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Chapter
9 Inventory Management
Inventory Management
1. Inventories are important to all types of organizations and their employees.
2. Inventory a boon or bane?
1. Inventory Tradeoffs
1. Use the water tank analogy to show how inventories are created
2. Pressures for small inventories
a.
b.
c.
d.
3. Pressures for large inventories
a.
b.
c.
d.
e.
f.
2. Types of inventory
1. Aggregate categories, for accounting purposes:
a.
b.
c.
• What is the distinction among the three categories of inventories based on the nature
of the demand they experience?
2. Operational inventories: Classified by how it is created
a.
b.
c.
d.
3. Inventory Reduction Tactics
1. Cycle inventory
a. Primary lever
b. Secondary levers
2. Safety stock inventory
a. Primary lever
b. Secondary levers
3. Anticipation inventory
a. Primary lever
b. Secondary levers
4. Pipeline inventory
a. Primary lever
b. Secondary levers
4. ABC Analysis
Stock-keeping unit (SKU)
The goal of ABC analysis
Class A SKUs
Class B SKUs
Class C SKUs
Cycle counting
5. Economic Order Quantity
1. Five assumptions for the economic order quantity (EOQ)
a.
b.
c.
d.
e.
2. Guidelines on when to use or modify the EOQ.
a. Don’t use the EOQ if:
b. Modify the EOQ if:
c. Use the EOQ if:
3. Calculating the EOQ
a. Annual holding cost
Annual holding cost = Q
2H
( )
b. Annual ordering cost
Annual ordering cost = D
QS
( )
c. Total inventory cost (C)
)()(
2S
Q
D
H
Q
C+=
• A more efficient approach is to use the EOQ formula (derived from calculus).
2
OQ H
DS
E=
• Time between orders (TBO).
( )
months/yr 12
EOQ
EOQ D
TBO =
• Application 9.1: Finding the EOQ, Total Cost, and TBO.
Suppose that you are reviewing the inventory policies on an $80 item stocked at a hardware
store. The current policy is to replenish inventory by ordering in lots of 360 units. Additional
information is:
D = 60 units per week, or 3120 units per year
S = $30 per order
H = 25% of selling price, or $20 per unit per year
a. What is the EOQ?
== H
DS
EOQ 2
___ units
b. What is the total annual cost of the current policy (Q = 360), and how does it
compare with the cost with using the EOQ?
Current policy
EOQ policy
360=Q
units
=Q
____ units
=C
( / )( ) + ( / )( )
=C
( / )( ) + ( / )( )
=C
+
=C
+
=C
=C
c. What is the time between orders (TBO) for the current policy and the EOQ policy,
expressed in weeks?
D
Q
TBO =
360
(52 weeks per year) = _____ weeks
D
EOQ
TBOEOQ =
(52 weeks per year) = ____ weeks
4. Managerial insights from EOQ
a. A change in demand rate
b. A change in the order/setup costs
c. A change in the holding costs
d. Errors in estimating
D
,
H
, and
S
.
6. Continuous Review System
Other names
The focus is on inventory control systems for ________________________.
Tracks inventory position (IP)
BOSROHIP −+=
where
=IP
=OH
=SR
=BO
• Application 9.2: Placing Orders with a Continuous Review System
The on-hand inventory is only 10 units, and the reorder point R is 100. There are no
backorders and one open order for 200 units. Should a new order be placed?
=−+= BOSROHIP
R = 100
Decision:
1. Selecting the reorder point when demand and lead time are constant
2. Selecting the reorder point when demand is variable and lead time is constant
a. The need for safety stock
b. Definition of reorder point
c. Set the safety stock level
d. Finding the reorder point
• Step 1: service-level policy
• Step 2: demand during lead time
• Step 3: safety stock and reorder point levels
dLT
z
stock Safety =
Application 9.3: Selecting the Safety Stock and R
Suppose instead that the demand during lead time is normally distributed with an average of
85 and
dLT
= 40.
Find the safety stock, and reorder point R, for a 95 percent cycle-service level.
Safety stock =
=
dLT
z
____ units
R = Average demand during lead time + Safety stock
=
Ld
+ Safety stock
= _______ units
Find the safety stock, and reorder point R, for an 85 percent cycle-service level.
Safety stock =
=
dLT
z
____ units
R = Average demand during lead time + Safety stock
R = ___ units
3. Selecting the reorder point when both demand and lead time are variable.
a. Demand and lead time are independent.
• Safety stock
dLT
z
=
• R = (Average weekly demand × Average lead time) + Safety stock
Ld=
+ Safety stock
Application 9.4. Reorder Point for Variable Demand and Variable Lead Time.
Grey Wolf lodge is a popular 500-room hotel in the North Woods. Managers need to
keep close tabs on all of the room service items, including a special pint-scented bar soap.
The daily demand for the soap is 275 bars, with a standard deviation of 30 bars. Ordering
cost is $10 and the inventory holding cost is $0.30/bar/year. The lead time from the
supplier is 5 days, with a standard deviation of 1 day. The lodge is open 365 days a year.
What should the reorder point be for the bar of soap if management wants to have a
99 percent cycle-service?
Solution:
=d
bars
=L
days
=
d
bars
=
LT
day
=
dLT
=+ 2
2
2LTddL
= bars
Consult the body of the Normal Distribution appendix for 0.9900, which corresponds
to a 99 percent cycle-service level to find the corresponding z value.
We calculate the safety stock and reorder point as follows;
Safety stock
( )( )
____________ == dLT
z
= __________________ bars
Reorder point
Ld=
+ safety stock = (______)(___) + _____ = ______ bars
4. Systems Based on the Q System
a. Two-bin system
b. Base-stock systems
5. Calculating total
Q
systems costs
• Total cost = Annual cycle inventory holding costs + Annual ordering costs
+ Annual safety stock holding cost
• Formula:
( ) ( )
stock)safety )((
2HS
Q
D
H
Q
C++=
b. Application 9.5: Continuous Review System: Putting It All Together
The Discount Appliance Store uses a continuous review system (Q system). One of the
company’s items has the following characteristics:
Demand = 10 units/wk (assume 52 weeks per year)
Ordering and setup cost (S) = $45/order
Holding cost (H) = $12/unit/year
Lead time (L) = 3 weeks (constant)
Standard deviation in weekly demand = 8 units
Cycle-service level = 70%
What is the EOQ for this item?
D =
= yrwkwk /52/10
____ units
== H
DS
EOQ 2
____ units
What is the desired safety stock?
L
ddLT
=
=
L
____ units
Safety stock =
=
dLT
z
___ units
What is the desired reorder point R?
R = Average demand during lead time + Safety stock
R = _____ units
What is the total annual cost?
( ) ( )
dLT
HzS
Q
D
H
Q
C
++= 2
=
Suppose that the current policy is
Q
= 80 and R = 150. What will be the changes in
average cycle inventory and safety stock if your EOQ and R values are implemented?
Reducing
Q
from ___ to ___
Cycle inventory reduction = ___ units
Safety stock reduction = ___ units
Reducing R from ___ to ___
6. The primary advantages of the Q systems
a.
b.
c.
7. Periodic Review System
Also called _________________
Original EOQ assumptions maintained
Application 9.6:
Placing Orders with a Periodic Review System
The on-hand inventory is 10 units, and T is 400. There are no back orders, but one
scheduled receipt of 200 units. Now is the time to review. How much should be
reordered?
=−+= BOSROHIP
=− IPT
Decision:
1. Selecting the time between reviews
2. Selecting a target inventory level (
T
) when demand is variable and lead time is constant
a. The new order must be large enough to make the inventory position, IP
b. The average demand during the protection interval is
( )
LPd +
, or
( )
interval protectionfor stock Safety ++= LPdT
c. We compute safety stock for a
P
system much as we did for the
Q
system.
Safety stock =
z
s
P+L
, where
s
P+L
=
LP
d+
d. Selecting the target inventory level when demand and lead time are variable.
•
•
•
e. Systems Based on the P System
• Single-Bin System
• Optional Replenishment System
f. Calculating total P system costs
• Formula:
( ) ( )
LP
HzS
Pd
D
H
Pd
C+
++=
2
• Application 9.7: Periodic Review System: Putting It All Together
Return to Discount Appliance Store (Application 12.5), but now use the P system for the
item.
Previous information
Demand = 10 units/wk (assume 52 weeks per year) = 520
EOQ = 62 units (with reorder point system)
Lead time (L) = 3 weeks (constant)
Standard deviation in weekly demand = 8 units
z = 0.525 (for cycle-service level of 70%)
Reorder interval P, if you make the average lot size using the Periodic Review System
approximate the EOQ.
P =
( )( )
=52DEOQ
____ weeks
Safety stock
=+= LP
d
zstockSafety
___ units
Target inventory:
( )
interval protectionfor stock Safety ++= LPdT
=T
___ units
Total cost
( ) ( )
=++= +LP
HzS
Pd
D
H
Pd
C
2
g. The primary advantages of the P systems
•
•
•
