1. Chapter 14 Inventory Control2

2. OBJECTIVES Definition and Purpose of Inventory Inventory Costs
Independent vs. Dependent Demand
Single-Period Inventory Model
Multi-Period Inventory Models: Basic Fixed-Order Quantity Models
Multi-Period Inventory Models: Basic Fixed-Time Period Model
Miscellaneous Systems and Issues 2

3. Inventory System Defined
Inventory is the stock of any item or resource used in an organization. They are carried in anticipation of use and can include:
raw materials
finished products
component parts
supplies, and
work-in-process
An inventory system is 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 3

4. Problems of Inventory Management
When to order the products
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

5. Purposes of Inventory 1. To maintain independence of operations
2. To meet variation in product demand
3. To allow flexibility in production scheduling
4. To provide a safeguard for variation in raw material delivery time
5. To take advantage of economic purchase-order size 4

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

7. Inventory Costs Holding (or carrying) costs: H
Costs for physical storage space
Handling
Taxes and insurance, etc.
Breakage, spoilage, deterioration, obsolescence
Cost of capital
Setup (or production change) costs: S
Costs for arranging specific equipment setups, etc. 5

8. Inventory Costs: Continued
Ordering costs: S
Costs (clerical) of someone placing an order (phone, typing, etc.)
Supplies and order processing, etc.
Shortage costs:
Costs of canceling an order
Rain checks (backorders)
Loss of customer goodwill, etc.
Outdate costs (for perishable products)
Purchase cost: C

9. Independent vs. Dependent Demand
Independent Demand (Demand for the final end-product or demand not related to other items)
Finished
product
Dependent Demand
(Derived demand items for component parts,
subassemblies,
raw materials, etc)
E(1)
Component parts 6

10. Classification of Inventory Systems: Single Period Models
Single-Period Inventory Model
One time purchasing decision:
Example:
Vendor selling T-shirts at a football game
Newspaper sales (Newsboy Model)
Seeks to balance the costs of inventory overstock and under stock 7

11. Classifying Inventory Models:
Multi-Period 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

12. Single-Period Inventory Model
This model states that we should continue to 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 8

13. Single Period Model Example
Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game?
Cu = $10 and Co = $5; P ≤ $10 / ($10 + $5) = .667
Z.667 = .432 (use NORMSDIST(.667) or Appendix E)
therefore we need 2, (350) = 2,551 shirts

14. Multi-Period Models: Fixed-Order Quantity Model Model Assumptions (Part 1)
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

15. Multi-Period Models: Fixed-Order Quantity Model Model Assumptions (Part 2)
Inventory holding cost is based on average inventory
Ordering or setup costs are constant
All demands for the product will be satisfied (No back orders are allowed) 9

16. Basic Fixed-Order Quantity Model and Reorder Point Behavior
1. You receive an order quantity Q.
4. The cycle then repeats.
R = Reorder point
Q = Economic order quantity
L = Lead time L Q R
Time
Number
of units
on hand
2. Your start using them up over time.
3. When you reach down to a level of inventory of R, you place your next Q sized order.

17. Cost Minimization Goal
By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs
Total Cost C O S T
Holding
Costs
QOPT
Annual Cost of
Items (DC)
Ordering Costs
Order Quantity (Q) 11

18. Basic Fixed-Order Quantity (EOQ) Model Formula
TC=Total annual cost
D =Demand
C =Cost per unit
Q =Order quantity
S =Cost of placing an
order or setup cost
R =Reorder point
L =Lead time
H =Annual holding and
storage cost per unit
of inventory
Total
Annual =
Cost
Annual
Purchase
Cost
Annual
Ordering
Cost
Annual
Holding
Cost + + 12

19. Deriving the EOQ
Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt
We also need a reorder point to tell us when to place an order 13

20. EOQ Example (1) Problem Data
Given the information below, what are the EOQ and reorder point?
Annual Demand = 1,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = $2.50
Lead time = 7 days
Cost per unit = $15 14

21. EOQ Example (1) Solution
In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units. 15

22. EOQ Example (2) Problem Data
Determine the economic order quantity and the reorder point given the following…
Annual Demand = 10,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = 10% of cost per unit
Lead time = 10 days
Cost per unit = $15 16

23. EOQ Example (2) Solution
Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units. 17

24. Fixed-Order Quantity Model Model With Safety Stock
An amount added to R due to uncertainty of demand during the lead time
Could be constant or variable (based on known service level)
Where,
= number of standard deviations for a given service probability
= Standard deviation of usage during the lead time

25. Fixed-Time Period Model with Safety Stock Formula
q = Average demand + Safety stock – Inventory currently on hand 18

26. Multi-Period Models: Fixed-Time Period Model: Determining the Value of sT+L
The standard deviation of a sequence of random events equals the square root of the sum of the variances 20

27. Example of the Fixed-Time Period Model
Given the information below, how many units should be ordered?
Average daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The daily demand standard deviation is 4 units. 21

28. Example of the Fixed-Time Period Model: Solution (Part 1)
The value for “z” is found by using the Excel NORMSINV function, or as we will do here, using Appendix D. By adding 0.5 to all the values in Appendix D and finding the value in the table that comes closest to the service probability, the “z” value can be read by adding the column heading label to the row label.
So, by adding 0.5 to the value from Appendix D of , we have a probability of , which is given by a z = 1.75 22

29. Example of the Fixed-Time Period Model: Solution (Part 2)
So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period 23

30. Variants of EOQ: Price-Break or Discount Models
Seller offers you incentive to buy more
Larger lot sizes result in cheaper/unit cost
Two possibilities:
Holding cost is constant or variable:
Compute Q using the appropriate H
If Q corresponds to lowest price break, it is optimal
Else, find TC for Q and those for lower price breaks
The Q corresponding to lowest TC is optimal

31. Price-Break (Discount) Model Formula
Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula:
i = percentage of unit cost attributed to carrying inventory
C = cost per unit
Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value 13

32. Discount Example: Fixed Holding Cost
Demand for tires 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 of more will cost $24/unit. Order cost is $150/order and holding cost is $5/unit/year. What policy should the company adopt?

33. Discount 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

34. Discount Example: VHC Continued
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?

35. Price-Break Example Problem Data (Part 1)
A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units?
Order Quantity(units) Price/unit($)
0 to 2, $1.20
2,500 to 3,
4,000 or more 14

36. Price-Break Example Solution (Part 2)
First, plug data into formula for each price-break value of “C”
Annual Demand (D)= 10,000 units
Cost to place an order (S)= $4
Carrying cost % of total cost (i)= 2%
Cost per unit (C) = $1.20, $1.00, $0.98
Next, determine if the computed Qopt values are feasible or not
Interval from 0 to 2499, the Qopt value is feasible
Interval from , the Qopt value is not feasible
Interval from 4000 & more, the Qopt value is not feasible 15

37. Price-Break Example Solution (Part 3)
Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why?
Because the total annual cost function is a “u” shaped function
Total annual costs
So the candidates for the price-breaks are 1826, 2500, and 4000 units
Order Quantity 15

38. Price-Break Example Solution (Part 4)
Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price-break
TC(0-2499) =(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)
= $12,043.82
TC( ) = $10,041
TC(4000&more) = $9,949.20
Finally, we select the least costly Qopt, which is this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units 15

39. Variant of the EOQ: The EPQ Model
Product produced and consumed simultaneously
Plant within a plant situation
EOQ definitions apply plus:
d = constant usage rate
p = production rate
EPQ =
TC =

40. EPQ: Example
A product, X, is assembled with another component, Xi, which is produced in another department at a rate of 100 units/day. The use rate for Xi at assembly department is 40/day. Find optimal production order size, reorder point, and total cost if there are 250 working days/year, S=$50, H=$.5/unit/year, P=$7/Xi, L=7 days, and D=10000.
Solution:
EPQ =
R = dL = 40(7) = 280 units
TC =

41. Miscellaneous Systems: Optional Replenishment System
Maximum Inventory Level, M
Actual Inventory Level, I
q = M - I I M
Q = minimum acceptable order quantity
If q > Q, order q, otherwise do not order any. 24

42. Miscellaneous Systems: Bin Systems
Two-Bin System
Full
Empty
Order One Bin of
Inventory
One-Bin System
Periodic Check
Order Enough to
Refill Bin 25

43. ABC Classification System
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 26

44. ABC Classification System
Based on Pareto Study
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

45. ABC Classification System
The 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

46. ABC Classification: Example
Use ABC method to classify the following five products in a company’s inventory.
Item Annual Demand Cost/Unit
$ 200
$ 200
$ 800
$ 100
$ 200
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

47. Inventory Accuracy and Cycle Counting Defined
Inventory accuracy refers to how well the inventory records agree with physical count
Cycle Counting is a physical inventory- taking technique in which inventory is counted on a frequent basis rather than once or twice a year 27