1. Chapter 13
Inventory Management

2. Independent vs. Dependent Demand
Independent Demand
(Chapter 13) A
Dependent Demand
(Chapter 15)
B(4)
C(2)
D(2)
E(1)
D(3)
F(2)
Independent demand is uncertain
Dependent demand is certain
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3. Types of Inventories (1 of 2)
Raw materials & purchased parts
Partially completed goods called work in progress
Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)
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4. Types of Inventories (2 of 2)
Replacement parts, tools, & supplies
Goods-in-transit (pipeline) to warehouses or customers
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5. Functions of Inventory
Meet anticipated demand
Smooth production requirements
Decouple components (areas) of the production-distribution
Protect against stock-outs
Take advantage of order cycles
Help hedge against price increases or to take advantage of quantity discounts
Permit operations (operation lead time)
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6. Concerns of Inventory Management
Level of customer service
have the right goods, in sufficient quantities, in the right place, at the right time
in other words, the customer gets what ever he/she wants when he/she wants it
Inventory-related costs
ordering costs
carrying costs
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7. Objectives of Inventory Management (1 of 2)
Achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Two fundamental decisions
how much to order
when to place the order
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8. Objectives of Inventory Management (2 of 2)
Possible performance measures
customer satisfaction
number of backorders/lost sales
number of customer complaints
inventory turnover
ratio of annual cost of goods sold to average inventory investment
days of inventory
expected number of days of sales that can be supplied from existing inventory
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9. Requirements for Effective Inventory Management
A system to keep track of the inventory on hand and on order
A classification system for inventory items
A reliable forecast of demand that includes an measure of forecast error
Reasonable estimates of inventory holding costs, ordering costs, and shortage costs
Knowledge of lead times and lead time variability
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10. Inventory Counting Systems (1 of 2)
Perpetual Inventory (Continual) System
Keeps track of removals from and receipts into inventory continuously
Periodic System
Physical count of items made at periodic intervals
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11. Inventory Counting Systems (2 of 2)
Universal Product Code - Bar code printed on a label that has information about the item to which it is attached
Cycle counting - taking physical counts of items and reconciling with records on a continual rotating basis
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12. ABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly
A - very important
B - mod. important
C - least important
Annual
$ volume
of items A B C
High
Low
Few
Many
Number of Items
Figure 13-1
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13. Demand Forecast and Lead Time Information
Reliable estimates of the amount and timing of demand
Lead time - time interval between ordering and receiving the order
Extent of variability in demand and lead time
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14. The Typical Procurement Cycle
Internal Order Cycle
Order Request/Requisition
Authorization signatures obtained
Verification by inventory control
Purchasing researches vendors,
obtains quotes, etc.
Order transferred to vendor
Vendor Cycle
Receives and enters order
Manufactures or “picks”
order
Ships order
Internal Receiving Cycle
Receiving
Incoming inspection
Inventory control receives
order, updates records,
and notifies department
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15. Chapter 13 Inventory Management
Cost Information
Holding or carrying costs
Ordering costs
Shortage costs
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16. Holding or Carrying Costs
Cost to carry a unit in inventory for a length of time
Includes interest (opportunity cost), insurance, taxes, depreciation, obsolescence, deterioration
May be expressed as a percentage of unit price or as a dollar amount per unit
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17. Chapter 13 Inventory Management
Ordering Costs
Cost of ordering and receiving inventory
Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality
Generally expressed as a fixed dollar amount, regardless of order size
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18. Chapter 13 Inventory Management
Shortage Costs
Result when demand exceeds the inventory on hand
Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime
Difficult to measure, thus may have be subjectively estimated
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19. Basic Systems for Independent Demand
Fixed-order-quantity systems
basic economic order quantity (EOQ) model [purchasing model]
basic economic order quantity model with incremental or noninstantaneous replenishment [production order quantity]
quantity discount model
Fixed-order-interval systems
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20. Basic Model Assumptions
Only one product is involved
Annual demand requirements are known
Demand is spread evenly throughout the year so that the demand rate is reasonable constant
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts, i.e., the price is constant
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21. How the Basic Fixed- Order-Quantity Model Works
Profile of Inventory Level Over Time Q
Usage
rate
Quantity
on hand
Reorder
point
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Figure 13-2
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22. Chapter 13 Inventory Management
How Much to Order
Goal is to minimize total annual costs
Total
Annual =
cost
Annual
carrying
cost
Annual
ordering
cost + Q 2 H D S
TC = +
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23. Cost Minimization Goal
The Total Cost Curve is U-Shaped
Annual Cost
Annual
Carrying Costs
Annual
Ordering Costs QO
(optimal order quantity)
Order Quantity (Q)
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24. Chapter 13 Inventory Management
Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
Alternatively we can use calculus by taking the first derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
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25. Chapter 13 Inventory Management
Example 2, page 555
D=9,600 tires/year
H=$16/tire/year
S=$75/order
a. What is the EOQ?
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26. Chapter 13 Inventory Management
Example 2, page 555
D=9,600 tires/year
H=$16/tire/year
S=$75/order
b. How many times per year does the store
reorder?
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27. Example 2, page 555 D=9,600 tires/year H=$16/tire/year S=$75/order
c. What is the length of an order cycle?
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28. Chapter 13 Inventory Management
Example 2, page 555
D=9,600 tires/year
H=$16/tire/year
S=$75/order
d. What is the total cost if the EOQ quantity
is ordered?
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29. Fixed Order Quantity Model with Incremental Replenishment
Used to determine the order size, production lot, if an item is produced at one stage of production and then sent to the next stage or the customer
Differs from the basic model because orders are assumed to be supplied or produced at a uniform rate (p) rather than the order being received all at once
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30. Fixed Order Quantity Model with Incremental Replenishment
Profile of Inventory Level Over Time
Production rate
- usage rate Q
Quantity
on hand
Usage
rate
Reorder
point
Time
Start to
receive
order
Finish
receiving
order
Place
order
Start to
receive
order
Place
order
Receive
order
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Lead time

31. Fixed Order Quantity Model with Incremental Replenishment
It is also assumed that the supply rate, p, is greater than the usage rate, u
The change in maximum inventory level requires modification of the TC equation
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32. Fixed Order Quantity Model with Incremental Replenishment
The optimization results in
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33. Chapter 13 Inventory Management
Example 4, page 558
D=48,000 wheels/year
p=800 wheels/day
H=$1/wheel/year
S=$45/setup
a. Optimal run size
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34. Example 4, page 558 D=48,000 wheels/year p=800 wheels/day
H=$1/wheel/year
u=200 wheels/day
S=$45/setup
b. Minimum total annual cost for carrying and setup
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35. Example 4, page 558 D=48,000 wheels/year p=800 wheels/day
H=$1/wheel/year
u=200 wheels/day
S=$45/setup
c. Cycle time for the optimal run size
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36. Chapter 13 Inventory Management
Example 4, page 558
D=48,000 wheels/year
p=800 wheels/day
H=$1/wheel/year
u=200 wheels/day
S=$45/setup
d. Run time
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37. Quantity Discount Model
This model differs from the basic model because the price per unit (P) may vary with the quantity ordered
The supplier offers a lower unit price if larger quantities are ordered at one time
This is presented as a price or discount schedule, i.e., a certain unit price covers a certain order quantity range
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38. Discount Schedule Problem 14, page 588
Quantity
Price
$10 $9
600+ $8
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39. Chapter 13 Inventory Management
Quantity Discount
Under this condition, annual product cost becomes an incremental cost and must be considered in the determination of the EOQ
The total annual costs (TC) = Annual holding cost + annual setup cost + annual product cost
TC = (Q/2)H + (D/Q)S + DP
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40. Costs Functions Under Quantity Discount
Total Cost Curve
for Price 1
Figure 13-8
Order Quantity
Total Cost Curve
for Price 2
$ cost
Total Cost Curve
for Price 3
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41. Costs Functions Under Quantity Discount
Total Cost Curve
for Price 1
Order Quantity
Total Cost Curve
for Price 2
$ cost
Total Cost Curve
for Price 3
Quantity at which
price 1 ends and
price 2 begins
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42. Costs Functions Under Quantity Discount
Total Cost Curve
for Price 1
Total Cost Curve
for Price 2
$ cost
Total Cost Curve
for Price 3
Quantity at which
price 2 ends and
price 3 begins
Order Quantity
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43. Costs Functions Under Quantity Discount
TOTAL COST CURVE
$ cost
Order Quantity
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44. Chapter 13 Inventory Management
Quantity Discount
To find the EOQ, the following procedure is used
Compute the basic EOQ.
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45. Chapter 13 Inventory Management
Quantity Discount
Using the appropriate price for the for the EOQ found in Step 1, compute the TC
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46. Chapter 13 Inventory Management
Quantity Discount
Compute the TC for all quantities greater than Step 1’s EOQ where a discount begins. Select the quantity with the lowest TC as the EOQ
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47. Chapter 13 Inventory Management
Problem 14a, page 588
600
P=$10
$ cost
P=$9
P=$8
$41,000
400
Order Quantity
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48. Chapter 13 Inventory Management
Problem 14b, page 588
D=25 stones/day x 200 days/year
= 5,000stones/year
H=.30 x P
600
P=$10
S=$48/order
$ cost
P=$9
P=$8
400
Order Quantity
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49. Chapter 13 Inventory Management
Quantity Discount
To find the EOQ, the following procedure is used
Compute the basic EOQ using the lowest unit price and H=IP where I is an interest rate. If the resulting EOQ is feasible, i.e., that quantity can be purchased at the price used, it is optimal. Otherwise, go on to Step 2
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50. Chapter 13 Inventory Management
Problem 14b, page 588
D=5,000 stones/year
H=.30 x $8 = $2.40/year/stone
S=$48/order
Compute the basic EOQ
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51. Chapter 13 Inventory Management
Quantity Discount
Using the EOQ from Step 1 and the discount schedule, find the price that should have been used and compute a new EOQ using this price. This new EOQ should be feasible.
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52. Chapter 13 Inventory Management
Quantity Discount
Compute the TC for the feasible EOQ found in Step 2
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53. Chapter 13 Inventory Management
Quantity Discount
Compute the TC for all quantities greater than Step 2’s EOQ where a discount begins. Select the quantity with the lowest TC as the EOQ
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54. Chapter 13 Inventory Management
The Reorder Point
In the fixed quantity system, the question of “when to order” is answered by setting a reorder point (ROP), an inventory level
When the inventory drops to this level, the activities involved in the ordering or replenishment process are triggered.
The time that it takes to complete these activities is the lead time
The lead time period ends when the order is received
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55. Chapter 13 Inventory Management
The Reorder Point
During this lead time, customer demand continues and the inventory continues to decrease
This is the only time you can run out of inventory (stockout)
Management wants to set the reorder point sufficiently high to serve most of the customers, but not so high that carrying costs are excessive; a tradeoff
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56. Chapter 13 Inventory Management
The Reorder Point
One way to handle this tradeoff is for management to specify the customer service level they want their inventory management system to maintain
order cycle service level is the probability that demand will not exceed the reorder point during the lead time
annual service level is the percentage of demand filled directly from inventory
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57. Setting the Reorder Point
If the demand during the lead time is constant, the reorder point would be set equal to that demand
If the demand during the lead time is not constant, i.e., there is variability, the demand is assumed to follow some distribution
Typically the distribution is assumed to be a normal distribution
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58. Distribution of Demand Over the Lead Time
Quantity Demanded
Normal distribution with a
mean, , and a standard deviation, 
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59. Chapter 13 Inventory Management
If the ROP is set at the mean of the distribution, what would the order cycle service level be?
Quantity Demanded
ROP
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60. Chapter 13 Inventory Management
What if management wanted the order cycle service level to be greater than 50%?
Quantity Demanded
Service
level
ROP
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61. Basis for Setting the Reorder Point
Determinants of the reorder point
The parameters (mean and standard deviation) of the distribution of demand over the entire lead time
The probability that demand will not exceed the reorder point during the lead time acceptable to management, order cycle service level
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62. Developing the Demand Distribution Parameters
We assume that the demand for each time period (usually a day) comes from a normal distribution with a mean of and a standard deviation of
We also assume the lead time is constant at some number of time periods (usually days)
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63. Chapter 13 Inventory Management
Lead Time Demand
To determine the parameters of the distribution of demand over the entire lead time period, we need to add together the demand distributions for each day of the lead time
Lead Time
Place
order
Receive
order
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64. Chapter 13 Inventory Management
Lead Time Demand
Summation + + + +
Since the daily demand distributions are assumed to be identical, the distribution has a mean of and a standard deviation of
Lead Time
Place
order
Receive
order
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65. Chapter 13 Inventory Management
Reorder point
Given the order cycle service level, the proper safety stock is calculated using the normal table. The reorder point is found by adding this safety stock amount to the mean (expected demand)
Lead Time Demand
Given the order cycle service level, the proper safety stock is calculated using the normal table.
safety stock
Lead Time
Place
order
Receive
order
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66. Chapter 13 Inventory Management
Reorder point
Lead Time Demand
safety stock
The safety stock is where is found in the normal table based on the specified order cycle service level
Lead Time
Place
order
Receive
order
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67. Chapter 13 Inventory Management
Reorder point
Lead Time Demand
Order cycle service level
Risk of shortage
safety stock
Lead Time
Place
order
Receive
order
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68. Reorder Point Calculation
Order cycle service level
Risk of
a stockout
Probability of
no stockout
Quantity
Mean or expected demand =
Standard deviation =
Safety
stock
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69. Administration of the System
Using the perpetual counting system, a signal is given when the records indicate that the inventory reaches the ROP
Using the periodic counting system, a two-bin system could be used
two bins of inventory
bin A holds an amount equal to the reorder point
bin B holds the remainder of the order
customers are supplied out of bin B
when bin B is empty, it is time to reorder
customers are then supplied out of bin A until the order arrives
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70. Fixed-Order-Interval Model

71. Basic Fixed-Order-Interval System
Figure 13-15
Target Maximum
Inventory Level Over Time
Order
Quantity
Order
Quantity
Order
Quantity
Order
Quantity
How much
to order
Inventory Level
Minimum Inventory OI OI OI OI
When to order
Time
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72. Operation of Fixed-Order-Interval Systems
As demand for the inventoried item occurs, the inventory level drops
When a prescribed period of time has elapsed, the ordering process is triggered, i.e., the time between orders is fixed or constant
At that time the order quantity is determined using order quantity = target maximum level - current inventory level
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73. Operation of Fixed-Order-Interval Systems
After the lead time elapses, the ordered quantity is received, and the inventory level increases
The maximum inventory level is expected demand during protection interval + safety stock, or
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74. Administration of the System
Using the periodic counting system, the inventory is reviewed (counted) at the end of each order interval
Using the perpetual counting system, an item’s inventory level is checked in the inventory at the end of each order internal
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75. Chapter 13 Inventory Management
Reasons to Use
Supplier’s policy might encourage use
Some situations do not lend themselves to continuous monitoring
Used where it is desirable to physically count inventory each time an order is placed
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76. Chapter 13 Inventory Management
Benefits/Advantages
Benefits
results in tight control needed for A items in a A-B-C classification
grouping ordering to one supplier may result in savings
Ordering
Packing
Shipping costs
Disadvantages
larger amount of safety stock needed for the same service level
cost of periodic reviews
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