Chapter 12
Independent Demand
Inventory Management
What is “Independent Demand”
• If demand is not fully predictable, then it is
called independent demand.
Examples: customer demand, demand for repair and
maintenance, demand for production varying with
the market, …
• Number of components required in a product
is called dependent demand.
Example: four tires for a car, or 400 tires required for
producing 100 cars.
What is “inventory”
• Your inventory refers to the items you
keep at your cost for future use. Or
• Your inventory refers to the items for
which you have put your money in but
have not got the money back.
Types of Inventory
Functions of Inventory (1)
• As a cushion / buffer.
– To absorb uncertainties of demand and
suppliers,
– To maintain smooth operations.
– Example:
•
•
•
•
finished good inventory,
material inventory,
MRO inventory,
WIP inventory
Functions of Inventory (2)
• As the result of scale of economy or
lot size.
– lot size inventory,
– transportation inventory.
• As a speculation.
Bad Side of Inventory
•
•
•
•
Inventory is money that is put aside.
Inventory costs money to hold.
Inventory does not add value to product.
Inventory risks shrinkage due to
pilferage, obsolescence and
deterioration.
More or Less Inventory?
• Higher inventory is good to avoid
stockout and to absorb uncertainties, but
is bad in high cost of inventory.
• Lower inventory is good in saving
money, but is bad in increased risk of
stockout, customer dissatisfaction, and
process interruption.
Tasks of Inventory Management
• “Customer satisfaction”.
– Customers are those who will use the inventoried
items, such as external customers and internal
production process.
• Keep inventory cost low.
• Maintain inventoried items.
– Keep accurate records,
– Items are kept so as to be safe and free of
damage, convenient to be located, …
Measurement of Inventory (1)
• Inventory turnover
annualcost of goods sold

avg.inventoryin $
• It tells how many times the inventory can
be used up in a year.
• The higher the turnover the more efficient
the inventory.
Measurement of Inventory (2)
• Weeks of Supply
avg.inventoryon handin $

avg. weekly usage in $
• It tells how many weeks on average the
inventory can sustain.
• The smaller the more efficient.
Measurement of Inventory (3)
• Relationship between weeks of supply
and inventory turnover:
number of weeks per year
Turnover
weeks of supply
Example (p.457)
• Last year, total cost of good sold =
$5,200,000
• Average inventory = $1,040,000
• 52 weeks in a year.
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Example (p.457-458) (cont.)
$5,200,000
T urnover
 5 (t urns/yr)
$1,040,000
$5,200,000
Avg. weekly demand 
 $100,000/week
52
$1,040,000
Weeksof supply 
 10.4(weeks),or
$100,000
52 weeks
Weeksof supply 
 10.4 weeks
5 t urnovers
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Determine Inventory Level
• Inventory level for a product item is
measured by number of units on hand.
• “A product item” here is known as stockkeeping-unit (SKU). For example, a pair
of same jeans with size 32x34 stored in
three storages is viewed as three
different SKUs.
Inventory Level
Changes All the Time
• For each SKU, number of units on hand
would change every day or every minute.
• It goes down when some units are used.
• It goes up when some units are received
from the supplier.
Inventory
on hand
(units)
Inventory Dynamic
Q,
units
in an
order
Q/2
0
Time (day)
Order receiving
Average Inventory
• Average inventory is the measure of
inventory level
• Average daily inventory level
highest levelof invent ory

2
quant it iyin an order

2
Costs Related to Inventory
•
•
•
•
Inventory holding cost
Ordering cost
Shortage cost
Item cost (cost of goods)
Carrying Cost
• Includes:
– Capital cost
– Opportunity costs,
– Storage space rental, and labor and
facilities for storage,
– Cost of obsolescence and damage,
– Insurance.
• Varies with the amount of inventory.
Ordering Cost
• Includes:
– Shipping and handling cost,
– Cost of processing orders, such as forms,
papers, labor.
• Typically, this cost does not change with
number of units in an order.
Shortage Cost
• Includes:
– Lost sale,
– Expediting and back ordering expenses,
– Cost of reputation and goodwill
Some Basic Calculations (1)
D = Annual demand in units
S = Ordering cost per order
H = Holding cost per unit per year
Q = Number of units in an order.
• Number of orders required in a year
annualdemandin units
D


number of unitsin an order Q
Some Basic Calculations (2)
•
•
•
•
•
Q
2
Avg. inventory =
Q
Total annual inv. holding cost = H
2
D
Number of orders in a year  Q
D
Total annual inv. ordering cost  Q S
Total annual inventory cost
Q
D

H S
2
Q
Example
•
•
•
•
•
Annual demand (D) = 10,000 units
Item cost = $3 per unit
Ordering cost (S) = $75 per order
Holding cost (H) = $6 per unit per year
Current order quantity (Q) = 100 unit /order
Example (continuing)
• If order quantity is 100 units/order, calculate:
(a) Average inventory level;
(b) Total annual inventory holding cost;
(c) Number of orders to place in a year;
(d) Total annual ordering cost;
(e) Total annual inventory cost;
(f) Total annual cost including inventory and item
cost.
Example (continuing)
• If order quantity is 1,000 units/order,
calculate:
(a) Average inventory level;
(b) Total annual inventory holding cost;
(c) Number of orders to place in a year;
(d) Total annual ordering cost;
(e) Total annual inventory cost;
(f) Total annual overall cost that includes inventory
and item cost.
Economic Order Quantity (EOQ)
• EOQ is the order quantity at which the
total annual inventory cost (annual
holding cost + annual ordering cost) is
minimized.
EOQ Total Costs
Total annual costs
= annual ordering costs + annual holding costs
Formula for EOQ
Let Q* be Economical Order Quantity (EOQ):
2DS
EOQ  Q* 
H
Example (Revisit)
• Calculate EOQ amount Q*.
• Calculate the total annual inventory cost
associated with Q*.
• Calculate the overall annual total cost
associated with Q*, which includes
inventory cost and cost of good.
Cost of Goods
• Cost of good of inventoried items is
not in the EOQ formula, since total
item cost remains a constant Dprice,
no matter what size of order is.
• Sometime, unit carrying cost is a
percent of the purchase cost of the
item.
• Item cost must be considered if
volume discount presents.
Features of EOQ
• EOQ is the ‘optimal’ lot size, which means any
lot size other than EOQ would cause higher
total inventory cost than EOQ.
• Greater D would cause a greater EOQ.
• Greater S would cause a greater EOQ.
• Greater H would cause a smaller EOQ.
• At EOQ, total annual holding cost = total
annual ordering cost.
Basic Decisions in Inventory
Management:
How Much?
When!
Reorder Point (1)
• It tells when to place an order.
• Reorder point is in terms of number of
units on hand, at which an order should
be placed.
• Reorder point must be at least the
demand during the delivery time (lead
time).
Reorder Point (2)
•
Demand during the lead time
= (avg. daily demand)(lead time)
Safety Stock and Uncertainties
Reorder Point (3)
• If demand and lead time are uncertain,
then reorder point is calculated as:
R = (Demand during the lead time) + (safety stock)
= (avg. daily demand)(lead time)
+ (Safety Stock)
= (d)(L)+SS
Example
• Procomp’s annual demand is 8,000 units.
There are 200 work days per year. Lead
time = 3 days, and safety stock = 20 units
• What is the reorder point?
Safety Stock
• Safety stock is the extra stock to help
deal with uncertainties after order is
placed so as to reduce the risk of
stockout.
• The more uncertain the higher the safety
stock.
• The more you care stockout, the higher
the safety stock you apply.
Determining Safety Stock
• SS=zdL
where
z = number of standard deviations derived with
the % risk you could take for stockout from
Appendix B p.671;
dL = standard deviation (in units) of demand
during the lead time.
Example (p.485)
• Demand during the lead time averages 5,000
units with a standard deviation 300 units.
• Manager can take up to 4% of stockout risk.
• What is the safety stock? Reorder point?
• Note: Taking at most 4% of stockout risk means at least 96%
of chance with no stocktout is tolerable. In the half-Normalgraph as in Appendix B on p.671, the corresponding shaded
area is thus 96%-50%=46%=0.46. Find 0.46 in the table, then
z value is on the left and top.
Trial-and-Error Method for SS
• Progressive adjustment.
– Managers may adjust safety stock by trialand-error, based on the historical data and
their experience.
Average Inventory with Safety
Stock
• If safety stock is SS, then the average
inventory formula is:
Q
 SS
Avg. Inventory =
2
How Does EOQ Work in Inventory
Control?
• For each item k, calculate its economic
order quantity Qk* and its reorder point
Rk.
• Keep watching the inventory on hand. If
the stock of item k drops to Rk, order Qk*
units of item k.
EOQ Assumptions
•
•
•
•
•
Demand rate is constant.
No quantity discounts are available
Ordering (or setup) costs are constant
All demand is satisfied (no shortages)
The ordered units are delivered in a
single shipment
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Quantity Discount EOQ Model
• Assumptions are same as EOQ except that unit
price depends upon the quantity ordered
• The best order quantity must make the overall
total cost (total inventory cost plus total cost
of good) minimized.
D  Q 
T Coverall   S   H   Price* D
Q   2 
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Example on p.477-478
• D = 5,200 lbs / year
• S = $50 / order;
H = 30% of unit price
Discount brackets
Unit price (P)
0 – 499 lbs / order
$7.50
500 – 999 lbs / order
$6.90
1,000 lbs up / order
$6.20
H = P * 30%
To Determine Order Quantity under
Volume Discount
• Calculate EOQ Q* (If holding cost H is a % of unit
price, use the lowest possible unit price P first; if Q*
is not in the discount bracket for price P, then recalculate EOQ using the next lowest possible unit
price; until Q* is consistent with the assumed price P.
(see ex. p.477-479))
• Compare the TCoverall for Q* and TCoverall for
each of discount break points that are more
than Q*. (see ex. p. 480, and Prob. 3, p.496-497)
• The order quantity is with the lowest TCoverall.
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Example (p.480)
•
•
•
•
Annual demand (D) = 780 units.
Ordering cost (S) = $15 / order.
Holding cost (H) = $3 per unit per year.
Prices discounted with volume:
1-73 units
74-144 units
$60 / unit,
$56 / unit,
145 or more
$53 / unit.
• Determine the best order quantity.
Economic Production Quantity
(EPQ)
• The assumptions of EPQ are same as
EOQ except that the ordered units arrive
piece by piece.
• Application example:
• a company's finished good inventory that is
supplied by the company's production
department.
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EPQ Profile
52
EPQ Formula
d = daily demand in units,
p = daily production capacity in units,
D, H, S are defined same as before,
then
*
Q 
2 DS
d
H (1  )
p
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Meaning of Q* in EPQ
• Q* here is still the “order quantity”
(number of units in an order), but now the
“order” is issued to the production
department of the same company.
• Therefore, Q* is actually the production
batch size or lot size.
54
Formulas in EPQ (1)
• Maximum Inventory Level, Imax:
d
I max  Q * (1  )
p
• Average Inventory Level
I max
=
2
55
Formulas in EPQ (2)
D
S
• Total annual ordering cost =
Q
(same as for EOQ)
Q
d
• Total annual holding cost  (1  ) H
2
p
I max

H
2
• Total annual inventory cost
D
Q
d
 S  (1  ) H
Q
2
p
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Example
Monthly demand = 1,500 units;
Setup (ordering) cost = $800/order
Holding cost = $18/unit/year
There are 20 work days in a month. The
company can produce 2,500 units per month.
Once a unit is finished, it is counted into the
inventory. Lead time is 5 days.
57
Example (cont.)
(a) Calculate the best production batch size
(economic production quantity).
(b) Calculate the total annual inventory cost
associated with the EPQ you just found.
(c) If the current production batch size is 1,200
units, what is the current total annual
inventory cost?
(d) Calculate the reorder point.
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Other Order Quantity Approaches
• Lot-for-lot:
– Order exactly what is needed
• Min-max system:
– When inventory falls to a pre-set minimum
level, place an order to the predetermined
maximum level
• Order enough for n periods
• Periodic review
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Periodic Review System
• At specified intervals, order up to a
predetermined target level
• Target inventory TI  d RP  L  SS
• Order quantity Q  TI  OH
where TI=target inventory (in units)
d=average daily demand (in units)
RP=review period (in days)
L=Lead time (in days)
SS=safety stock (in units)
OH=inventory on hand (in units)
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Single-Period Inventory
• Inventoried items are for a short season,
such as holiday decorations, Christmos
trees, newspapers, vegetable salad.
• Generate a decision table, order amounts
vs. demands, and determine the best order
quantity by using Decision Making
theory (learned in BSNS2120).
Example (p.489)
• Possible demands for a T-shirt in Walk for Diabetes:
80 shirts
0.2 probability
90 shirts
100 shirts
110 shirts
120 shirts
0.25 probability
0.3 probability
0.15 probability
0.1 probability
• A T-shirt will be priced at $20 and cost at $8 per unit.
Unsold shirts will be sold for rags at $2 per unit.
• How many T-shirts should be ordered?
ABC Classification
• There is a critical few and trivial many.
• Pareto’s law:
– Roughly 20% of inventories will account
for 80% of inventory value
• Divide inventories into A, B, and C
categories based on value, risk, ...
More management efforts will be given
to more important items.
63
Annual Dollar Usage
• An item’s inventory value (in $) tends to
be high if its unit cost is high, and/or it
has a large demand.
• Annual dollar usage (ADU) is a measure
of the combination of unit cost and
demand of an item :
ADU = annual demand X unit cost
64
Steps of ABC Classification
• Calculate ADU for each item;
• Sort items on ADUs in descending order;
• Calculate %-of-ADU and cumulative-%-ofADU for each item;
• Classify the items into groups (class A items
takes 60% to 80% of total ADU, class C
items take 3% to 15% of total ADU)
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Example (p.462)
• Follow the steps of ABC classification in
the last slide.
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An Application of ABC
• Inventoried items should be counted
periodically to reconcile the records with
actual on-hand.
• When ABC analysis is applied, one may
count, for example, class A items once a
day, class B items once a week, and class
C once a month or a year.
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Towards JIT
• In a JIT system, order quantity and
production batch size are as small as
possible.
• Reviewing the formulas for EOQ and
EPQ, the best way to reduce order
quantity and production batch size is to
reduce ordering cost or setup cost.
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