1. Chapter 13 - Inventory Management
BUAD306
Chapter 13 - Inventory Management

2. Everyday Inventory
Food
Gasoline
Clean clothes…
What else?

3. Inventory Stock or quantity of items kept to meet demand
Takes on different forms
Final goods
Raw materials
Purchased/component parts
Labor
In-process materials
Working capital

4. Inventory Static – only one opportunity to buy and sell units
Dynamic – ongoing need for units; reordering must take place

5. Demand Dependent Demand Independent Demand
Items are used internally to produce a final product
Independent Demand
Items are final products demanded by external customers

6. Reasons To Hold Inventory
To meet anticipated demand
To smooth production requirements
To decouple components of the production-distribution system
To protect against stock-outs
To take advantage of order cycles
To hedge against price increases or to take advantage of quantity discounts
To permit operations

7. Inventory Costs Carrying Costs Ordering Costs
Costs of holding an item in inventory
Ordering Costs
Costs of replenishing inventory
Shortage (stockout) Costs
Temporary or permanent loss of sales when demand cannot be met

8. Inventory Management How much and when to order inventory?
Objective: To keep enough inventory to meet customer demand and also be cost-effective
Purpose: To determine the amount of inventory to keep in stock - how much to order and when to order

9. Inventory Management Requirements
A system to keep track of the inventory on hand and on order
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of inventory costs
A classification system for inventory items (ABC)

10. Inventory Control Systems
Control the level of inventory by determining how much to order and when
Continuous (Perpetual) Inventory System - a continual record of the inventory level for every item is maintained
Periodic Inventory System - inventory on hand is counted at specific time intervals

11. Other Control Systems/Tools
Two-Bin System - two containers of inventory; reorder when the first is empty
Universal Product Code (UPC) - Bar code printed on a label that has information about the item to which it is attached
RFID Tags

12. Considerations Lead Time Cycle Counting Usage Rate
Time interval between ordering and receiving the order
Cycle Counting
Physical count of items in inventory
Usage Rate
Rate at which amount of inventory is depleted

13. Profile of Inventory Level Over Time
Inventory Cycle
Profile of Inventory Level Over Time Q
Usage
rate
Quantity
on hand
Reorder
point
Time
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time

14. Economic Order Quantity
The EOQ Model determines the optimal order size that minimizes total inventory costs

15. Inventory Costs
Carrying Costs – cost associated with keeping an item in stock
Includes: storage, warehousing, insurance, security, taxes, opportunity cost, depreciation, etc.
Ordering Costs – cost associated with ordering and receiving inventory
Determining quantities needed, preparing documentation, shipping, inspection of goods, etc.

16. Optimal Order Quantity
2DS H
2 (Annual Demand) (Order Cost) Q = = o
Annual Holding Cost per unit Qo D
Length of order cycle = D Qo
# Orders / Year =

17. Basic EOQ Model Annual carrying cost ordering Total cost = + Qo 2 H D
TC =
Where: Qo = Economic order quantity in units
H = Holding (carrying) cost per unit
D = Demand, usually in units per year
S = Ordering cost

18. Cost Minimization Goal
The Total-Cost Curve is U-Shaped
Annual Cost
Carrying Costs
Ordering Costs QO
(optimal order quantity)
Order Quantity (Q)

19. EOQ Example 1 A) What is the EOQ?
A local office supply store expects to sell 2400 printers next year. Annual carrying cost is $50 per printer, and ordering cost is $30. The company operates 300 days a year.
A) What is the EOQ?
B) How many times per year does the store reorder?
C) What is the length of an order cycle?
D) What is the total annual cost if the EOQ quantity is ordered?

20. Given:. Demand = D = 2400. Holding Cost = H = $50 per unit per year
Given: Demand = D = Holding Cost = H = $50 per unit per year Ordering Cost = S = $30
What is the EOQ?
B. How many times per year does the store reorder?
C. What is the length of an order cycle?

21. Given:. Demand = D = 2400. Holding Cost = H = $50 per unit per year
Given: Demand = D = Holding Cost = H = $50 per unit per year Ordering Cost = S = $30
D. What is the total annual cost if the EOQ quantity is ordered?
TC = Carrying cost + Ordering cost

22. EOQ Example 2 A) What is the EOQ?
A local electronics store expects to sell 500 flat-screen TVs each month during next year. Annual carrying cost is $60 per TV, and ordering cost is $50. The company operates 364 days a year.
A) What is the EOQ?
B) How many times per year does the store reorder?
C) What is the length of an order cycle?
D) What is the total annual cost if the EOQ quantity is ordered?

23. Given:. Demand = D = 6,000. Holding Cost = H = $60 per unit per year
Given: Demand = D = 6,000 Holding Cost = H = $60 per unit per year Ordering Cost = S = $50
What is the EOQ?
B. How many times per year does the store reorder?
C. What is the length of an order cycle?

24. Given:. Demand = D = 6,000. Holding Cost = H = $60 per unit per year
Given: Demand = D = 6,000 Holding Cost = H = $60 per unit per year Ordering Cost = S = $50
D. What is the total annual cost if the EOQ quantity is ordered?
TC = Carrying cost + Ordering cost

25. Other Considerations
Safety Stock
Reorder Point
Seasonality

26. Carrying cost + Ordering cost + Purchasing cost =
Quantity Discounts
A price discount on an item if predetermined numbers of units are ordered
TC =
Carrying cost + Ordering cost + Purchasing cost =
(Q / 2) H + (D / Q) S + PD
where P = Unit Price

27. Quantity Discount Example
Campus Computers 2Go Inc. wants to reduce a large stock of laptops it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule as shown below. Given the discount schedule and its known costs, the bookstore wants to determine if it should take advantage of this discount or order the basic EOQ order size.
Quantity
Price
1 – 49
$1,500
50 – 89
$1,000
90 +
$800
Carrying Cost:
$200
Ordering Cost
$1,000
Annual Demand
400 units

28. First, determine the optimal size and cost with the basic EOQ model.
QO =
This order size is eligible for the discount price of $1,000… now we compute the total cost
TC =
Compare this cost to an ordering size of $800:
TC = (Q / 2) H + (D / Q) S + PD =

29. What if a new discount was offered where they would receive a price of $790 if they were to order 150 or more?

30. HW #13
A mail-order house uses 18,000 boxes a year. Carrying costs are $.60 per box per year and ordering costs are $96. The following price schedule is offered. Determine the EOQ and the # of orders per year.
# Boxes
Unit Price
$1.25
$1.20
$1.15
10000+
$1.10

31. EOQ with Incremental Replenishment (EPQ)
Used when company makes its own product
Considers a variety of costs/terms:
Carrying Cost
Setup Cost (analogous to ordering costs)
Maximum and Average Inventory Levels
Economic Run Quantity
Cycle Time
Run Time

32. EOQ with Incremental Replenishment (EPQ)
Definitions
S = Setup Cost
H = Holding Cost
Imax = Maximum Inventory
Iavg = Average Inventory
D = Demand/Year
p = Production or Delivery Rate
u = Usage Rate

33. EOQ with Incremental Replenishment
Total Cost = Carrying Cost + Setup Cost
(Imax/2) H + (D/Qo) S
Economic run quantity
Qo = 2DS/H * p/(p-u)
Cycle time (time between runs)
Qo /u
Run time (production phase)
Qo /p
Maximum Inventory Level
Imax = (Qo /p)(p-u)
Average Inventory Level
Iaverage = Imax /2

34. Assumptions Only one item is involved Annual demand is known
Usage rate is constant
Usage occurs continually, production periodically
Production rate is constant
Lead time doesn’t vary
No quantity discounts

35. EOQ Replenishment Example
A toy manufacturer uses 48,000 rubber wheels per year for its product. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the:
Optimal run size
Minimum total annual cost for carrying and setup
Cycle time for the optimal run size
Run time

36. S = $45 H = $1 per wheel per year p = 800 wheels per day
D = 48,000 wheels per year
S = $ H = $1 per wheel per year
p = 800 wheels per day
u = 48,000 wheels per 240 days, or 200 wheels per day
Qo = 2DS/H * p/(p-u) =
Imax = (Qo /p)(p-u) =
TCmin = (Imax/2) H + (D/Qo) S =
Cycle time = Qo /u =
Run time = Qo /p =

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