1. Chapter 17
Inventory Control

2. Learning Objectives
Explain the different purposes for keeping inventory.
Understand that the type of inventory system logic that is appropriate for an item depends on the type of demand for that item.
Calculate the appropriate order size when a one-time purchase must be made.
Describe what the economic order quantity is and how to calculate it.
Summarize fixed–order quantity and fixed–time period models, including ways to determine safety stock when there is variability in demand.
Discuss why inventory turn is directly related to order quantity and safety stock.

3. Inventory
You should visualize inventory as stacks of money sitting on forklifts, on shelves, and in trucks and planes while in transit
For many businesses, inventory is the largest asset on the balance sheet at any given time
Inventory is often not very liquid
It is a good idea to try to get your inventory down as far as possible
The average cost of inventory in the United States is 30 to 35 percent of its value
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4. Inventory
Inventory—stock of any item/resource used in an organization. Carried in anticipation of use and can include:
raw materials
finished products
component parts
supplies
work-in-process
people, etc.
Inventory system—set of policies & controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

5. Inventory Problems When to order the products How much to order
Issue of timing
How much to order
Issue of quantity
These problems often addressed with the objective of inventory cost minimization
Total annual cost
And meet prescribed service levels

6. Purposes of Inventory To maintain independence of operations
To meet variation in product demand
To allow flexibility in production scheduling
To provide a safeguard for variation in raw material delivery time
To take advantage of economic purchase-order size

7. for Carrying Inventory
Wrong Reasons
for Carrying Inventory
Poor quality
Inadequate maintenance of machines
Poor production schedules
Unreliable suppliers
Poor worker’s attitudes
Just-in-case

8. Supply Chain Inventories—Make-to-Stock Environment
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9. Models Discussed The single-period model Fixed–order quantity model
Used when we are making a one-time purchase of an item
Fixed–order quantity model
Used when we want to maintain an item “in-stock,” and when we restock, a certain number of units must be ordered
Fixed–time period model
The item is ordered at certain intervals of time
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10. Definition of Inventory
Inventory: the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process
Manufacturing inventory: refers to items that contribute to or become part of a firm’s product
Inventory system: the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be
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11. Purposes of Inventory To maintain independence of operations
To meet variation in product demand
To allow flexibility in production scheduling
To provide a safeguard for variation in raw material delivery time
To take advantage of economic purchase-order size
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12. Inventory Costs Holding (or carrying) costs: H
Costs for storage, handling, insurance, taxes, spoilage, capital, and so on
Setup (or production change) costs: S
Costs for arranging specific equipment setups, and so on
Ordering costs: S
Costs of placing an order, clerical, supplies
Shortage costs:
Costs of running out, rain checks, goodwill
Purchase cost: C
Outdate costs (for perishable products)
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13. Independent Versus Dependent Demand
Independent demand: the demands for various items are unrelated to each other
For example, a workstation may produce many parts that are unrelated but meet some external demand requirement
Dependent demand: the need for any one item is a direct result of the need for some other item
Usually a higher-level item of which it is part
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14. Inventory Control-System Design Matrix: Framework Describing Inventory Control Logic

15. Inventory Systems Single-period inventory model
One time purchasing decision (Example: vendor selling t-shirts at a football game)
Example:
Vendor selling T-shirts at sporting events
Newspaper sales (Newsboy Model)
Seeks to balance the costs of inventory overstock and under stock
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16. Inventory Systems Multi-period inventory models
Fixed-order quantity models
Event triggered (Example: running out of stock)
Inventory is monitored all the time
Order Q when inventory reaches R, the reorder point
Also known as FOSS, (Q, R) or EOQ system
Fixed-time period models
Time triggered (Example: Monthly sales call by sales representative)
Inventory is monitored periodically
Also known as FOIS, (S, s), or EOI system

17. A Single-Period Inventory Model
Consider the problem of deciding how many newspapers to put in a hotel lobby
Too few papers and some customers will not be able to purchase a paper and they will lose the profit associated with these sales
Too many papers and will have paid for papers that were not sold during the day, lowering profit
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18. A Simple View of the Problem
Consider how much risk we are willing to take for running out of inventory
Assume a mean of 90 papers and a standard deviation of 10 papers
Assume they want an 80 percent chance of not running out
Assuming that the probability distribution associated of sales is normal, stocking 90 papers yields a 50 percent chance of stocking out
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19. A Simple View of the Problem Continued
To be 80 percent sure of not stocking out, we need to carry a few more than 90 papers
From the “cumulative standard normal distribution” table, we see that we need approximately 0.85 standard deviation of extra papers to be 80 percent sure of not stocking out
With Excel, “=NORMSINV(0.8)” =
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20. Single-Period Inventory Model Formulas
We should increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of Cu/Co+Cu
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21. Example 17.1: Hotel Reservation
Mean of 5
Standard deviation of 3
Cost $80
Overbook cost is $200
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22. Example: Hotel Reservations
Cost of overbooking by n=Expected cost you overbooked by n + Expected cost of m no shows
Best overbooking strategy is one with minimum cost
Example n=4: .05(800) + .08(600) (400) + .01(480) = $239
Number of Reservations Overbooked
No Proba-
Shows bility
Total Cost ($)
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23. Multi-Period Models
There are two general types of multi-period inventory systems
Fixed–order quantity models
Also called the economic order quantity, EOQ, and Q-model
Event triggered
Fixed–time period models
Also called the periodic system, periodic review system, fixed-order interval system, and P-model
Time triggered
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24. Key Differences
To use the fixed–order quantity model, the inventory remaining must be continually monitored
In a fixed–time period model, counting takes place only at the review period
The fixed–time period model
Has a larger average inventory
Favors more expensive items
Is more appropriate for important items
Requires more time to maintain
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25. Fixed–Order Quantity and Fixed–Time Period Differences
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26. Comparison for Fixed–Order Quantity and Fixed–Time Period Inventory Systems
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27. Fixed-Order Quantity Model Models
Demand for the product is constant and uniform throughout the period
Lead time (time from ordering to receipt) is constant
Price per unit of product is constant
Inventory holding cost is based on average inventory
Ordering or setup costs are constant
All demands for the product will be satisfied
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28. Basic Fixed–Order Quantity Model
Lead time
Place Order
Receive order
Use inventory
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29. Basic Fixed-Order Quantity (EOQ) Model Formula
Definitions of Symbols:
TC = Total cost ($)
H = Holding cost ($/unit)
S = Setup cost ($/unit)
Q = Order quantity (units)
C = Cost/unit ($)
D = Annual demand (units)
R = Reorder point (units)
L = Lead time (time units) Q
Max
Q Min
D*C
and
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30. Annual Product Costs, Based on Size of the Order
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31. Example 17.2
We wish to find the economic order quantity and the reorder point given annual demand of 1,000 units, ordering cost of $5 per order, holding costs of $1.25 per unit per year, a lead time of 5 days and per unit cost of $12.50.
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32. Establishing Safety Stock Levels
Safety stock: amount of inventory carried in addition to expected demand
Safety stock can be determined based on many different criteria
A common approach is to simply keep a certain number of weeks of supply
A better approach is to use probability
Assume demand is normally distributed
Assume we know mean and standard deviation
To determine probability, we plot a normal distribution for expected demand and note where the amount we have lies on the curve
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33. Fixed–Order Quantity Model with Safety Stock
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34. Fixed–Order Quantity Model with Safety Stock
Safety stock variable (based on Service Level)
Where,
= number of standard deviations for a given service probability
= standard deviation of usage during the lead time
See problems 24 & 25
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35. Example 17.4
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36. Fixed-Time Period Models
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37. Fixed–Time Period Inventory Model
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38. Example 17.5 Daily demand of 10 units
Daily standard deviation of 3 units
Review period of 30 days
Lead time of 14 days
Satisfying 98 percent of demand from items in stock
150 Units in inventory
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39. Inventory Control and Supply Chain Management
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40. Price Break Models Seller offers you incentive to buy more
Price varies with the order size
Two possibilities
The Holding Cost is fixed
Compute Q using H
Find TC for Q and lower cost C
Q corresponding to lowest-cost TC is opyimal
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41. Example: Fixed Holding Cost
Demand for tires at a local Goodyear Gemini service workshop is 12,000 units/year. Normal cost for tires is $30/unit. Orders between will cost $27.75/unit, will cost $25.5/unit, and 1000 units or more will cost $24/unit. Ordering cost is $150/order and holding cost is $5/unit/year. What policy should the company adopt?
Q Cost/Unit
$30.00 1.
$27.75
2. Since 500<849<999 ignore 1 & 2 and compare 3 & 4?
$25.50
« 849 »
$24.00 TC $
TC+
TC+
Policy: Order 1000 at a time, at cost of $24/unit Q*

42. Price Break Models Holding cost is variable
Sort prices from lowest to highest and calculate the order quantity for each price until a feasible order quantity is found
If the first feasible order quantity is the lowest price, this is best, otherwise, calculate the total cost for the first feasible quantity and calculate total cost at each price lower than the first feasible order quantity
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43. Example: Variable Holding Cost
Suppose in the discount tire example that holding cost is charged at 18% of the cost of the tires. What policy should the company adopt?
The Q could be infeasible
The Q could be semi-feasible
The Q could be feasible
Q Cost/Unit $H/Unit
$ (.18) = 5.40
$ (.18) = 5.00
$ (.18) = 4.59
866
$ (.18) = 4.32
913
Semi-feasible
& are infeasible
Feasible
Policy: Order 1000 at a time cost of $24/unit

44. Curves for Three Separate Order Quantity Models in a Three-Price-Break Situation
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45. Example 17.8: The Data and Order Quantities
i = 20 percent
Cost per unit…
1-499 $5.00
$4.50
1,000 and up $3.90
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46. Example 17.8: The Solution
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47. Example: Variable Holding Cost
Flagstaff Products offers the following discount schedule for its 4’x8’ sheets of plywood.
Order Quantity Unit Cost
9 Sheets or less $ 18.00
10 to 50 Sheets $ 17.50
More than 50 Sheets $ 17.25
Home Sweet Home Company (HSH) orders plywood from Flagstaff Products. HSH has an ordering cost of $ The carrying cost is 20% of cost, and the annual demand is 100 sheets. What do recommend as the ordering policy for HSH?
Infeasible
Infeasible
Feasible

48. Economic Production Quantity (EPQ)
Product produced and consumed simultaneously
Plant within a plant situation
EOQ definitions apply plus:
d = constant usage rate
p = production rate
EPQ =
TC =

49. Example: EPQ
A product, , is assembled with another component, , which is produced in another department at a rate of 100 units/day. The use rate for at assembly department is 40/day. Find optimal production order size, reorder point, and total cost if there are 250 working days/year, S=$50, H=$0.5/unit/year, P=$7/ , L=7 days, and D=10000.
EPQ =
R = dL = 40(7) = 280 units
TC =

50. ABC Classification
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51. ABC Classification
Items kept in inventory are not of equal importance in terms of:
dollars invested
profit potential
sales or usage volume
stock-out penalties 30 60 A B C
% of
$ Value
Use
So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items

52. ABC Classification Based on Pareto Study The scheme
20% of people 80% of wealth (80/20 rule)
Used in most areas of business
The scheme
Class A items
Fewest in number—10-20%
Highest in dollar value—70-80%
Exercise greatest control here

53. ABC Classification The Scheme Natural break or company policy scheme
Class B items
Moderate in number %
Moderate in dollar value %
Exercise average control here
Class C items
Highest in number--about 50%
Lowest in dollar value--5-10%
Exercise the least control here
Natural break or company policy scheme

54. Example: ABC Classification
Use ABC method to classify the following five products in a company’s inventory.
Annual Cost/
Item Demand Unit (1) (2) Item ADU (3) (4)
1 50 x $ 200 = K 80% 80
2 10 x $ 200 = K 10% 10
3 100 x $ 800 = K 5% 15
4 50 x $ 100 = K 3% 03
5 15 x $ 200 = K 2% 05
$ 100,000
STEP A B C
Steps for the ABC Classification
Find annual dollar usage (ADU) for each item
Rank ADU in descending order of magnitude
Find percentage of usage to total inventory cost
Find running sum of percentage of dollar usage and classify

55. Inventory Accuracy and Cycle Counting
Inventory accuracy: refers to how well the inventory records agree with physical count
Cycle counting: a physical inventory- taking technique in which inventory is counted on a frequent basis rather than once or twice a year
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56. Rudolph Manufacturing
Example:
Rudolph Manufacturing
H=$0.10
S=$50
C=$1
p=100 units
Order Quantity
units
Holding $
Setup $
Total $ 1 2 3 4
# Production Runs 3 6 9 12
Time b/w Runs
Then Or If
Inventory $