D = 50,000

Cap = 60,000

$4

$5

$2

$3

$4$5

$2

$1

$2

$0

P1 to WH1 $3

P1 to WH2 $7P2 to WH1 $7P2 to WH 2 $4

P1 to WH1 $4P1 to WH2 $6P2 to WH1 $8P2 to WH 2 $3


Market #1 is served by WH1, Markets 2 and 3are served by WH2

Heuristic #2:

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D = 50,000

D = 100,000

D = 50,000

Cap = 60,000

Cap = 200,000

$5 x 90,000

$2 x 60,000

$3 x 50,000

$1 x 100,000

$2 x 50,000

$0 x 50,000

P1 to WH1 $3

P1 to WH2 $7P2 to WH1 $7P2 to WH 2 $4



Total Cost = $920,000

Heuristic #2:Choose the warehouse where the total deliverycosts to and from the warehouse are the lowest

[Consider inbound and outbound distributioncosts]

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The Optimization Model

The problem described earlier can be framed as thefollowing linear programming problem.

Let

x(p1,w1), x(p1,w2), x(p2,w1) and x(p2,w2) be the flowsfrom the plants to the warehouses.

x(w1,c1), x(w1,c2), x(w1,c3) be the flows from thewarehouse w1 to customer zones c1, c2 and c3.

x(w2,c1), x(w2,c2), x(w2,c3) be the flows fromwarehouse w2 to customer zones c1, c2 and c3

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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.

The Optimization Model

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Optimal Solution

Facilitywarehouse

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

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Simulation Models

Useful for a given design and a micro-levelanalysis. Examine:

Individual ordering pattern.

Specific inventory policies.

Inventory movements inside the warehouse.

Not an optimization model

Can only consider very few alternatemodels

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Which One to Use?

Use mathematical optimization for staticanalysis

Use a 2-step approach when dynamics insystem has to be analyzed: Use an optimization model to generate a

number of least-cost solutions at the macrolevel, taking into account the most importantcost components.

Use a simulation model to evaluate thesolutions generated in the first phase.

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DSS for Network Design

Flexibilityto incorporate a large set of preexistingnetwork 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

3 3 I P i i i d

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3.3 Inventory Positioning andLogistics 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 theimpact of this interaction on the inventory policy of each

facility Ways to manage:

Wait for specific orders to arrive before starting to manufacturethem [make-to-order facility]

Otherwise, decide on where to keep safety stock?

Which facilities should produce to stock and which shouldproduce to order?

Si l P d t Si l F ilit

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Single Product, Single FacilityPeriodic Review Inventory Model

Assume -

SI:amount of time between when an order is placeduntil the facility receives a shipment (IncomingService Time)

S:Committed Service Timemade by the facility to itsown customers.

T: Processing Timeat the facility.

Net Lead Time = SI + T - S

Safety stock at the facility:

STSI

STSIzh

2 Stage System

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2-Stage System

Reducing committed service time from facility 2to facility 1 impacts required inventory at bothfacilities

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.

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ElecComp Case

Large contract manufacturer of circuit boards and otherhigh 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 leadtimes

N S l Ch i St t

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New Supply Chain Strategy OBJECTIVES:

Reduce inventory and financial risks Provide customers with competitive response times.

ACHIEVE THE FOLLOWING: Determining the optimal locationof inventory across the various

stages Calculating the optimal quantity of safety stock for each component at

each stage

Hybrid strategy of Push and Pull Push Stages produce to stock where the company keeps safety stock Pull stages keep no stock at all.

Challenge: 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%

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Notations Used

FIGURE 3-11: How to read the diagrams

Trade Offs

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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 basedstrategy

Montgomery facility keeps inventory and hence ismanaged with a Push or Make-to-Stock strategy.

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Current Safety Stock Location

FIGURE 3-12: Current safety stock location

Optimized Safety Stock

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Optimized Safety StockLocation

FIGURE 3-13: Optimized safety stock

C t S f t St k ith L

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Current Safety Stock with LesserLead Time

FIGURE 3-14: Optimized safety stock with reduced lead time

Supply Chain with

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Supply Chain withMore Complex Product Structure

FIGURE 3-15: Current supply chain

Optimized Supply Chain with

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Optimized Supply Chain withMore Complex Product Structure

FIGURE 3-16: Optimized supply chain

K P i t

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Key Points

Identifying the Push-Pull boundary

Taking advantage of the risk pooling concept

Demand for components used by a number offinished products has smaller variability and

uncertainty than that of the finished goods. Replacing traditional supply chain strategies

that are typically referred to as sequential, orlocal, optimization by a globally optimized

supply chain strategy.

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Local vs. Global Optimization

FIGURE 3-17: Trade-off between quoted lead time and safety stock

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Global Optimization

For the same lead time, cost is reducedsignificantly

For the same cost, lead time is reduced

significantly

Trade-off curve has jumps in variousplaces

Represents situations in which the location ofthe Push-Pull boundary changes

Significant cost savings are achieved.

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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

Integrating Inventory Positioning

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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?

Integrating Inventory Positioningand Network Design

Integrating Inventory Positioning

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Integrating Inventory Positioningand Network Design

FIGURE 3-18: Sample plot of each SKU by volume and demand

Three Different Product

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Three Different ProductCategories

High variability - low volume products

Low variability - high volume products, and

Low variability - low volume products.

Supply Chain Strategy Different for

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pp y gythe Different Categories

High variability low volume products Inventory risk the main challenge for Position them mainly at the primary warehouses

demand from many retail outlets can be aggregatedreducing inventory costs.

Low variability high volume products 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.

3 4 Resource Allocation

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3.4 Resource Allocation

Supply chain master planning

The process of coordinating and allocatingproduction, and distribution strategies andresources to maximize profit or minimizesystem-wide cost

Process takes into account: interaction between the various levels of the supply

chain identifies a strategy that maximizes supply chain

performance

Global Optimization and DSS

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Global Optimization and DSSFACTORS TO CONSIDER

Facility locations: plants, distribution centers anddemand points

Transportation resources including internal fleet andcommon carriers

Products and product information Production line information such as min lot size,

capacity, costs, etc.

Warehouse capacities and other information such ascertain technology (refrigerators) that a specificwarehouse has and hence can store certain products

Demand forecast by location, product and time.

Focus of the Output

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Focus of the Output

Sourcing Strategies:

where should each product be producedduring the planning horizon, OR

Supply Chain Master Plan:

production quantities, shipment size andstorage requirements by product, location andtime period.

The Extended Supply Chain: From

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The Extended Supply Chain: FromManufacturing to Order Fulfillment

FIGURE 3-19: The extended supply chain: from manufacturing to order fulfillment

Questions to Ask During the

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gPlanning 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 andhence inventory levels but significantly increasestransportation cost.

Should we rebalance inventory between warehouses orreplenish from the plants to meet unexpected regional

changes in demand?

SUMMARY

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Network Planning Characteristics

Network Design Inventory Positioningand 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

SUMMARY

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SUMMARY Optimizing supply chain performance is difficult

conflicting objectives demand and supply uncertainties supply chain dynamics.

Through network planning, firms can globallyoptimize supply chain performance Combines network design, inventory positioning and

resource allocation Consider the entire network

account production Warehousing transportation inventory costs service level requirements.

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SUMMARY

Demonstrate applicability of risk poolingand postponement, EOQ modeling, andinventory sizing to improve customer

service in make-to-order job shop setting Demonstrates value from getting and

looking at data

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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

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Metallurgical Products

Make-to-order job shop operation

600 SKUs 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 23 weeks

Limited data


All Rights Reserved

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Production Order #1

4 Bar 1/4 Plate 1/8 Plate 0.015 Sheet Tubing

Production Order #2 Production Order #3

CleanRoll AnnealSheet Bar

(forged ingot)

Repeat0 n 3

Finish(cut, weld, etc.)

Production Orders


All Rights Reserved

Why Is Customer Lead Time 7

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Why Is Customer Lead Time 7Weeks?

From sales order to process order takes 2weeks

Typical order requires multiple process

orders, each 23 weeks

Expediting as scheduling rule

Self fulfilling prophecy?


All Rights Reserved

What Are Benefits From

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What Are Benefits FromReducing Lead Time?

New accounts and new business

Protect current business from switching tosubstitutes or Chinese competitor

Possibly less inventory

Better planning and better customerservice

Savings captured by customers?


All Rights Reserved

How Might Starck Reduce

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How Might Starck ReduceCustomer 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?


All Rights Reserved

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Two-Product Optimal Cycle Time

*

*

2 2

2

2 400 400 0.02 years.06 100 526000 .06 125 183000

B F B B F F

B F

B B F F

K K h D h DCost T T

T

K KT

h D h D

T


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I t di t I t

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Intermediate Inventory

Characterize demand by possibleintermediate 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


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1999 Invoiced Sales - Pounds per month

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Popularity Material Gauge - Description Jan Feb Mar Apr May Jun Jul Aug Sep Total Cum %

1 1011 0.002 Foil 618 1,079 1,215 1,188 1,020 290 1,590 849 1,017 8,866 22%

2 1004 0.015 Sheet 68 611 1,263 167 1,917 803 321 377 404 5,931 37%

3 1003 0.005 Sheet 263 576 584 812 617 969 572 359 909 5,661 50%

4 1029 0.500 Disk - 10" dia 275 0 353 0 581 0 530 414 1,017 3,170 58%5 1009 0.030 Sheet 0 122 614 275 422 360 686 246 177 2,902 65%

6 1008 0.040 Sheet 321 101 191 486 8 98 263 176 690 2,334 71%

7 1002 0.010 Sheet 20 56 287 179 41 204 560 143 276 1,766 76%

8 1014 0.250 Plate 6 12 0 770 0 752 0 0 174 1,714 80%

9 1007 0.060 Plate 0 146 32 117 129 414 581 26 191 1,636 84%

10 1012 0.125 Plate 228 8 32 90 432 17 8 0 450 1,265 87%

11 1013 0.150 Plate 1,100 0 0 0 0 35 0 0 0 1,135 90%

12 1028 0.500 Ring - 10" OD x 8.5" ID 0 189 0 48 293 93 0 0 174 797 92%13 1010 0.020 Sheet 0 54 102 183 45 54 126 92 119 775 94%

14 1017 0.750 Tube - 3/4" 0 0 0 8 12 558 0 0 12 590 95%

15 1015 0.375 Plate 0 0 0 0 0 0 375 0 0 375 96%

16 1018 0.015 Tube - 1.0" OD 8 0 0 0 0 230 0 41 0 279 97%

17 1001 0.005 Sheet - 1.0" x 23.75" 171 0 0 20 0 0 0 17 0 208 97%

18 1016 0.500 Tube - 0.50" OD 3 0 0 51 6 54 33 27 33 207 98%

19 1023 0.010 Sheet - 1.0" x 23.75" 0 99 14 18 0 0 0 0 0 131 98%

20 1027 0.015 Sputter Target - 2.0" x 5.0" 0 105 0 0 0 0 0 0 0 105 98%Other - - 17 Other Items 217 36 57 86 100 40 52 43 35 666 100%

40,513

1999 Invoiced Sales - Pounds per month

Alloy 1Stephen C. Graves Copyright 2003

All Rights Reserved

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Sales

Rank Material Gauge - Description Jan Feb Mar Apr May Jun Jul Aug Sep Total Cum %

1 2040 0.015 Welded Tube .75" OD 296 936 2,989 1,366 2,468 989 657 528 1,392 11,623 27%

2 2031 0.020 Sheet Annealed 761 521 826 671 889 1,004 3,975 27 7 8,681 48%

3 2035 0.030 Sheet Annealed 1,638 116 1,138 634 524 579 1,672 703 517 7,520 65%

4 2041 0.020 Welded Tube .75" OD 0 50 316 3 379 0 2,856 0 0 3,604 74%5 2043 0.015 Welded Tube 1.0" OD 0 0 480 444 0 77 118 343 0 1,462 77%

6 2027 0.060 Plate Annealed 0 0 277 323 60 0 504 12 205 1,382 80%

7 2050 0.015 Welded Tube 1" OD With Cap 0 0 0 1,003 0 0 176 0 0 1,179 83%

8 2029 0.045 Sheet Annealed 137 122 430 18 37 16 0 368 5 1,133 86%

9 2026 0.010 Sheet Annealed 0 0 435 0 251 412 0 0 0 1,098 88%

10 2051 0.022 Welded Tube 1.25" OD 0 0 0 1,014 0 0 0 0 0 1,014 91%

11 2025 0.002 Foil Annealed 551 0 0 0 0 0 0 0 0 551 92%

12 2034 0.125 Plate Annealed 0 35 78 63 34 0 0 208 0 418 93%

13 2045 0.030 Welded Tube 1.0" OD 0 0 370 0 0 1 0 0 41 412 94%

14 2044 0.020 Welded Tube 1.0" OD 0 0 0 32 241 108 4 0 0 386 95%

15 2047 0.030 Welded Tube 1.5O" OD 0 255 100 0 0 0 0 0 0 355 96%

16 2039 0.020 Welded Tube .50" OD 0 0 181 142 0 0 0 0 0 323 96%

17 2052 0.035 Tube 1.25" OD 0 0 302 0 0 0 0 0 0 302 97%

18 2036 0.015 Sheet Annealed 108 0 13 56 0 27 0 0 1 205 98%

19 2046 0.015 Welded Tube 1.5" OD 0 0 0 0 40 0 133 0 0 173 98%

20 2012 0.045 4" Repair Disk 0 8 6 15 0 84 7 9 8 137 98%

Other - - 35 Other Items 77 118 64 67 113 133 44 24 112 753 100%

42,709

1999 Invoiced Sales - Pounds per Month

Alloy 2


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Alloy #1 Product Heirarchy

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(Top 20 Items - 98% of Sales)

4

8

12

15

10

11

2

5

6

9

13

14

16

18

20

1

3

7

17

19

0.030" Sheet

2,053 lbs/mo

28% RSD

1/8" Plate4,104 lbs/mo

30% RSD

1/4" Plate

5,463 lbs/mo

23% RSD

4" Bar

6,817 lbs/mo

25% RSD


All Rights Reserved

Alloy #2 Product Heirarchy

(Top 20 Items - 98% of Sales)

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(Top 20 Items 98% of Sales)

6

12

2

3

4

8

1013

14

15

16

17

20

1

5

7

18

19

0.015" Sheet

1,808 lbs/mo

65% RSD

11

9

0.030" Sheet

204 lbs/mo

126% RSD

1/8" Plate

5,181 lbs/mo59% RSD

1/4" Plate

6,726 lbs/mo

59% RSD

4" Bar

7,474 lbs/mo

59% RSD


All Rights Reserved

Sales Total Monthly Standard

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Rank Material Gauge - Description Jan Feb Mar Apr May Jun Jul Aug Sep (Pounds) Average Deviation % RSD

From 0.030" Sheet

1 1011 0.002 Foil 618 1,079 1,215 1,188 1,020 290 1,590 849 1,017 8,866 985 372 38%

3 1003 0.005 Sheet 263 576 584 812 617 969 572 359 909 5,661 629 235 37%

7 1002 0.010 Sheet 20 56 287 179 41 204 560 143 276 1,766 196 168 85%

19 1023 0.010 Sheet - 1.0" x 23.75" 0 99 14 18 0 0 0 0 0 131 15 32 223%

17 1001 0.005 Sheet - 1.0" x 23.75" 171 0 0 20 0 0 0 17 0 208 23 56 242%

Monthly Subtotal 1,072 1,810 2,100 2,217 1,678 1,463 2,722 1,368 2,20290% Input required at yield 1,191 2,011 2,333 2,463 1,864 1,626 3,024 1,520 2,447 18,480 2,053 569 28%

From 0.125" Plate

0.030" Sheet to Supply Above 1,191 2,011 2,333 2,463 1,864 1,626 3,024 1,520 2,447 18,480 2,053 569 28%

2 1004 0.015 Sheet 68 611 1,263 167 1,917 803 321 377 404 5,931 659 594 90%

16 1018 0.015 Tube - 1.0" OD 8 0 0 0 0 230 0 41 0 279 31 76 245%

20 1027 0.015 Sputter Target - 2.0" x 5.0" 0 105 0 0 0 0 0 0 0 105 12 35 300%

18 1016 0.015 Tube - 0.50" OD 3 0 0 51 6 54 33 27 33 207 23 22 94%

14 1017 0.015 Tube - 3/4" 0 0 0 8 12 558 0 0 12 590 66 185 282%

13 1010 0.020 Sheet 0 54 102 183 45 54 126 92 119 775 86 54 63%

5 1009 0.030 Sheet 0 122 614 275 422 360 686 246 177 2,902 322 224 70%

6 1008 0.040 Sheet 321 101 191 486 8 98 263 176 690 2,334 259 214 83%9 1007 0.060 Plate 0 146 32 117 129 414 581 26 191 1,636 182 194 107%

Monthly Subtotal 1,591 3,150 4,535 3,750 4,403 4,197 5,034 2,505 4,073

90% Input Required at Yield 1,768 3,500 5,039 4,167 4,893 4,663 5,594 2,783 4,525 36,932 4,104 1213 30%

From 0.250" Plate

0.125" Plate to Supply Above 1,768 3,500 5,039 4,167 4,893 4,663 5,594 2,783 4,525 36,932 4,104 1213 30%

10 1012 0.125 Plate 228 8 32 90 432 17 8 0 450 1,265 141 185 131%

11 1013 0.150 Plate 1,100 0 0 0 0 35 0 0 0 1,135 126 365 290%



From 4.0" Sheet Bar

0.250" Plate to Supply Above 3,870 4,385 6,339 5,321 6,656 5,894 7,002 3,479 6,219 49,165 5,463 1273 23%

8 1014 0.250 Plate 6 12 0 770 0 752 0 0 174 1,714 190 328 172%

15 1015 0.375 Plate 0 0 0 0 0 0 375 0 0 375 42 125 300%

4 1029 0.500 Disk - 10" dia 275 0 353 0 581 0 530 414 1,017 3,170 352 337 96%

12 1028 0.500 Ring - 10" OD x 8.5" ID 0 189 0 48 293 93 0 0 174 797 89 107 121%



Alloy 1Stephen C. Graves Copyright 2003All Ri hts Reserved

Sales

Rank Material Gauge - Description Jan Feb Mar Apr May Jun Jul Aug Sep

Total

(Pounds)

Monthly

Average

Standard

Deviation % RSD

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g p p y g p

From 0.030" Sheet

11 2025 0.002 Foil Annealed 551 0 0 0 0 0 0 0 0 551 61 184 300%

9 2026 0.010 Sheet Annealed 0 0 435 0 251 412 0 0 0 1,098 122 190 156%

Monthly Subtotal 551 0 435 0 251 412 0 0 0

90% Input required at yield 612 0 484 0 279 458 0 0 0 1,833 204 256 126%

From 0.015" Sheet

1 2040 0.015 Welded Tube .75" OD 296 936 2,989 1,366 2,468 989 657 528 1,392 11,623 1291 900 70%

5 2043 0.015 Welded Tube 1" OD 0 0 480 444 0 77 118 343 0 1,462 162 202 125%

7 2050 0.015 Welded Tube 1" OD With Cap 0 0 0 1,003 0 0 176 0 0 1,179 131 332 254%

18 2036 0.015 Sheet Annealed 108 0 13 56 0 27 0 0 1 205 23 37 163%

19 2046 0.015 Welded Tube 1.5" OD 0 0 0 0 40 0 133 0 0 173 19 45 232%

Monthly Subtotal 404 936 3,483 2,869 2,508 1,093 1,084 871 1,393

90% Input required at yield 449 1,040 3,870 3,188 2,787 1,215 1,205 967 1,548 16,269 1,808 1175 65%

From 0.125" Sheet

0.030" Sheet to Supply Above 612 0 484 0 279 458 0 0 0 1,833 204 256 126%

0.015" Sheet to Supply Above 449 1,040 3,870 3,188 2,787 1,215 1,205 967 1,548 16,269 1808 1175 65%

2 2031 0.020 Sheet Annealed 761 521 826 671 889 1,004 3,975 27 7 8,681 965 1184 123%

4 2041 0.020 Welded Tube .75" OD 0 50 316 3 379 0 2,856 0 0 3,604 400 933 233%

14 2044 0.020 Welded Tube 1.0" OD 0 0 0 32 241 108 4 0 0 386 43 83 193%16 2039 0.020 Welded Tube .50" OD 0 0 181 142 0 0 0 0 0 323 36 72 200%

10 2051 0.022 Welded Tube 1.25" OD 0 0 0 1,014 0 0 0 0 0 1,014 113 338 300%

3 2035 0.030 Sheet Annealed 1,638 116 1,138 634 524 579 1,672 703 517 7,520 836 533 64%

13 2045 0.030 Welded Tube 1.0" OD 0 0 370 0 0 1 0 0 41 412 46 122 268%

15 2047 0.030 WELDED TUBE 1.5O" OD 0 255 100 0 0 0 0 0 0 355 39 87 221%

17 2052 0.035 Tube 1.25" OD 0 0 302 0 0 0 0 0 0 302 34 101 300%

8 2029 0.045 Sheet Annealed 137 122 430 18 37 16 0 368 5 1,133 126 163 130%

20 2012 0.045 4" Repair Disk 0 8 6 15 0 84 7 9 8 137 15 26 171%


90% Input required at yield 3,997 2,347 8,913 6,352 5,706 3,849 10,798 2,305 2,363 46,630 5,181 3053 59%

From 0.250" Plate

0.125" Sheet to Supply Above 3,997 2,347 8,913 6,352 5,706 3,849 10,798 2,305 2,363 46,630 5181 3053 59%6 2027 0.060 Plate Annealed 0 0 277 323 60 0 504 12 205 1,382 154 183 119%

12 2034 0.125 Plate Annealed 0 35 78 63 34 0 0 208 0 418 46 67 145%


80% Input required at yield 4,996 2,978 11,585 8,423 7,251 4,811 14,128 3,156 3,210 60,538 6,726 3990 59%

From 4.0" Sheet Bar

0.250" Plate to Supply Above 4,996 2,978 11,585 8,423 7,251 4,811 14,128 3,156 3,210


Alloy 2Stephen C. Graves Copyright 2003All Ri hts Reserved

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Material

Monthly

Demand

Monthly

Sigma

Period

(Weeks)

Average

(Pipeline)

Period

Sigma

Service

Level

Reliability

Factor Buffer Safety TotalAlloy #1

0.125" Plate 4,104 1,213 1 947 583 95% 90% 958 191 2,100

0.030" Sheet 2,053 569 1 474 273 95% 90% 450 92 1,020

Alloy #2

0.125" Plate 5,181 3,053 1 1,196 1,467 95% 90% 2,412 361 3,9700.015" Sheet 1,808 1,175 1 417 564 95% 90% 928 135 1,480

Estimated Inventory Requirements

chap003 (1)

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