Chapter 11
Inventory:Managing to
Meet Demand
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc. 2008
Learning Objectives
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Explain why businesses carry inventory.
Describe the costs associated with inventory.
Compare independent and dependent demand inventory.
Calculate days-of-supply.
Explain how a reorder point system works.
Describe the contribution made by a safety stock.
Compute the reorder point for a desired service level.
Make computations for the economic order quantity models.
Describe weaknesses of the economic order quantity.
Compute the appropriate order quantity for a fixed interval, variable quantity
system.
Describe the information inputs necessary to manage dependent demand
inventory.
Compute planned order releases using material requirements planning.
Explain ABC analysis.
Compute dollar days for a given inventory.
11-2
Introduction: A Balancing Act for Management
• Both the presence and absence of inventory
contribute to value and to costs.
– Too much inventory is an investment that will provide no
return.
– Too little inventory results in missed or late sales and
deliveries.
• Carrying the correct amount of inventory is a difficult
balancing act.
11-3
Why Should Businesses Carry Inventory?
• Decoupling: Reducing the direct dependency of a
process step on its predecessor. This could be in a
process or in the supply chain.
– Decouple customer from supplier and machine from machine
– Disruptions, if decoupled, don’t have as serious of an impact
– Decoupling enhances reliability and response time
11-4
Why Should Businesses Avoid Carrying
Too Much Inventory?
• Inventory is an investment that should provide a
financial return.
• Excess inventory is an investment that provides no
return.
• In addition to the cost of purchasing it, inventory also
has other “carrying” costs:
– Cost of storage
– Cost of insurance
– Reduction in flexibility
11-5
Costs and Benefits
•
•
•
•
•
Order cost:The fixed cost associated with ordering inventory.
Changeover (setup) cost:The cost of changing equipment from producing
one product or service to another. Analogous to order cost.
Carrying cost:Costs associated with carrying inventory. Insurance, storage,
opportunity cost of money tied up in inventory.
Stockout cost:Costs associated with not having inventory when a customer
wants it.
Purchasing cost:Cost of purchasing the actual inventory. Sometimes
quantity discounts lower this cost, but this comes at the expense of raising
carrying costs.
11-6
Costs and Benefits
• If inventory is replenished when it reaches zero, average
inventory is half the order quantity.
• Order costs and carrying costs are inversely related. Large
orders increase average inventory and carrying cost, but the
larger the orders, the less frequently you have to order.
Exhibit 11.1 Average Inventory as Q/2
11-7
Retailing and Finished-Product Inventories
•
Continuous
Replenishment
– The delivery of
inventory, frequently,
and in small quantities.
– Results in lower
average levels of
inventory.
Exhibit 11.2 Frequent Small
Deliveries versus Infrequent Large
Deliveries
11-8
Retailing and Finished-Product Inventories:
Independent Demand Inventories
• Independent Demand Inventory is inventory whose
demand is dictated by the marketplace.
– Finished products
– Retailer stocks
– Maintenance, Repair, and Operating (MRO) Inventory
(Inventory that consists of items consumed in the day-to-day
activities of a business).
11-9
Retailing and Finished-Product Inventories:
Inventory and Time
• Inventory provides a supply or coverage for a given
length of time.
• Days-of-supply is inventory on hand divided by
average daily demand.
• Stockout
– An instance when demand cannot be satisfied by existing
inventory.
– Delays in replenishment can cause stockouts.
11-10
Retailing and Finished-Product Inventories:
Days-of-Supply Calculation
Calculate days of supply when average demand is 40
gallons per day, and 60 gallons remain
On  Hand Inventory
Days of Supply 
Average Daily Demand
60
Days of Supply 
40
Days of Supply  1.5 days
11-11
Retailing and Finished-Product Inventories:
Days-of-Supply Example
•
•
•
If a retailer has a six-day supply of a product, how soon a stockout occurs
depends on the rate demand. If the rate is “average” it will last for six days
If demand is less than average, it will last longer.
If demand is greater than average, it won’t last as long
Exhibit 11.3 Example of Days’ Supply
11-12
Retailing and Finished-Product Inventories:
Inventory and Time
• Level production in manufacturing uses finishedgoods inventory to reduce the need to change the
output rate to match demand changes.
– Production is greater than demand during low-demand periods.
– Production is less than demand during high-demand periods.
– Inventory accumulated during low demand is then used to
satisfy high demand.
Exhibit 11.4 Inventory to Buffer
against Seasonal Demand
11-13
Component and Raw Materials Inventory
• Work-in-process inventory (WIP)
– Inventory that has begun processing, but has not yet completed it.
• Transfer batch
– The quantity produced at a workcenter before transferring the products to
the next step in the process.
• Pipeline inventory
– Inventory in transit.
• Inventory in oil pipelines, on trucks, planes, and so on
• Reducing transit times reduces pipeline inventory
• SKUs (stock-keeping units)
– Unique numbers that identify items in inventory.
11-14
Dependent Demand Inventory
• Dependent demand inventory is inventory whose demand is
determined by the production schedule for finished products
– It usually consists of components and raw materials
11-15
Inventory Decisions
• When should it be ordered?
• How many should be ordered?
11-16
Managing Independent Demand Inventory
• Service Level: Percent of orders satisfied from existing
inventory.
• Replenishment Lead Time: The time required to
receive inventory that has been ordered.
• Since there is a replenishment lead time, orders must be
made before the inventory has run out.
• Two general approaches:
– Fixed quantity, variable interval systems
– Fixed interval, variable quantity systems
11-17
Fixed Quantity, Variable Interval System:
The Reorder Point Model
• Demand during the replenishment lead time is uncertain.
• Assume:
– Demand averages 60 units per week and is normally distributed
– The replenishment lead time is 2 weeks
• When should inventory be reordered?
11-18
Fixed Quantity, Variable Interval System:
The Reorder Point Model
If the order is placed when the onhand inventory is equal to the average
demand during the replenishment lead time (120), what is the
probability having enough inventory to meet demand?
50%
11-19
Fixed Quantity, Variable Interval System:
The Reorder Point Model
If the order is placed when the onhand inventory is equal to 1 standard
deviation above the average demand during the replenishment leadtime
(132) , what is the probability of having enough inventory to meet
demand?
84.13%
11-20
Fixed Quantity, Variable Interval System:
The Reorder Point Model
If the order is placed when the onhand inventory is equal to 3 standard
deviations above the average demand during the replenishment
leadtime (132) , what is the probability of having enough inventory to
meet demand?
99.87%
11-21
Fixed Quantity, Variable Interval System:
The Reorder Point Model
Safety Stock: Additional inventory (above mean demand)
maintained to increase service levels in response to demand
variability.
A safety stock of 36
units increases
the probability of
not stocking
out during the
replenishment
lead time from 50%
to 99.87%
11-22
Fixed Quantity, Variable Interval System:
The Reorder Point Model
• To meet demand during the replenishment lead time, the reorder
point must include a safety stock linked to demand variability.
ROP  d LT  σ LT Z
Where:
ROP = Reorder Point (i.e., quantity at which more inventory is ordered)
dLT = Average demand during replenishment lead time
σLT = Standard deviation of demand during replenishment lead time
Z
= Number of standard deviations above the average demand during
replenishment lead time required for desired service level.
11-23
Fixed Quantity, Variable Interval System:
The Reorder Point Model
•
The diagram shows how a fixed-quantity reorder point system
works.
• What should the reorder point be if we wanted a 99% service
level?
Exhibit 11.6 Reorder Point System
11-24
Fixed Quantity, Variable Interval System:
The Reorder Point Model
ROP  d LT  σ LT Z
• A service level of 99% implies an inventory level that is 2.33
standard deviations above the mean demand during the
replenishment lead time.
• The mean is 120 and standard deviation is 12
• ROP = 120 + 2.33(12) = 120 + 28 = 148
• A ROP of 148 would be sufficient to satisfy demand during
the replenishment lead time with 99% confidence.
11-25
Fixed Quantity, Variable Interval System:
The Reorder Point Model
Exhibit 11.7 ROP at 2.33s
Service Levels
3σ provides 99.87%
confidence
2.33σ provides 99.00%
confidence
2σ provides 97.73%
confidence
1σ provides 84.13%
confidence
The mean provides
50.00% confidence
11-26
Fixed Quantity, Variable Interval System:
The Reorder Point Model
• Inventory is reordered when there is enough inventory
remaining to meet demand during the replenishment lead
time.
• Assume:
– Demand is always exactly 60 units per week
– Replenishment lead time is always exactly 2 weeks
• The reorder point would be 120 units and would always
be just enough. In the real world, though, demand is
variable.
11-27
Fixed Quantity, Variable Interval System:
Reorder Point Model Example
• Suppose. . .
– Lead time is 2 weeks
– Average weekly demand is 62
– Weekly standard deviation is 13
• Compute a reorder point with a 95% service level
11-28
Fixed Quantity, Variable Interval System:
Reorder Point Model Example
•
Solution:
Average demand during lead time = 2*62 = 124
Standard deviation of demand during the lead time = 18.38
Weekly Standard Deviation (σ) = 13
Therefore, weekly variance (σ2) = 169
Therefore, the variance over the lead time = 2*169 = 338
Therefore, the standard deviation over the lead time =
 2  338  18.38
Z for a (approximate) 95% service level is 1.645
11-29
Fixed Quantity, Variable Interval System:
Reorder Point Model Example
ROP  d LT  σ LT Z
Where:
ROP
dLT
σLT
Z
= Reorder Point (i.e., quantity at which more inventory is ordered)
= Average demand during replenishment lead time
= Standard deviation of demand during replenishment lead time
= Number of standard deviations above the average demand during
replenishment lead time required for desired service level.
ROP = 124 + 18.385(1.645) = 154.243 = 155
Notes:
– Pay attention to interval over which standard deviation is calculated. Make sure
it matches the lead time demand interval.
– Adjust using variance (σ2) and convert back to standard deviation.
– Round up to the next highest unit to ensure that the safety stock will be sufficient
for the desired service level.
11-30
How Many to Order:
The Economic Order Quantity
• The ROP tells us when to order, but the order quantity (how
many?) still needs to be determined.
• The economic order quantity (EOQ) model is used to
determine an order quantity that minimizes the sum of
ordering and carrying costs. The basic EOQ model makes the
following assumptions:
–
–
–
–
–
–
Annual demand is known
Demand is even
Lead time is constant
No quantity discounts
Only one product is involved
Orders are received in single deliveries
11-31
How Many to Order:
The Economic Order Quantity
• These assumptions allow us to use a simple calculation for total
costs related to the quantity we order.
TC  H(Q/2)  S(D/Q)
Where:
TC = Total cost
H = Carrying or holding cost per unit, on an annual basis
Q = Order quantity
S = Cost of ordering
D = Annual demand
11-32
How Many to Order:
The Economic Order Quantity
• The relationships among the ordering cost, carrying costs,
and total cost curve:
Exhibit 11.8 Carrying Costs, Ordering Cost, and Total Cost in EOQ
Ordering at this quantity
will minimize the total
costs
11-33
How Many to Order:
The Economic Order Quantity
• By taking the first derivative with respect to Q of the formula
for the total cost curve, we obtain the formula for the optimal Q
which is the EOQ:
2DS
Qopt 
 EOQ
H
• Step-by-Step: The Economic Order Quantity Calculation
– Determine the annual demand (D)
– Determine the inventory carrying cost per unit (H). If carrying costs are given as
a percentage of the item value, H will be the percentage (i) multiplied by the item
value (P)
– Determine the cost of ordering (S) per order
– Use the formula above to compute EOQ
11-34
Economic Order Quantity Calculation
•
The University Bookstore wished to utilize the EOQ formula to determine the
appropriate order quantity for its most popular backpack. Determine the EOQ given the
following information:
– Annual demand = 600
– Order cost = $13 per order
– Carrying cost = $3.25 per unit, per year
2DS
2
*
600
*
13


 4800  69.282
EOQ
H
3.25
As a matter of practice we would round up to order 70 units.
11-35
Weaknesses of the EOQ Model
• The EOQ has been criticized for inflating order quantities.
Many feel it underestimates carrying costs by ignoring
well-accepted nonfinancial costs of carrying inventory:
– Loss of flexibility
– Increased quality feedback time
– Increased lead times
11-36
How Many to Order: The Economic Order
Quantity with Quantity Discounts
•
•
Various modifications of the basic EOQ model are used as the assumptions
are relaxed.One such commonly relaxed assumption relates to quantity
discounts
If discounts are available for certain order quantities, the order quantity no
longer just affects order costs and carrying costs—it also affects the cost of
purchasing it. In that scenario, the total cost consists of order cost, carrying
cost, and purchase cost.
•
Step-by-step: EOQ with quantity discounts
– Compute basic EOQ. It will fall within one of the price ranges specified by the supplier.
– If the EOQ falls within the cheapest price range, the EOQ is the optimal order quantity.
– If the EOQ does not, all price ranges having lower prices than the range the EOQ falls in
must be evaluated.
– The optimal quantity will be at the lowest allowable quantity of a price range. For each
quantity, compute the total cost (carrying, order, and purchase price) for the quantity at
each price break.
11-37
How Many to Order: The Economic Order
Quantity with Quantity Discounts
• Total cost with quantity discounts:
TC = D/Q(S) + Q/2(H) + DP
Where
D = annual demand
Q = order quantity
S = cost per order
H = carrying cost
P = price per unit
11-38
Quantity Discount Model Calculation
• Given the following quantity discount information . . .
1-20 units: $229 each
21-60 units: $210 each
61-120 units: $199 each
120 units: $175 each
Order cost: $20 per order
Carrying cost: $36 per unit per year
Annual demand: 476 units
What would the low-cost order quantity be?
11-39
Quantity Discount Model Calculation
• Solution:
– Calculate Basic EOQ
Qopt
2DS
2 * 476 * 20


 528.89  22.99
H
36
– Calculate TC for EOQ and lower priced quantities
TC  H(Q/2)  S(D/Q)  DP
– TC at 23 units per order = $100,787.91
– TC at 61 units per order = $95,978.07
– TC at 121 units per order = $85,556.68
Order 121 units per order
11-40
Fixed Interval, Variable Quantity Systems
• Periodic Review System: An independent demand
management system that orders inventory on fixed
time intervals.
– If the timing cannot vary, the order quantity must vary
to meet demand
– This system is used when user needs to order at
periodic intervals because of supplier shipment
schedules, or needs to combine orders for different
products to save on transaction costs
11-41
Fixed Interval, Variable Quantity Systems
• The order quantity must cover the expected demand during the
order interval and replenishment lead time.
Order Quantity = Target Inventory Level –Inventory On Hand
Q = TI - A
The target inventory level =
TI  d OI  LT  SS
Where
d OI  LT
= the average demand during the order interval and lead time
SS = the safety stock
OI = the number of days in the order interval
LT = the number of days in the replenishment lead time
11-42
Fixed Interval, Variable Quantity Systems
• The safety stock is calculated as
SS  Z OI  LT
Where
 Z t OI  LT
SS = the safety stock
OI – the number of days in the order interval
LT = the number of days in the replenishment lead time
Z = the number of standard necessary for the desired confidence level
σOI+LT = the standard deviation of demand over the OI and LT
σt = the daily standard deviation
11-43
Fixed Interval, Variable Quantity Systems
• Step-by-Step: Determining the Order Quantity
– Based on the average daily demand, determine the average
demand during the order interval
– Based on the average daily demand, determine the average
demand during the replenishment lead time
– Identify the Z value from Appendix B and the desired service
level
– Determine the amount of inventory on hand currently
– Using formula 11.8, determine the safety stock
– Using formula 11.7, determine the target inventory level
– Using formula 11.6, determine the order quantity
11-44
Fixed Interval, Variable Quantity Systems
• The periodic review model
Periodic order is placed here
Order quantity must be enough to cover
demand until the next order arrives, here.
Order arrives here
Exhibit 11.9 Periodic Review System
11-45
Periodic Review Model Example
Compute safety stock
•
•
•
•
•
•
Average daily demand: 3.6 units
Replenishment lead time: 2 days
Standard deviation of demand (daily): 5
Inventory on hand: 5
Service level desired: 95%
Order Interval: 7 days.
SS  Z t OI  LT
=1.645(.5)(3)
=2.4675
Compute target inventory level
TI  d OI  LT  SS
= 32.4 + 2.4675
= 34.87
Round up to 35
Subtract on hand inventory
Q = TI – A
= 35 – 5
= 30
11-46
Managing Dependent Demand Inventory:
Material Requirements Planning
• Material Requirements Planning (MRP) is an inventory
management approach used to manage dependent demand
inventory that plans order releases for the future based on
production schedules.
– The same two questions get answered: ‘When?’ and ‘How many?’
– “How many” is determined by a process called netting:
computing net requirements. Net requirements are total quantity
needed less on-hand inventory
– “When” is determined by backward scheduling, where a known
completion date or due date is used to determine a start date
11-47
Managing Dependent Demand Inventory:
Material Requirements Planning
• Netting and backward scheduling in MRP require information
that comes from master production schedules (MPS), bills of
material, and inventory master files.
Exhibit 11.10 Material Requirements Planning Inputs
11-48
Managing Dependent Demand Inventory:
Material Requirements Planning
• Master Production Schedule (MPS): A schedule of end
products that must be completed in a specific time period.
Exhibit 11.11 Master Production Schedule (MPS) for Staple Remover
11-49
Managing Dependent Demand Inventory:
Material Requirements Planning
• Bill of material: A file containing information about the materials
required to produce a product or component.
Exhibit 11.12 Structure for Staple Remover
11-50
Managing Dependent Demand Inventory:
Material Requirements Planning
• Inventory master file: A file containing information about an
inventory item such as the quantity on hand, the cost, and so on.
• More MRP terms:
– Gross requirements: The total quantity needed to meet demand
– Beginning on-hand inventory: Inventory at the beginning of a time
period
– Ending on hand inventory: Inventory at the end of a time period
– Net requirements: Gross requirements less beginning on-hand inventory
– Planned order receipt: The planned receipt of material that results from
a planned order release
– Planned order release: An order planned to be released to satisfy a
future net requirement
11-51
Managing Dependent Demand Inventory:
Material Requirements Planning
• MRP takes individual component lead times into account to make
sure that required components arrive on time
Depending on how long it takes to get
each one, they must be ordered here.
All components must be available here
If staple remover order is due here, and
assembly takes one week . . .
Exhibit 11.14 Time Line for Staple Remover Component Orders
11-52
Managing Dependent Demand Inventory:
Material Requirements Planning
How many does the
MPS say I need?
(usage)
Exhibit 11.13 Quantity and Timing for Staple Remover Orders (Staple Remover MRP Record)
How many do I
already have? (Ending
Inventory from previous
week)
How many will be
left? (Beginning +
Receipts - Usage)
How many more do I
need? (Gross
Requirement - Beginning
Inventory)
How many should be ordered (or produced) this week in
order to meet the demand?
How many will be
received? (receipts)
11-53
Managing Dependent Demand Inventory: Material
Requirements Planning
“Parent” Item
Gross requirements for
components come from
“planned order release” of
the parent
Component
Item
11-54
Managing Dependent Demand Inventory:
Material Requirements Planning
If I am going to need 62
units of the “parent” in
week 8…,
I need to release the
order (start making them)
in week 7 …,
so I need the component
in week 7 …,
And I need to order (or
start making) it in week 6
(it has a 1-week lead
time)
11-55
Managing Dependent Demand Inventory:
Material Requirements Planning
Component
Lead Time
Staple Remover (parent) 1 week
Outer jaw
1 week
Inner jaw
1 week
Connecting Pin
2 weeks
Spring
2 weeks
…, also, where I
ordered the outer jaw
one week before I
needed it …,
…, I have to order
connecting pins two
weeks before I need
them.
11-56
Managing Dependent Demand Inventory:
Extended MRP
• Lot-for-lot ordering: Ordering exactly the amount of the
net requirements.
– Used in previous example
• Fixed-quantity order policy: Rather than ordering the
quantity of the net requirements, orders are placed in
increments of a fixed quantity.
– Trades off reduction in ordering costs against increases in
carrying costs
11-57
Managing Dependent Demand Inventory:
Extended MRP
• As products included in MRP logic become more complex, the
logic must accommodate various potential situations.
– Components may be used in different end products
– Demand for some components may be both dependent and
independent
11-58
Prioritizing Inventory: ABC Analysis
• Managing inventory can be expensive.
– Reorder point systems require continuous review of inventory
levels, but stockouts can only occur in the replenishment lead time
– A primitive form of a reorder point system is the two-bin system,
where two bins full of inventory are kept and more inventory is
ordered when one of them becomes empty.
– Periodic review systems have a constant risk of stockout
• Sophistication of the management approach (and therefore
investment) should be relative to cost of getting it wrong.
– e.g., stocking out
11-59
Prioritizing Inventory: ABC Analysis
• Based on the Pareto principle, which states that 80% of the effects
are the result of 20% of the causes.
– Categorization of inventory items by importance (demand or dollar
usage) as “A”, “B”, and “C” items
– “A” items are most important. Generally, around 10% of inventory
items are “A” items
– “B” items are next, generally comprising around 30-40% of items
– “C” items make up the rest, and are relatively unimportant
• Classification of items will determine what type of inventory
management system to use, service level, number of suppliers or
backup suppliers, etc.
11-60
Measuring Inventory Productivity
• Inventory turns: A measure of inventory productivity
computed by dividing sales by the average value of inventory.
– Could be improved by increasing sales, but this isn’t the usual
interpretation
– Can be improved by reducing inventory
– Turnover should be increased in a way that will not harm service
quality or delivery reliability
11-61
Measuring Inventory Productivity:
Dollar Days
• Dollar days: The dollar value of an item in inventory
multiplied by the number of days until it will be sold.
– Targets high cost inventory
– Targets slow-moving inventory
Example 11.7
The value of a particular camcorder inventoried by an electronics shop is exactly
$1000, and the annual demand is 730 units (2 per day). Currently, there are 12
units in inventory. Another product, an autofocus 35mm camera, has a value of
$214.29 and has an annual demand of 52 units (essentially one every seven days)
and 7 units on hand. What are the dollar days associated with each of these items?
11-62
Measuring Inventory Productivity:
Dollar Days
• Camcorder
– $1000 value
– Annual demand = 730
– 12 units on hand
• Consumption:
–
–
–
–
–
–
2 sold in one day
2 more in two days
2 more in three days
2 more in four days
2 more in five days
last 2 in six days
* $1000
11-63
Measuring Inventory Productivity:
Dollar Days
• 35mm camera
– $214.29 value
– Annual demand = 52
– 7 units on hand
• Consumption:
–
–
–
–
–
–
–
1 sold in 7 days
1 more in 14 days
1 more in 21 days
1 more in 28 days
1 more in 35 days
1 more in 42 days
last 1 in 49 days
* $214.29
11-64
Measuring Inventory Productivity:
Dollar Days
• Dollar days for both items = $42,000
– Eliminating one camcorder reduces dollar days by 6,000
– Eliminating one 35mm camera reduces dollar days by 10,500
• Also consider impact of reduction on service levels
– Reducing inventory of the camcorder reduces service level and sales.
– Reducing inventory of the 35mm camera is of very little consequence
11-65