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© Wiley 2010
Chapter 12 – Independent Demand Inventory Management
Operations Managementby
R. Dan Reid & Nada R. Sanders4th Edition © Wiley 2010
PowerPoint Presentation by R.B. Clough – UNH M. E. Henrie - UAA
© Wiley 2010
Wall Street Speaks(compiled by Teradata, a division of NCR)
“Shares of Intel Corp. fell to an 11-month low on Wednesday, leading a decline in semiconductor-industry stocks a day after the world’s largest chipmaker warned that its inventories had risen sharply”, this despite 96% growth in quarterly profit. –Reuters, July 14, 2004
“Cisco Systems Inc. on Tuesday reported that quarterly profit surges 41%, but its shares fell sharply in after-hours trade on a rise in inventories.” - Reuters, August 10, 2004
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Wall Street Speaks(compiled by Teradata, a division of NCR)
“The day Nike announced the breakdown in its chain, the company’s stock dropped 20%, an amount so staggering that it makes the $100 million loss (in sales) seem like pocket change.” – Computer World, November 10, 2003
“General Motors was down 3.1%, or $1.37, at $42.75, after analysts with Goldman Sachs and Lehman Brothers downgraded their ratings of the stock, amid worries of inventory buildup.” –AP, July 30, 2004
“Blind execution [of a production plan] in the face of variation can tie up hundreds of millions in working capital and prevent you from supporting customer demand.” -Teradata
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Types of Inventory Inventory comes in many shapes and
sizes such as Raw materials – purchased items or
extracted materials transformed into components or products
Components – parts or subassemblies used in final product
Work-in-process – items in process throughout the plant
Finished goods – products sold to customers Distribution inventory – finished goods in
the distribution system
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Types of Inventory
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Uses of Inventory Anticipation or seasonal inventory Fluctuation Inventory or Safety stock: buffer
demand fluctuations Lot-size or cycle stock: take advantage of
quantity discounts or purchasing efficiencies Transportation or Pipeline inventory Speculative or hedge inventory protects
against some future event, e.g. labor strike Maintenance, repair, and operating (MRO)
inventories
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Principal Quantitative Models in Ch. 12
Inventory Turnover & Days or Weeks of Supply
P-Models: Periodic Review Models
Q-Models: Continuous Review Models
ABC Classification
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Inventory Investment Measures Example 1: The Coach Motor Home Company has annual cost of goods sold of $10,000,000. The average inventory value at any point in time is $384,615. Calculate inventory turnover and weeks/days of supply. Assume 52 weeks.
Inventory Turnover:
Weeks/Days of Supply:
turns inventory 26$384,615
0$10,000,00
value inventory average
sold goods ofcost annualTurnover
2weeks0/52$10,000,00
$384,615
dollarsin usage weekly average
dollarsin handon inventory averageSupply of Weeks
If there are 5 work days per week, that is 10 days of supply.
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Inventory Investment Measures Example 2: At Genuine Reproductions, the annual cost of goods sold was $3,000,000 last year. The average inventory value was $250,000. Calculate inventory turnover, the weeks of supply, and days of supply for last year. (Ch. 12, #3)
Inventory Turnover:
Weeks/Days of Supply:
turnsinventory 12$250,000
$3,000,000
valueinventory average
sold goods of cost annualTurnover
weeks4.33/52$3,000,000
$250,000
dollars inusage ekly average we
dollars in hand oninventory average Supply of Weeks
That means (5)(4.33) = 21.67 days of supply.
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Inventory Control ModelsFeature Q-Model:
Continuous Review
P-Model:Periodic Review
Order Quantity Q - constant q – variable
When to order When inventory hits reorder level R
At review period, every T time units
Recordkeeping At each + or - Only at review time T
Inventory Size Qq all else equal
Maintenance higher lower
Types of items High value ordinarySource: Chase, Jacobs, & Aquilano (McGraw-Hill)
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Most Important Inventory Costs
Holding Costs
Denoted H; includes the variable expenses incurred by the plant related to the volume of inventory held e.g. 15-25%
Ordering Cost
Denoted S; fixed, constant dollar amount incurred for each order placed
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Periodic (P) Review Systems Orders are placed at specified, fixed-time
intervals (e.g. every Friday), for a order size (q) to bring on-hand inventory (OH) up to the target inventory (TI), similar to the min-max system.
Advantages are: No need for a system to continuously monitor item Items ordered from the same supplier can be reviewed
on the same day saving purchase order costs Disadvantages:
Replenishment quantities (q) vary Order quantities may not quality for quantity discounts On the average, inventory levels will be higher than Q
systems-more stockroom space needed
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Managing Periodic (P) Review Systems
Prior to implementation, management must decide Replenishment period, i.e.,
time between orders Can use convenience or EOQ approximation
calculation to determine RP Cycle service level, i.e., the
probability of satisfying customer demand
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Periodic Review System Calculations
LRPtLRP
Safety Stock SS = zσRP+L
where z denotes the z-score needed for the desired service level, and
is the standard deviation of demand during the combined Review Period and Lead Time. Here we need to be given σt the standard deviation of demand per unit time (day or week).P-Models always include Safety Stock!
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Periodic Review System Calculations
Target Inventory level: TI = d(RP + L) + SS
d = average period demand RP = review period (days, wks)L = lead time (days, wks)SS = Safety Stock (as above)
Replenishment Quantity (q)=TI-OH OH is on-hand inventory
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Periodic Review System Calculations
days.) of instead units timeas used becan (Weeks
H2
dL-TIS
daysin period review
yearin work days no.
Cost HoldingAnnual AverageCost OrderingAnnual
Cost Annual Total
Note: This formula is not clearly stated in the text!
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Periodic Review (P) Model, Example 1: Your firm’s demand is normally distributed with mean 48/week and standard deviation 8. Lead time is 2 weeks, and the desired cycle service level is 94%. Initially, your review period is 1 week (every Friday you take inventory). Find the safety stock and the Target Inventory Level. [Ch. 12 #27.]
Safety Stock SS = z94σRP+L
ZZ9494 = 1.55 = 1.55
Stockout!Stockout!Tail Area = .06Tail Area = .06
Area = .44Area = .44
zz00
Area Area left of y-left of y-axis axis = .50= .50
z94 =1.55
86.13
)732.1()8(
21)8(
Safety Stock SS = (1.55)(13.86) = 21.48 -> 22
LRPtLRP
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Periodic Review (P) Model, Example 1, continued: [Ch. 12 #27.]
We found Safety Stock SS = (1.55)(13.86)
= 21.48 -> 22
Next find the Target Inventory level (TI):
TI = d(RP + L) + SS
= (48)(1+2) + 22
= 166 units
Follow-up: if you have 100 units on hand (OH =100),
Order quantity q = TI – OH = 66
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Periodic Review (P) Model, Example 1, extended: [Ch. 12 #27.] Suppose that the unit order cost is S = $25 and the unit holding cost is H=$2. Assuming 50 working weeks in the year, what is the total annual cost of inventory?
H2
dL-TIS
in weeks period review
yearin work weeksno.
Cost HoldingAnnual AverageCost OrderingAnnual
Cost Annual Total
22
)2()48(166
1
50
= $50 + $70 = $120
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Economic Order Quantity EOQ Assumptions:
Demand is known & constant - no safety stock is required
Lead time is known & constant
No quantity discounts are available
Ordering (or setup) costs are constant
All demand is satisfied (no shortages)
The order quantity arrives in a single shipment
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Total Annual Inventory Cost with EOQ Model
H2
Qcost
)()( holdingunitlevelinventoryaverageCostsHoldingAnnual
Let D= annual demand
Total annual cost= annual ordering cost + annual holding costs S
Q
Dcost
)().( orderingunityearperordersnoCostOrderingAnnual
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Total Annual Inventory Cost with EOQ Model
H2
QS
Q
DCost Annual Total
H
2DSQ
Quantity OrderEconomic the at
minimized is Cost Annual Total
EOQ
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Reorder Point for Q-Model
Reorder when the stock level drops to the amount that will be used during the lead time; thus
R = dL
where d is the daily demand and L is the lead time in days.
[Note that time units of weeks can also be used. Just make sure units match.]
L
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EOQ (Q)
Reorder Point (R)
Total Inventory Cost (TC)
units 500$6
$75*10,000*2
H
2DSQ
units 200days 5*days 250
10,000LdR
$3000$1500$1500$62
500$75
500
10,000TC
Continuous Review (Q) Model, Example 1: A computer assembler has annual demand of 10,000. They want to manage inventory for circuit boards which have an annual holding cost (H) of $6 per unit, and an ordering cost (S) of $75. Calculate the EOQ, the reorder point (R), and TC if the purchasing lead time is 5 days; assume 250 working days per year.
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Safety Stock for probabilistic Q-Model
If demand or lead time is uncertain, safety stock can be added to improve order-cycle service levels
Revised Reorder Point
R = dL +SS Here safety stock SS
=zσdL, where z is the number of standard deviations for the desired
service level, and σdL is standard deviation of the demand during lead time
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Computing Safety Stock
Order-cycle service level is the probability that demand during lead time will not exceed on-hand inventory
A 95% service level means the stockout risk is 5%, and has a z-score Z95=1.645
ZZ9595 = 1.645 = 1.645 zz00
Stockout!Stockout!Tail Area = .05Tail Area = .05
Area = .45Area = .45
Area Area left of y-left of y-axis axis = .50= .50
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Safety Stock Continuous Review (Q) Model, Example 1: Back to the computer assembler with an annual demand of 10,000. Now suppose that they determine that demand is probabilistic and in particular normally distributed. Calculate the Reorder Point with safety stock for a 95% service level if σdL =10 units.
Revised Reorder Point
R = dL +SS
units
dL
45.216
10645.
1days5 40
zdays5 days250
10,00095
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Q-model versions Economic Order Quantity (EOQ)
An optimizing method used for determining order quantity and reorder points; can include safety stock
Economic Production Quantity (EPQ) A model that allows for incremental product
delivery Quantity Discount Model
Modifies the EOQ process to consider cases where quantity discounts are available
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ABC Inventory Classification ABC classification is a method for determining level
of control and frequency of review of inventory items A Pareto analysis can be done to segment items into
value categories depending on annual dollar volume A Items – typically 20% of the items accounting for
80% of the inventory value-use Q system B Items – typically an additional 30% of the items
accounting for 15% of the inventory value-use Q or P C Items – Typically the remaining 50% of the items
accounting for only 5% of the inventory value-use P
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The AAU Corp. is considering doing an ABC analysis on its entire inventory but has decided to test the technique on a small sample of 15 of its SKU’s. The annual usage and unit cost of each item is shown below
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(A) First calculate the annual dollar volume for each item
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B) List the items in descending order based on annual dollar volume. (C) Calculate the cumulative annual dollar volume as a percentage of total dollars. (D) Classify the items into groups
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Graphical solution For Example 12.15 showing the ABC classification of materials
The A items (106 and 110) account for 60.5% of the value and 13.3% of the items The B items (115,105,111,and 104) account for 25% of the value and 26.7% of the
items The C items make up the last 14.5% of the value and 60% of the items How might you control each item classification? Different ordering rules for each?
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Determining Order Quantities
Lot-for-lot Order exactly what is needed
Fixed-order quantity
Specifies the number of units to order whenever an order is placed
Min-max system
Places a replenishment order when the on-hand inventory falls below the predetermined minimum level.
Order n periods
Order quantity is determined by total demand for the item for the next n periods
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Examples of Ordering Approaches
Lot for Lot Example 1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85Projected-on-Hand (30) 0 0 0 0 0 0 0Order Placement 40 70 65 60 55 85 75 85
Fixed Order Quantity Example with Order Quantity of 2001 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85Projected-on-Hand (30) 160 90 25 165 110 25 150 65Order Placement 200 200 200
Min-Max Example with min.= 50 and max.= 250 units1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85Projected-on-Hand (30) 180 110 185 125 70 165 90 165Order Placement 220 140 180 160
Order n Periods with n = 3 periods1 2 3 4 5 6 7 8
Requirements 70 70 65 60 55 85 75 85Projected-on-Hand (30) 135 65 0 140 85 0 85 0Order Placement 175 200 160
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Justifying Smaller Order Quantities
JIT or “Lean Systems” would recommend reducing order quantities to the lowest practical levels
Benefits from reducing Q’s: Improved customer responsiveness (inventory = Lead
time) Reduced Cycle Inventory Reduced raw materials and purchased components
Justifying smaller EOQ’s:
Reduce Q’s by reducing setup time (S). Consider S as a variable. “Setup reduction” is a well documented, structured approach to reducing S.
H
2DSQ
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Inventory Record Accuracy Inaccurate inventory records can
cause: Lost sales Disrupted operations Poor customer service Lower productivity Planning errors and expediting
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Inventory Record Accuracy
Two methods are available for checking record accuracy
Periodic counting - physical inventory is taken periodically, usually annually
Cycle counting-daily counting of prespecified items provides the following advantages:
Timely detection and correction of inaccurate records Elimination of lost production time due to unexpected
stock outs Structured approach using employees trained in cycle
counting
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Ultimate Objective of Inventory Management
Provide desired customer service level Customer service is the ability to satisfy
customer requirements Percentage of orders shipped on schedule Percentage of line items shipped on
schedule Percentage of dollar volume shipped on
schedule Idle time due to material and component
shortages
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Customer Service Level Examples
Percentage of Orders Shipped on Schedule Good measure if orders have similar value. Does not capture value. If one company represents 50% of your business but only 5% of your
orders, 95% on schedule could represent only 50% of value Percentage of Line Items Shipped on Schedule
Recognizes that not all orders are equal, but does not capture $ value of orders. More expensive to measure. Ok for finished goods. A 90% service level might mean shipping 225 items out of the total
250 line items totaled from 20 orders scheduled Percentage Of Dollar Volume Shipped on Schedule
Recognizes the differences in orders in terms of both line items and $ value
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Inventory Management Across the Organization Inventory management policies
affect functional areas throughout Accounting is concerned of the cost
implications of inventory Marketing is concerned as stocking
decision affect the level of customer service
Information Systems is involved to tack and control inventory records
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Chapter 12 Highlights Raw materials, purchased components,
work-in-process, finished goods, distribution inventory and maintenance, repair and operating supplies are all types of inventory. Inventories have several uses: anticipation inventory is built before it is needed; fluctuation stock provides a cushion; cycle stock is a result of the company’s ordering quantity; transportation inventory includes items in transit; speculative inventory is a buildup to protect against some future event and MRO inventory supports daily operations
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Chapter 12 Highlights The objectives of inventory management are to
provide the desired level of customer service, to allow cost-efficient operations, and to minimize inventory investment. Customer service can be measured in several ways, including as a percentage of orders shipped on schedule, a percentage of line items shipped on schedule, a percentage of dollar volume shipped on schedule, or idle time due to material and component shortages. Cost-efficient operations are achieved by using inventory as buffer stocks allowing a stable year-round workforce, and spreading the setup cost over a larger number of Inventory performance is measured by turns/supply.
Inventory costs include item cost, holding cost, ordering cost, and shortage cost.
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Chapter 12 Highlights (continued)
Inventory investment is measured in inventory turnover and/or level of supply. Inventory performance is calculated as inventory turnover or weeks, days, or hours of supply.
Relevant inventory costs include items costs, holding costs, and shortage costs. Holding costs include capital costs, storage costs, and risk costs. Ordering costs are fixed costs for placing an order or performing a setup. Shortage costs included costs related to additional paperwork, additional shipping expense, and the intangible cost of lost customer goodwill.
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Chapter 12 Highlights (continued)
Lot-for-lot, fixed-order quantity, min-max systems, order n periods, periodic review systems, EOQ models, quantity discount models, and single-period models can be used to determine order quantities.
Ordering decisions can be improved by analyzing total costs of an inventory policy. Total costs include ordering cost, holding cost, and material cost
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Chapter 12 Highlights (continued)
Practical considerations can cause a company to not use the optimal order quantity, that is, minimum order requirements
Smaller lot sizes give a company flexibility and shorter response times. The key to reducing order quantities is to reduce ordering or setup costs.
Calculating the appropriate safety stock policy enables companies to satisfy their customer service objective at minimum costs. The desired customer service level determines the appropriate z value.
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Chapter 12 Highlights (continued)
Inventory decisions about perishable products can be made using the single-period inventory model. The expected payoff is calculated to assist the quantity decision
The ABC classification system allows a company to assign the appropriate level of control and frequency of review of an item based on its annual dollar volume
Cycle counting is a method for maintaining accurate inventory records. Determining what and when to count are the major decisions
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Chapter 12 Highlights (continued)
Order Q’s can be determined by using L4L, fixed order Q’s, min-max, order n periods, quantity discounts, and single period systems.
Ordering decisions can be improved by analyzing TC Smaller lot sizes increase flexibility and reduce response
time. Safety stock can be added to reorder point calculations
to meet desired service level z value. Inventory decisions about perishable products can be
made by using the single-period inventory model. ABC analysis can be used to assign the appropriate level
of control and review frequency based on the annual dollar volume of each item.
Cycle counting of pre-specified items is an accepted method for maintaining inventory records
