Inventory
Management
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You should be able to:
LO 13.1
LO 13.2
LO 13.3
LO 13.4
LO 13.5
LO 13.6
LO 13.7
LO 13.8
LO 13.9
LO 13.10
LO 13.11
LO 13.12
LO 13.12
Define the term inventory
List the different types of inventory
Describe the main functions of inventory
Discuss the main requirements for effective management
Explain periodic and perpetual review systems
Describe the costs that are relevant for inventory management
Describe the A-B-C approach and explain how it is useful
Describe the basic EOQ model and its assumptions and solve typical
problems
Describe the economic production quantity model and solve typical
problems
Describe the quantity discount model and solve typical problems
Describe reorder point models and solve typical problems
Describe situations in which the fixed-order interval model is appropriate
and solve typical problems
Describe situations in which the single-period model is appropriate, and
solve typical problems
13-2
 Inventory
 A stock or store of goods
 Independent demand items
 Items that are ready to be sold or used
Inventories are a vital part of business: (1) necessary for
operations and (2) contribute to customer satisfaction
A “typical” firm has roughly 30% of its current
assets and as much as 90% of its working capital
invested in inventory
LO 13.1
13-3
 Raw materials and purchased parts
 Work-in-process (WIP)
 Finished goods inventories or merchandise
 Tools and supplies
 Maintenance and repairs (MRO) inventory
 Goods-in-transit to warehouses or customers (pipeline
inventory)
LO 13.2
13-4
 Inventories serve a number of functions such as:
1.
To meet anticipated customer demand
2. To smooth production requirements
3. To decouple operations
4. To protect against stockouts
5. To take advantage of order cycles
6. To hedge against price increases
7. To permit operations
8. To take advantage of quantity discounts
LO 13.3
13-5
 Inventory management has two main concerns:
1. Level of customer service
 Having the right goods available in the right quantity in the
right place at the right time
2. Costs of ordering and carrying inventories
 The overall objective of inventory management is to achieve
satisfactory levels of customer service while keeping
inventory costs within reasonable bounds
1. Measures of performance
2. Customer satisfaction
 Number and quantity of backorders
 Customer complaints
3. Inventory turnover
LO 13.3
13-6
 Requires:
1.
A system keep track of inventory
2. A reliable forecast of demand
3. Knowledge of lead time and lead time variability
4. Reasonable estimates of

holding costs

ordering costs

shortage costs
5. A classification system for inventory items
LO 13.4
13-7
 Periodic System
 Physical count of items in inventory made at periodic
intervals
 Perpetual Inventory System
 System that keeps track of removals from inventory
continuously, thus monitoring current levels of each
item
 An order is placed when inventory drops to a
predetermined minimum level
 Two-bin system
 Two containers of inventory; reorder
when the first is empty
LO 13.5
13-8
 Universal product code (UPC)
 Bar code printed on a label that has information about
the item to which it is attached
 Radio frequency identification (RFID) tags
 A technology that uses radio waves to identify objects,
such as goods, in supply chains
LO 13.5
13-9
 Purchase cost
 The amount paid to buy the inventory
 Holding (carrying) costs
 Cost to carry an item in inventory for a length of time, usually
a year
 Ordering costs
 Costs of ordering and receiving inventory
 Setup costs
 The costs involved in preparing equipment for a job
 Analogous to ordering costs
 Shortage costs
 Costs resulting when demand exceeds the supply of
inventory; often unrealized profit per unit
LO 13.6
13-10
 A-B-C approach
 Classifying inventory according to some measure of importance, and
allocating control efforts accordingly
 A items (very important)
 10 to 20 percent of the number of items in inventory and about 60 to 70
percent of the annual dollar value
 B items (moderately important)
 C items (least important)
 50 to 60 percent of the number
of items in inventory but only
about 10 to 15 percent of the
annual dollar value
LO 13.7
13-11
 Cycle counting
 A physical count of items in inventory
 Cycle counting management
 How much accuracy is needed?
 A items: ± 0.2 percent
 B items: ± 1 percent
 C items: ± 5 percent
 When should cycle counting be performed?
 Who should do it?
LO 13.7
13-12
 Economic order quantity models identify the optimal
order quantity by minimizing the sum of annual costs
that vary with order size and frequency
1.
2.
3.
LO 13.8
The basic economic order quantity model
The economic production quantity model
The quantity discount model
13-13
 The basic EOQ model is used to find a fixed order
quantity that will minimize total annual inventory
costs
 Assumptions:
1.
2.
3.
4.
5.
6.
LO 13.8
Only one product is involved
Annual demand requirements are known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
13-14
Profile of Inventory Level Over Time
Q
Usage
rate
Quantity
on hand
Reorder
point
Receive
order
Place
order
Receive
order
Time
Place
order
Receive
order
Lead time
LO 13.8
13-15
Total Cost  Annual Holding Cost  Annual Ordering Cost
Q
D

H

S
2
Q
where
Q  Order quantity in units
H  Holding (carrying) cost per unit, usually per year
D  Demand, usually in units per year
S  Ordering cost per order
LO 13.8
13-16
Annual Cost
The Total-Cost Curve is U-Shaped
Q
D
TC  H  S
2
Q
Holding Costs
Ordering Costs
QO (optimal order quantity)
LO 13.8
Order Quantity
(Q)
13-17
 Using calculus, we take the derivative of the total cost
function and set the derivative (slope) equal to zero and
solve for Q.
 The total cost curve reaches its minimum where the
carrying and ordering costs are equal.
2 DS
2(annual demand)(or der cost)
QO 

H
annual per unit holding cost
LO 13.8
13-18
 The batch mode is widely used in production. In certain
instances, the capacity to produce a part exceeds its usage
(demand rate)
 Assumptions
LO 13.9
1.
Only one item is involved
2.
Annual demand requirements are known
3.
Usage rate is constant
4.
Usage occurs continually, but production occurs periodically
5.
The production rate is constant
6.
Lead time does not vary
7.
There are no quantity discounts
13-19
Q
Production
and usage
Usage
only
Production
and usage
Usage
only
Production
and usage
Qp
Cumulative
production
Imax
Amount
on hand
Time
LO 13.9
13-20
TC min  Carrying Cost  Setup Cost
I
  max
 2
D

H

S

Q

where
I max  Maximum inventory

Qp
 p  u
p
p  Production or delivery rate
u  Usage rate
LO 13.9
13-21
2 DS
Qp 
H
LO 13.9
p
p u
13-22
 Quantity discount
 Price reduction for larger orders offered to customers to
induce them to buy in large quantities
Total Cost  Carrying Cost  Ordering Cost  Purchasing Cost
Q
D
 H  S  PD
2
Q
where
P  Unit price
LO 13.10
13-23
Adding PD does not change EOQ
LO 13.10
13-24
The total-cost curve
with quantity discounts
is composed of a
portion of the total-cost
curve for each price
LO 13.10
13-25
 Reorder point
 When the quantity on hand of an item drops to this amount, the
item is reordered.
 Determinants of the reorder point
1.
The rate of demand
2. The lead time
3. The extent of demand and/or lead time variability
4. The degree of stockout risk acceptable to management
LO 13.11
13-26
ROP  d  LT
where
d  Demand rate (units per period, per day, per week)
LT  Lead time (in same time units as d )
LO 13.11
13-27
 Demand or lead time uncertainty creates the possibility
that demand will be greater than available supply
 To reduce the likelihood of a stockout, it becomes
necessary to carry safety stock
 Safety stock
 Stock that is held in excess of expected demand due to variable
demand and/or lead time
Expected demand
ROP 
 Safety Stock
during lead time
LO 13.11
13-28
LO 13.11
13-29
 As the amount of safety stock carried increases, the
risk of stockout decreases.
 This improves customer service level
 Service level
 The probability that demand will not exceed supply during lead
time
 Service level = 100% - Stockout risk
LO 13.11
13-30
 The amount of safety stock that is appropriate for a
given situation depends upon:
The average demand rate and average lead time
2. Demand and lead time variability
3. The desired service level
1.
Expected demand
ROP 
 z dLT
during lead time
where
z  Number of standard deviations
 dLT  The standard deviation of lead time demand
LO 13.11
13-31
The ROP based
on a normal
Distribution of lead
time demand
LO 13.11
13-32
ROP  d  LT  z d LT
where
z  Number of standard deviations
d  Average demand per period (per day, per week)
 d  The stdev. of demand per period (same time units as d )
LT  Lead time (same time units as d )
Note: If only demand is variable, then
LO 13.11
 dLT   d LT
13-33
ROP  d  LT  zd LT
where
z  Number of standard deviations
d  Demand per period (per day, per week)
 LT  The stddev. of lead time (same time units as d )
LT  Average lead time (same time units as d )
Note: If only lead time is variable, then  dLT  d LT
LO 13.11
13-34
 Fixed-order-interval (FOI) model
 Orders are placed at fixed time intervals
 Reasons for using the FOI model
 Supplier’s policy may encourage its use
 Grouping orders from the same supplier can produce savings in
shipping costs
 Some circumstances do not lend themselves to continuously
monitoring inventory position
LO 13.12
13-35
Fixed Quantity
Fixed Interval
LO 13.12
13-36
Expected demand
Amount  during protection  Safety  Amount on hand
to Order
at reorder ti me
stock
interval
 d (OI  LT)  z d OI  LT  A
where
OI  Order interval (length of time between orders)
A  Amount on hand at reorder ti me
LO 13.12
13-37
 Single-period model
 Model for ordering of perishables and other items with limited
useful lives
 Shortage cost
 Generally, the unrealized profit per unit
 Cshortage = Cs = Revenue per unit – Cost per unit
 Excess cost
 Different between purchase cost and salvage value of items left
over at the end of the period
 Cexcess = Ce = Cost per unit – Salvage value per unit
LO 13.13
13-38
 The goal of the single-period model is to identify the order
quantity that will minimize the long-run excess and
shortage costs
 Two categories of problem:
 Demand can be characterized by a continuous distribution
 Demand can be characterized by a discrete distribution
LO 13.13
13-39
Cs
Service level 
C s  Ce
where
Cs  shortage cost per unit
Ce  excess cost per unit
Ce
Cs
Service level
Quantity
So
Balance Point
LO 13.13
So =Optimum
Stocking Quantity
13-40