Chapter 3 Network Planning.

Chapter 3 Network Planning

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

Three Hierarchical Steps
Network design 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. 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?

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

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

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

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.

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

Data Aggregation Customer Zone Product Groups
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.

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 zones usually results in no more than a 1 percent error in the estimation of total transportation costs

General Rules for Aggregation
Aggregate demand points into at least 200 zones Holds for cases where customers are classified into classes 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 the zone Aggregate products into 20 to 50 product groups

Customer Aggregation Based on 3-Digit Zip Codes

Product Aggregation

Transportation Rates Rates are almost linear with distance but not with volume Differences between internal rate and external rate

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.

External Transportation Rate Two 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 per truckload 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

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: product density, ease or difficulty of handling and transporting, and liability for damage. After establishing rating, identify rate basis number. 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

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 third-party logistics providers

Transportation Rate for Shipping 4,000 lbs.
FIGURE 3-7: Transportation rates for shipping 4,000 lb

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 For large distances

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

Chicago-Boston Distance
lonChicago = latChicago = 41.85 lonBoston = 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!

Warehouse Costs Handling costs Fixed costs Storage costs
Labor and utility costs Proportional to annual flow through the warehouse. Fixed costs 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.

Determining Fixed Costs
FIGURE 3-8: Warehouse fixed costs as a function of the warehouse capacity

Determining Storage Costs
Multiply inventory turnover by holding cost Inventory Turnover = Annual Sales / Average Inventory Level

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

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

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

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

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

Number of Warehouses Optimal Number of Warehouses

Industry Benchmarks: Number of Distribution Centers
Pharmaceuticals Food Companies Chemicals Avg. # of WH 3 14 25 - High margin product - Service not important (or easy to ship express) - Inventory expensive relative to transportation - Low margin product - Service very important - Outbound transportation expensive relative to inbound

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 Often the best way to identify errors in the data, problematic assumptions, modeling flaws. Make local or small changes in the network configuration to see how the system estimates impact on costs and service 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?

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.

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.

Unit Distribution Costs
Facility warehouse p1 p2 c1 c2 c3 w1 4 3 5 w2 2 1

Heuristic #1: Choose the Cheapest Warehouse to Source Demand
$2 x 50,000 $5 x 140,000 D = 100,000 $1 x 100,000 $2 x 60,000 Cap = 60,000 D = 50,000 $2 x 50,000 Total Costs = $1,120,000

Market #1 is served by WH1, Markets 2 and 3
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 P1 to WH1 $3 P1 to WH2 $7 P2 to WH1 $7 P2 to WH 2 $4 $4 $2 $5 $5 D = 100,000 P1 to WH1 $4 P1 to WH2 $6 P2 to WH1 $8 P2 to WH 2 $3 $4 $1 $2 Cap = 60,000 $2 D = 50,000 P1 to WH1 $5 P1 to WH2 $7 P2 to WH1 $9 P2 to WH 2 $4 Market #1 is served by WH1, Markets 2 and 3 are served by WH2

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 $3 P1 to WH2 $7 P2 to WH1 $7 P2 to WH 2 $4 $5 x 90,000 D = 100,000 P1 to WH1 $4 P1 to WH2 $6 P2 to WH1 $8 P2 to WH 2 $3 $1 x 100,000 $2 x 60,000 Cap = 60,000 $2 x 50,000 D = 50,000 P1 to WH1 $5 P1 to WH2 $7 P2 to WH1 $9 P2 to WH 2 $4 Total Cost = $920,000

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

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) = x(w1,c3) + x(w2,c3) = 50000 all flows greater than or equal to zero.

Optimal Solution Total cost for the optimal strategy is $740,000
Facility warehouse p1 p2 c1 c2 c3 w1 140,000 50,000 40,000 w2 60,000 Total cost for the optimal strategy is $740,000

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

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.

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

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?

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. Net Lead Time = SI + T - S Safety stock at the facility:

2-Stage System Overall objective is to choose:
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.

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

New Supply Chain Strategy
OBJECTIVES: Reduce inventory and financial risks Provide customers with competitive response times. ACHIEVE THE FOLLOWING: 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 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%

Notations Used FIGURE 3-11: How to read the diagrams

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.

Current Safety Stock Location
FIGURE 3-12: Current safety stock location

Optimized Safety Stock Location
FIGURE 3-13: Optimized safety stock

Current Safety Stock with Lesser Lead Time
FIGURE 3-14: Optimized safety stock with reduced lead time

Supply Chain with More Complex Product Structure
FIGURE 3-15: Current supply chain

Optimized Supply Chain with More Complex Product Structure
FIGURE 3-16: Optimized supply chain

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.

Local vs. Global Optimization
FIGURE 3-17: Trade-off between quoted lead time and safety stock

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.

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 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?

Integrating Inventory Positioning and Network Design
FIGURE 3-18: Sample plot of each SKU by volume and demand

Three Different Product Categories
High variability - low volume products Low variability - high volume products, and Low variability - low volume products.

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 demand from many retail outlets can be aggregated reducing 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 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

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.

Focus of the Output Sourcing Strategies: Supply Chain Master Plan:
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.

The Extended Supply Chain: From Manufacturing to Order Fulfillment
FIGURE 3-19: The extended supply chain: from manufacturing to order fulfillment

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?

SUMMARY Network Planning Characteristics
Network Design Inventory Positioning and Management Resource Allocation Decision focus Infrastructure Safety stock Production Distribution Planning Horizon Years Months Aggregation Level Family Item Classes Frequency Yearly Monthly/Weekly ROI High Medium Implementation Very Short Short Users Very Few Few

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.

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 Implemented in stages, slowed down by SAP problems and installation Proposed stocking 8 intermediates and cutting cycle on rolling mill to 1 week. 80% of products could be made with one rolling cycle; so a product could wait for 2 rolling cycles and still make 3 week lead time. Need initially 1 month of inventory, but this will allow excess stocks to be drawn down – eventually get 2 mm inventory reduction. Set in place max and min inventories for 30/1000 for alloy 1 and 15/1000 for alloy 2 Difficult to get sales to quote shorter lead times, due to lack of confidence -- w/o this production could not demonstrate their ability to meet shorter lead times, vicious cycle

Stephen C. Graves Copyright 2003
Case: H. C. Starck, Inc. Background and context Why are lead times long? How might they be reduced? What are the costs? benefits? This is a neat case. Intent is to look at internal supply chain with common problems and see what counter measures or tactics might apply. Another LFM internship Stephen C. Graves Copyright 2003 All Rights Reserved

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 Good example of product tree structure or proliferation; 100 – 200 sku’s are produced from a single input. A key observation is that there are standard intermediates: ¼“ plate, 1/8” plate, 3/100 “ sheet. Metallurgical products takes forged ingots and rolls into plates and sheet; plates and sheet then fabricated into parts, or sold as is. Inventory 3 – 4 months of raw stock, 1.5 months of WIP and 1 month of FG How do they plan production? Why is there so much raw inventory? How would you describe the product structure? Stephen C. Graves Copyright 2003 All Rights Reserved

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? Note that cycle time is 2 – 3 weeks, and they have lot of inventory in system (1 month of FG, 1.5 months of WIP); so why is customer lead time so long? Note that sales will put in false orders to get material in pipeline, and only hot jobs move. Also, case does not say what due dates are quoted – but if they are quoting 7 weeks, then that may also be a reason why. Drumbeat meeting is good idea in theory, if one has a plan; but if not, then it reverts to expediting. Need get a good understanding of how production control done – MTO, based on some estimates of how long each cycle takes. Production control guy releases work to shop based on gut feel --- work is pushed into shop based on rough lead times. Expediting meeting decides what to pull out of the shop, as it is needed. Stephen C. Graves Copyright 2003 All Rights Reserved

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

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? Note – by holding intermediate inventory, you would serve demand out of this stock, eliminating one or more process orders. Note – the replenishment of the intermediate inventory is make-to-stock, whereas we serve customer demand as make-to-order. Intermediate inventory is sort of an example of postponement – we postpone the point at which we make the final product. What dictates the cycle time for each process order? The large mill operates on two week cycle alternating between breakdown runs and finishing runs. Stephen C. Graves Copyright 2003 All Rights Reserved

Two-Product Optimal Cycle Time
Essentially EOQ model --- optimal cycle time is one week. Setups are 8 hours at 2*25 $ per hour. Holding cost is 6% for 100 $ per pound or 125 $ per pound. (Why is this not 9%) Need also to check to see if weekly setup is feasible. For Breakdown, pounds at 622 pound per hour (570 pounds in 55 minutes): requires 845 hours per year, half of one shift For Finish, pound per year, at 225 pounds per hour (450 pounds in 2 hours): requires 813 hours per year, half of one shift. So have enough capacity to cycle weekly – two setups per week. What’s the impact of this? Cuts process order time in half, from two weeks to one week. But why are they operating 3 shifts? Not clear from these numbers Stephen C. Graves Copyright 2003 All Rights Reserved

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 Two alloys are 80% of demand Top 20 products are 98% of demand Might use SIP for this Stephen C. Graves Copyright 2003 All Rights Reserved

RSD is sigma over mu, coefficient of variation for monthly demand These numbers are restated to reflect yield losses Bracketed are stocking points – driven by being a significant part of the volume, a significant point of proliferation, having significant benefits from risk pooling, and providing lead time benefits. Note lead time implications for stocked products --- at thinnest gauge, then just need to go to foil mill, and maybe fabrication. At 1/8 inch, need to make one pass – which can be in first week or second week and still get three week lead time. For thicker products, can make from raw stock – 4 inch bar in one or two passes; could give these priority. Stephen C. Graves Copyright 2003 All Rights Reserved

Note variance reduction at each intermediate Note – to do this, you need know more about processing than is in case, as to how each product is made; what the rolling passes are. Alloy 1 Stephen C. Graves Copyright 2003 All Rights Reserved

At 100 $ per pound the additional inventory is $850, But monthly demand ( at 100 $ per pound is about 1.3 MM $. Note – buffer here corresponds to what we have been calling safety stock; safety is an additional inventory held to protect against production variability Estimated Inventory Requirements Stephen C. Graves Copyright 2003 All Rights Reserved

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