Inventory

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/Irwin

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Overview of inventory

• Inventory functionality and definitions

• Inventory carrying cost• Planning inventory• Managing uncertainty• Inventory management

policies• Inventory management

practices

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Why do we have inventories?

Because the customer usually isn’t sitting at the plant exit!

Queen Elizabeth research station in Antarctica

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Risks associated with holding inventory

• Typical measures of exposure to investments in inventory– Time duration– Depth of commitment– Width of commitment

• Supply chain exposure based on location– Manufacturer’s exposure is typically narrow, but deep and of long

duration– Wholesaler’s exposure is wider than manufacturers and

somewhat deep• Duration is medium

– Retailer’s exposure is wide, but not very deep• Duration is usually short except for specialty retailers

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Functions of Inventory

• Geographical specialization allows us to specialize production across different locations

• Decoupling allows us to run processes for maximum economic lot sizes within a single facility

• Supply/Demand balancing accommodates the elapsed time between inventory availability and consumption

• Buffering uncertainty accommodates uncertainty related to – Demand in excess of forecast or – Unexpected delays in delivery (aka safety stock)

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Inventory policy

• Inventory policy is a firm’s guidelines concerning– What to purchase or manufacture– When to take action– In what quantity should action be

taken– Where products should be

located geographically

• Firm’s policy also includes decisions about which inventory management practices to adopt

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Service level

• Service level is a performance target specified by management and defines inventory performance objectives

• Common measures of service level include– Performance cycle is the elapsed time between

release of a purchase order by the buyer to the receipt of shipment

– Case fill rate is the percent of cases ordered that are shipped as requested

– Line fill rate is the percent of order lines (items) that were filled completely

– Order fill is the percent of customer orders filled completely

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Inventory definitions

• Inventory includes materials, components, work-in-process, and finished goods that are stocked in the company’s logistical system

– The cycle inventory (base stock) is the portion of average inventory that results from replenishment

– Order quantity is the amount ordered for replenishment

– Transit inventory represents the amount typically in transit between facilities or on order but not received

– Obsolete inventory is stock that is out-of-date or is not in recent demand

– Speculative inventory is bought to hedge a currency exchange or to take advantage of a discount

– Safety stock is the remainder of inventory in the logistics system

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Average inventory is the typical amount stocked over time

• Average inventory equals the maximum inventory plus the minimum inventory divided by two– Typically equal to ½ order quantity + safety stock + in-transit stock

Figure 7.1 Inventory Cycle for Typical Product

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Smaller replenishment order quantities results in lower average inventory

• Policy must decide how much inventory to order at a specified time– Reorder point defines when a replenishment order is initiated

• However, other factors are important like performance cycle uncertainty, purchasing discounts, and transportation economies

Figure 7.3 Alternative Order Quantity and Average Inventory

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Inventory carrying cost is the expense associated with maintaining inventory

• Inventory expense is– Annual inventory carrying cost percent times average inventory

value• Cost components

– Cost of capital is specified by senior management– Taxes on inventory held in warehouses– Insurance is based on estimated risk or loss over time and facility

characteristics– Obsolescence results from deterioration of product during

storage• E.g. food and pharmaceutical sell-by dates

– Storage is facility expense related to product holding rather than product handling

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Final carrying cost percent used by a firm is a managerial policy

Table 7.2 Inventory Carrying Cost Components

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Inventory ordering cost components

• Order preparation costs• Order transportation costs• Order receipt processing costs• Material handling costs• Total cost is driven by inventory planning

decisions which establish when and how much to order

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When to order

• Basic reorder formula if demand and performance are certain

– R = Reorder point in units– D = Average daily demand in units– T = Average performance cycle length in days

• If safety stock is needed to accommodate uncertainty the formula is

– R = Reorder point in units– D = Average daily demand in units– T = Average performance cycle length in days– SS = Safety stock in units

×= TR D

+ SS×= TR D

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How much to order

• Economic order quantity is the amount that balances the cost of ordering with the cost of maintaining average inventory– Assumes demand and

costs are relatively stable for the year

– Does not consider impact of joint ordering of multiple products Figure 7.4 Economic Order Quantity

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Standard mathematical solution for EOQ

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Example EOQ solution using Table 7.3

• Total ordering cost is $152 = (2400/300 x $19.00)• Inventory carrying cost is $150 = [300/2 x (5 x 0.20)]

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Simple EOQ model assumptions

• All demand is satisfied• Rate of demand is continuous, constant and know• Replenishment performance cycle time is constant and

known• Constant price of product that is independent of order

quantity or time• An infinite planning horizon exists• No interaction between multiple items of inventory• No inventory is in transit• No limit is placed on capital availability

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Relationships useful for guiding inventory planning

• EOQ is found at the point where annualized order placement cost and inventory carrying cost are equal

• Average base inventory equal one-half order quantity

• Value of the inventory unit, all other things being equal, will have a direct relationship with replenishment order frequency– Higher value products will be ordered more frequently

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Typical adjustments to EOQ

• Volume transportation rates offer a freight-rate discount for larger shipments– Compare total cost with each transportation rate option

• Quantity discounts offer a lower per unit cost when larger quantities are purchased– If discount is sufficient to offset added inventory carrying cost less the reduced

cost of ordering then it is viable choice• Other EOQ adjustments

– Production lot size– Multiple-item purchase– Limited capital– Dedicated trucking– Unitization

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Uncertainty in inventory management

• Inventory policy must deal with uncertainty– Demand uncertainty — when and how much product

will our customers order?– Performance cycle uncertainty — how long will it take

to replenish inventory with our customers?• Variations must be considered in both areas to

make effective inventory planning decisions

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Demand uncertainty can be managed using safety stock

• To protect against stockout when uncertain demand exceeds forecast we add safety stock to base inventory

• Planning safety stock requires three steps– Determine the likelihood of stockout using a probability

distribution– Estimate demand during a stockout period– Decide on a policy concerning the desired level of

stockout protection

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Probability theory enables calculation of safety stock for a target service level

• Service level is equal to 100% minus probability % of stockout– E.g. a service level of 99% results in a stockout probability of 1%

• The most common probability distribution for demand is the normal distribution– From analysis of historical demand data the safety stock required

to ensure a stock out only 1% of the time is possible– A one-tailed normal distribution is used because only demand

that is greater than the forecast can create a stockout

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Example of historical demand analysis using a normal distribution

Figure 7.7 Normal DistributionFigure 7.6 Historical Analysis of Demand History

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Performance cycle uncertainty means operations cannot assume consistent delivery

Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration

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Demand Uncertainty

Units Frequency(F) Deviation From Mean Deviation Squared FiDi2

0 1 -5 25 251 2 -4 16 322 2 -3 9 183 3 -2 4 12 4 4 -1 1 45 5 0 0 06 3 +1 1 37 3 +2 4 128 2 +3 9 18 9 2 +4 16 3210 1 +5 25 25N=28 s=5

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Continuation Demand Uncertainty

54.228

1812

n

DF ii

1812 iiDF

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Combined Demand and Performance Uncertainty

222tsc SDTS

Where:T=average performance cycle timeSt =standard deviation of the performance cycleD=average daily salesSs=standard deviation of daily sales, and

= standard deviation of the combined uncertaintyc

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Combined Demand and Performance Uncertainty

83.12)2(00.5)54.2(00.10 222 c

Round to 13

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Safety stock with combined uncertainty

• Planning for both demand and performance cycle uncertainty requires combining two independent variables

• The joint impact of the probability of both demand and performance cycle variation must be determined– Direct method is to combine standard deviations using a

convolution formula

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The fill rate is the magnitude rather than the probability of a stockout

• Increasing the replenishment order quantity decreases the relative magnitude of potential stockouts

• The formula for this relationship is

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3 approaches to introduce safety stock into dependent demand situations

• Put safety time into the requirements plan– E.g. order a component earlier than needed to assure timely

arrival• Over-planning top-level demand is a procedure to

increase the requisition by a quantity specified by some estimate of expected plan error– E.g. assume plan error will not exceed 5 percent

• Utilize statistical techniques to set safety stocks directly for a component rather than to the item of top-level demand

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Approaches to implementing inventory management policies

• Reactive (or pull) approach responds to customer demand to pull the product through the distribution channel

• Planning approach proactively allocates inventory on the basis of forecasted demand and product availability

• Hybrid approach uses a combination of push and pull

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Inventory control using reactive approaches

• Inventory control defines how often inventory levels are reviewed to determine when and how much to order– Perpetual review continuously

monitors inventory levels to determine inventory replenishment needs

– Periodic review monitors inventory status of an item at regular intervals such as weekly or monthly

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Reorder point formulas for reactive methods

Perpetual Review Periodic Review

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Assumptions of classical reactive inventory logic

• All customers, market areas, and product contribute equally to profits• Infinite capacity exists at the production facility• Infinite inventory availability at the supply location• Performance cycle time can be predicted and that cycle lengths are

independent• Customer demand patterns are relatively stable and consistent• Each distribution warehouse’s timing and quantity of replenishment

orders are determined independently of all other sites, including the supply source

• Performance cycle length cannot be correlated with demand

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Planning approaches coordinate requirements across multiple locations in the supply chain

• Two planning approaches– Fair share allocation provides each distribution facility

with an equitable distribution of available inventory• Limited ability to manage multistage inventories

– Requirements planning integrates across the supply chain taking into consideration unique requirements

• Materials requirements planning (MRP) is driven by a production schedule

• Distribution requirements planning (DRP) is driven by supply chain demand

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Example of fair share allocation method

• Allocation of 500 available units from plant– Warehouse 1 = 47– Warehouse 2 = 383– Warehouse 3 = 70

Figure 7.11 Fair Share Allocation Example

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Integrated planning approach for raw materials, work-in-process, and finished goods

Figure 7.12 Conceptual Design of Integrated MRP/DRP System

MRP system

DRP system

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Limitations to planning approaches

• Requires accurate and coordinated forecasts for each warehouse

• Requires consistent and reliable product movement between warehouse facilities

• Subject to frequent rescheduling (system nervousness) because of production breakdowns or delivery delays

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Collaborative inventory replenishment programs

• Replenishment programs are designed to streamline the flow of goods within the supply chain– Intent is to reduce reliance on forecasting and position inventory

using actual demand on a just-in-time basis• Quick response (QR) is a technology-driven cooperative

effort between retailers and suppliers to improve inventory velocity while matching supply to consumer buying patterns

• Vendor-managed inventory (VMI) is a modified QR that eliminates the need for replenishment orders

• Profile replenishment (PR) extends QR and VMI by giving suppliers the right to anticipate future requirements according to their knowledge of a product category

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Managerial considerations when developing an inventory policy

Table 7.18 Suggested Inventory Management Logic

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Inventory management practices

• Product/market classification groups products, markets, or customers with similar characteristics to facilitate inventory management– E.g. classify by sales, profit contribution, inventory value, usage rate or item

category• Segment strategy definition specifies all aspects of inventory

management process for each segment of inventory– E.g. service objectives, forecasting method, management technique, and

review cycle• Policies and parameters must be defined at a detailed level

– E.g. data requirements, software applications, performance objectives, and decision guidelines

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Example of product classification by sales

Table 7.19 Product Market Classification (Sales)

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Sample illustrating segment strategy definitions

Table 7.20 Integrated Strategy