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12 – 1
BIZ2121-04 Production & Operations Management
Inventory Management
Sung Joo Bae,
Assistant Professor
Yonsei University
School of Business
12 – 2
Wal-Mart’s Inventory Management
7,357 stores
2M employees
180M customers per week
56,000 suppliers
$36B worth of inventory
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Inventory Management
Inventories are important to all types of organizations
They have to be counted, paid for, used in operations, used to satisfy customers, and managed
Too much inventory reduces profitability
Too little inventory damages customer confidence
Inventory trade-offs
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ABC Analysis
Stock-keeping units (SKU)
An individual item or product that has an identifying code and is held in inventory
Divides SKUs into three classes according to their dollar value
Identify the classes so management can control inventory levels
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ABC Analysis
10 20 30 40 50 60 70 80 90 100
Percentage of SKUs
Pe
rce
nta
ge
of
do
lla
r va
lue
100 —
90 —
80 —
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0 —
Class C
Class A
Class B
Figure 12.1 – Typical Chart Using ABC Analysis
A Pareto chart : a type of chart that
contains both bars and a
line graph, where
individual values are
represented in descending
order by bars, and the
cumulative total is
represented by the line.
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Solved Problem 1
Booker’s Book Bindery divides SKUs into three classes, according to their dollar usage. Calculate the usage values of the following SKUs and determine which is most likely to be classified as class A.
SKU Number Description Quantity Used
per Year Unit Value
($)
1 Boxes 500 3.00
2 Cardboard (square feet)
18,000 0.02
3 Cover stock 10,000 0.75
4 Glue (gallons) 75 40.00
5 Inside covers 20,000 0.05
6 Reinforcing tape (meters)
3,000 0.15
7 Signatures 150,000 0.45
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Solved Problem 1
SKU Number
Description Quantity Used per
Year
Unit Value ($)
Annual Dollar Usage ($)
1 Boxes 500 3.00 = 1,500
2 Cardboard (square feet)
18,000 0.02 = 360
3 Cover stock 10,000 0.75 = 7,500
4 Glue (gallons) 75 40.00 = 3,000
5 Inside covers 20,000 0.05 = 1,000
6 Reinforcing tape (meters)
3,000 0.15 = 450
7 Signatures 150,000 0.45 = 67,500
Total 81,310
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Solved Problem 1
Percentage of SKUs
Pe
rce
nta
ge o
f D
olla
r V
alu
e
100 –
90 –
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 – 10 30 40 50 60 70 80 90 100 20
Class C
Class A
Class B
Figure 12.11 – Annual Dollar Usage for Class A, B, and C SKUs
12 – 9
RFID technology in inventory management
Provides an accurate knowledge of the current inventory.
Wal-Mart, RFID reduced Out-of-Stocks by 30 percent for products selling between 0.1 and 15 units a day.
Reduction of labor costs,
Simplification of business processes
Reduction of inventory inaccuracies
Boeing - high costs of aircraft parts
Challenges: unique sizes, shapes
During the first six months after integration, the company was able to save $29,000 in labor.
Less sophisticated methods (cycle counting) are still used
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Different costs related to inventory
Inventory holding cost: the cost for keeping items on hand (e.g. storage, handling, taxes, insurance, etc.)
Ordering cost: the cost of preparing a purchase order for a supplier or production order for the shop
Setup cost: the cost of changing over a machine to produce a different item
Right amount of inventory will minimize these costs
Inventory level should be low enough to avoid IHC, and high enough to reduce OC and SC
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Economic Order Quantity (EOQ)
The lot size, Q, that minimizes total annual inventory holding and ordering costs
Five assumptions
1. Demand rate is constant and known with certainty
2. No constraints are placed on the size of each lot
3. The only two relevant costs are the inventory holding cost and the fixed cost per lot for ordering or setup
4. Decisions for one item can be made independently of decisions for other items
5. The lead time is constant and known with certainty
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Economic Order Quantity
Don’t use the EOQ
Make-to-order strategy
Order size is constrained
Use the EOQ
Make-to-stock
Carrying and setup costs are known and relatively stable
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Calculating EOQ
Inventory depletion (demand rate)
Receive order
1 cycle
On
-han
d in
ve
nto
ry (
un
its)
Time
Q
Average cycle inventory
Q
2
Figure 12.2 – Cycle-Inventory Levels
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Calculating EOQ
Annual holding cost
Annual holding cost = (Average cycle inventory) (Unit holding cost)
Annual ordering cost
Annual ordering cost = (Number of orders/Year) (Ordering or setup costs)
Total annual cycle-inventory cost
Total costs = Annual holding cost + Annual ordering or setup cost
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An
nu
al
co
st
(do
llars
)
Lot Size (Q)
Holding cost
Ordering cost
Total cost
Calculating EOQ
Figure 12.3 – Graphs of Annual Holding, Ordering, and Total Costs
12 – 16
Calculating EOQ
Total annual cycle-inventory cost
where
C = total annual cycle-inventory cost
Q = lot size
H = holding cost per unit per year
D = annual demand
S = ordering or setup costs per lot
C = (H) + (S) Q
2 D
Q
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The Cost of a Lot-Sizing Policy
EXAMPLE 12.1
A museum of natural history opened a gift shop which operates 52 weeks per year.
Managing inventories has become a problem.
Top-selling SKU is a bird feeder.
Sales are 18 units per week, the supplier charges $60 per unit.
Ordering cost is $45.
Annual holding cost is 25 percent of a feeder’s value.
Management chose a 390-unit lot size.
What is the annual cycle-inventory cost of the current policy of using a 390-unit lot size?
Would a lot size of 468 be better?
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The Cost of a Lot-Sizing Policy
SOLUTION
We begin by computing the annual demand and holding cost as
D =
H =
C = (H) + (S) Q
2 D
Q
The total annual cycle-inventory cost for the alternative lot size is
= ($15) + ($45)
= $2,925 + $108 = $3,033
390
2
936
390
The total annual cycle-inventory cost for the current policy is
(18 units/week)(52 weeks/year) = 936 units
0.25($60/unit) = $15
C = ($15) + ($45) = $3,510 + $90 = $3,600 468
2
936
468
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The Cost of a Lot-Sizing Policy
3000 –
2000 –
1000 –
0 – | | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
An
nu
al
co
st
(do
llars
)
Current Q
Current cost
Lowest cost
Best Q (EOQ)
Total cost = (H) + (S)
Q
2 D
Q
Figure 12.4 – Total Annual Cycle-Inventory Cost Function for the Bird Feeder
Ordering cost = (S) D
Q
Holding cost = (H) Q
2
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Calculating EOQ
The EOQ formula:
EOQ = 2DS
H
Time between orders
TBOEOQ = (12 months/year) EOQ
D
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Finding the EOQ, Total Cost, TBO
EXAMPLE 12.2
For the bird feeders in Example 12.1, calculate the EOQ and its total annual cycle-inventory cost. How frequently will orders be placed if the EOQ is used?
SOLUTION
Using the formulas for EOQ and annual cost, we get
EOQ = = 2DS
H = 74.94 or 75 units
2(936)(45)
15
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Finding the EOQ, Total Cost, TBO
Figure 12.5 shows that the total annual cost is much less than the $3,033 cost of the current policy of placing 390-unit orders.
Figure 12.5 – Total Annual Cycle-Inventory Costs Based on EOQ Using Tutor 12.2
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Finding the EOQ, Total Cost, TBO
When the EOQ is used, the TBO can be expressed in various ways for the same time period.
TBOEOQ = EOQ
D
TBOEOQ = (12 months/year) EOQ
D
TBOEOQ = (52 weeks/year) EOQ
D
TBOEOQ = (365 days/year) EOQ
D
= = 0.080 year 75
936
= (12) = 0.96 month 75
936
= (52) = 4.17 weeks 75
936
= (365) = 29.25 days 75
936
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Managerial Insights
TABLE 12.1 | SENSITIVITY ANALYSIS OF THE EOQ
Parameter EOQ Parameter Change
EOQ Change
Comments
Demand ↑ ↑ Increase in lot size is in proportion to the square root of D.
Order/Setup Costs ↓ ↓
If you can decrease the order and setup costs, then smaller lot size is justified (lean system principle)
Holding Costs ↓ ↑ Larger lots are justified when holding
costs decrease.
2DS
H
2DS
H
2DS
H
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Inventory Control Systems
Two important questions:
How much?
When?
Nature of demand
Independent demand items: Items for which demand is influenced by market conditions and not related to the inventory decisions on other items
Dependent demand items: Items required as components or inputs to a service or a product
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Inventory Control Systems
Continuous review (Q) system
Reorder point system (ROP) and fixed order quantity system
For independent demand items
Tracks inventory position (IP)
Includes scheduled receipts (SR), on-hand inventory (OH), and back orders (BO)
Inventory position = On-hand inventory + Scheduled receipts
– Backorders
IP = OH + SR – BO
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Selecting the Reorder Point
Time
On
-han
d i
nven
tory
TBO TBO
L L
TBO
L
Order placed
Order placed
Order placed
IP IP IP
R
Q Q Q
OH OH OH
Order received
Order received
Order received
Order received
Figure 12.6 – Q System When Demand and Lead Time Are Constant and Certain
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Placing a New Order
EXAMPLE 12.3
Demand for chicken soup at a supermarket is always 25 cases a day and the lead time is always 4 days. The shelves were just restocked with chicken soup, leaving an on-hand inventory of only 10 cases. No backorders currently exist, but there is one open order in the pipeline for 200 cases. What is the inventory position? Should a new order be placed?
SOLUTION
R = Total demand during lead time = (25)(4) = 100 cases
= 10 + 200 – 0 = 210 cases
IP = OH + SR – BO
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Continuous Review Systems
Selecting the reorder point with variable demand and constant lead time
Reorder point = Average demand during lead time
+ Safety stock
= dL + safety stock
where
d = average demand per week (or day or months)
L = constant lead time in weeks (or days or months)
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Continuous Review Systems
Time
On
-han
d i
nven
tory
TBO1 TBO2 TBO3
L1 L2 L3
R
Order received
Q
Order placed
Order placed
Order received
IP IP
Q
Order placed
Q
Order received
Order received
0
IP
Figure 12.7 – Q System When Demand Is Uncertain
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Reorder Point
1. Choose an appropriate service-level policy
Select service level or cycle service level: the desired probability of running out of stock in any one ordering cycle
Protection interval: the period over which safety stock must protect the user from running out of stock
2. Determine the demand during lead time probability distribution
3. Determine the safety stock and reorder point levels
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Demand During Lead Time
Specify mean and standard deviation
Standard deviation of demand during lead time
σdLT = σd2L = σd L
Safety stock and reorder point
Safety stock = zσdLT
where
z = number of standard deviations needed to achieve the cycle-service level
σdLT = stand deviation of demand during lead time
Reorder point = R = dL + safety stock
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σt = 15
+ 75
Demand for week 1
σt = 25.98
225
Demand for 3-week lead time
+ 75
Demand for week 2
σt = 15
= 75
Demand for week 3
σt = 15
Demand During Lead Time
Figure 12.8 – Development of Demand Distribution for the Lead Time
12 – 34
Demand During Lead Time
Average demand
during lead time
Cycle-service level = 85%
Probability of stockout (1.0 – 0.85 = 0.15)
zσdLT
R
Figure 12.9 – Finding Safety Stock with a Normal Probability Distribution for an 85 Percent Cycle-Service Level (z=1.04)
12 – 35
Reorder Point for Variable Demand
EXAMPLE 12.4
Let us return to the bird feeder in Example 12.2. The EOQ is 75 units. Suppose that the average demand is 18 units per week with a standard deviation of 5 units. The lead time is constant at two weeks. Determine the safety stock and reorder point if management wants a 90 percent cycle-service level.
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Reorder Point for Variable Demand
SOLUTION
In this case, σd = 5, d = 18 units, and L = 2 weeks, so σdLT = σd L = 5 2 = 7.07. Consult the body of the table in the Normal Distribution appendix for 0.9000, which corresponds to a 90 percent cycle-service level. The closest number is 0.8997, which corresponds to 1.2 in the row heading and 0.08 in the column heading. Adding these values gives a z value of 1.28. With this information, we calculate the safety stock and reorder point as follows:
Safety stock = zσdLT = 1.28(7.07) = 9.05 or 9 units
2(18) + 9 = 45 units Reorder point = dL + Safety stock =
12 – 37
Reorder Point for Variable Demand and Lead Time
Often the case that both are variable
The equations are more complicated
Safety stock = zσdLT
where
d = Average weekly (or daily or monthly) demand
L = Average lead time
σd = Standard deviation of weekly (or daily or monthly) demand
σLT = Standard deviation of the lead time
σdLT = Lσd2 + d2σLT
2
R = (Average weekly demand Average lead time)
+ Safety stock
= dL + Safety stock
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Reorder Point
EXAMPLE 12.5
The Office Supply Shop estimates that the average demand for a popular ball-point pen is 12,000 pens per week with a standard deviation of 3,000 pens. The current inventory policy calls for replenishment orders of 156,000 pens. The average lead time from the distributor is 5 weeks, with a standard deviation of 2 weeks. If management wants a 95 percent cycle-service level, what should the reorder point be?
12 – 39
Reorder Point
SOLUTION
From the Normal Distribution appendix for 0.9500, the appropriate z value = 1.65. We calculate the safety stock and reorder point as follows:
σdLT = Lσd2 + d2σLT
2 =
We have d = 12,000 pens, σd = 3,000 pens, L = 5 weeks, and σLT = 2 weeks
(5)(3,000)2 + (12,000)2(2)2
= 24,919.87 pens
Safety stock = zσdLT =
Reorder point = dL + Safety stock =
(1.65)(24,919.87)
= 41,117.79 or 41,118 pens
(12,000)(5) + 41.118
= 101,118 pens
12 – 40
Continuous Review Systems
Two-Bin system
Visual system
An empty first bin signals the need to place an order
Calculating total systems costs
Total cost = Annual cycle inventory holding cost + Annual ordering cost + Annual safety stock holding cost
C = (H) + (S) + (H) (Safety stock) Q
2
D
Q
