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 $80 Cost (millions $) $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 0n3 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 0.030" Sheet 204 lbs/mo 126% RSD 1 5 7 18 19 Stephen C. Graves Copyright 2003 All Rights Reserved 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 1-87 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 1-88