1. Stevenson 13
Inventory Management

2. Learning Objectives
Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management.
Discuss the nature and importance of service inventories
Discuss periodic and perpetual review systems.
Discuss the objectives of inventory management.
Describe the A-B-C approach and explain how it is useful.

3. Learning Objectives
Describe the basic Economic Order Quantity (“EOQ”) model and its assumptions, and solve typical problems.
Describe the Economic Production Quantity (“EPQ”) model and solve typical problems.
Describe the quantity discount model and solve typical problems.
Describe reorder point models and solve typical problems.

4. Inventory Models
Independent demand – finished goods, items that are ready to be sold
E.g. a computer
Dependent demand – components of finished products
E.g. parts that make up the computer

5. Independent demand is uncertain. Dependent demand is certain.
Inventory
Independent Demand A
B(4)
C(2)
D(2)
E(1)
D(3)
F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Inventory: a stock or store of goods

6. Types of Inventories Replacement parts, tools, & supplies
Raw materials & purchased parts
Partially completed goods called work in progress
Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers (pipeline inventory)

7. Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stock-outs

8. Functions of Inventory (Cont’d)
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity discounts

9. Objective of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service
Costs of ordering and carrying inventory
Inventory turnover is the ratio of average cost of goods sold to average inventory investment.

10. Effective Inventory Management
A system to keep track of inventory
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system

11. Inventory Counting Systems
Periodic System
Physical count of items made at periodic intervals
Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

12. Inventory Counting Systems (Cont’d)
Two-Bin System - Two containers of inventory; reorder when the first is empty
Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached

13. Key Inventory Terms
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply

14. 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
$ value
of items A B C
High
Low
Percentage of Items

15. Economic Order Quantity Models
Economic order quantity (EOQ) model
The order size that minimizes total annual cost
Economic production model
Quantity discount model

16. Assumptions of EOQ Model
Only one product is involved
Annual demand requirements known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts

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

18. Total Cost Annual carrying cost Annual ordering cost Total cost = + Q2 H D S +
TC =
Q is Order Quantity (in units)
H is Holding (Carrying) cost per unit
D is Demand, usually in units per year
S is Ordering Cost per order

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

20. Deriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

21. Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D S =

22. EOQ Example
A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year.
What is the EOQ?
How many times per year does the store reorder?
What is the length of an order cycle (time between orders)?
What is the total annual cost if the EOQ quantity is ordered?

23. EOQ Example

24. EOQ Example
Piddling Manufacturing assembles security monitors. It purchases 3,600 black-and-white cathode ray tubes a year at $65 each. Ordering costs are $31, and annual carrying costs are 20 percent of the purchase price. Compute the optimal quantity and the total annual cost of ordering and carrying the inventory.

25. Economic Production Quantity (EPQ)
Production done in batches or lots
Capacity to produce a part exceeds the part’s usage or demand rate
Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

26. Economic Production Quantity Assumptions
Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continually
Production rate is constant
Lead time does not vary
No quantity discounts

27. Economic Run Size
p is production or delivery rate
u is usage rate

28. EPQ Example
A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. 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

29. EPQ Example

30. EPQ Example

31. EOQ Refresher

32. Total Costs with Purchasing Cost
Annual
carrying
cost
Purchasing
TC = + Q 2 H D S
ordering PD

33. Total Costs with PD Cost Adding Purchasing cost doesn’t change EOQ
TC with PD
TC without PD PD
Quantity
Adding Purchasing cost doesn’t change EOQ

34. Quantity Discount Example
The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost.

35. Quantity Discount Example

36. Quantity Discount Example
The 70 cases can be bought at $18 per case because 70 falls in the range of 50 to 79 cases. The total cost to purchase 816 cases a year, at the rate of 70 cases per order, will be
Because lower cost ranges exist, each must be checked against the minimum cost generated by 70 cases at $18 each. In order to buy at $17 per case, at least 80 cases must be purchased. (Because the TC curve is rising, 80 cases will have the lowest TC for that curve's feasible region.) The total cost at 80 cases will be
To obtain a cost of $16 per case, at least 100 cases per order are required, and the total cost at that price break will be

37. Quantity Discount Example
Order Quantity
Total Cost 70
14,968 80
14,154
100
13,354
100 cases per order yields the lowest total cost, 100 cases is the overall optimal order quantity.
With Quantity Discounts, purchase quantity will be equal to or greater optimal economic quantity.

38. When to Reorder with EOQ Ordering
Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered
Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
Service Level - Probability that demand will not exceed supply during lead time.

39. Determinants of the Reorder Point
The rate of demand
The lead time
Demand and/or lead time variability
Stockout risk (safety stock)
If demand and lead time are both constants, then ROP = dxLT

40. Safety Stock
Safety stock reduces risk of
stockout during lead time

41. Reorder Point Example
Rahim takes Two-a-Day vitamins, which are delivered to his home seven days after an order is called in. At what point should Rahim reorder?
Rahim should reorder when 14 vitamin tablets are left, which is equal to a seven-day supply of two vitamins a day.

42. Safety Stock
When variability is present in demand or lead time, it creates the possibility that actual demand will exceed expected demand. Consequently, it becomes necessary to carry additional inventory, called safety stock , to reduce the risk of running out of inventory (a stockout) during lead time. The reorder point then increases by the amount of the safety stock:
For example, if expected demand during lead time is 100 units, and the desired amount of safety stock is 10 units, the ROP would be 110 units

43. Service Level
Order cycle service level can be defined as the probability that demand will not exceed supply during lead time (i.e., that the amount of stock on hand will be sufficient to meet demand).
A service level of 95 percent implies a probability of 95 percent that demand will not exceed supply during lead time.
The risk of a stockout is the complement of service level; a customer service level of 95 percent implies a stockout risk of 5 percent.

44. Reorder Point The ROP based on a normal
Risk of
a stockout
Service level
Probability of
no stockout
Expected
demand
Safety
stock z
Quantity
z-scale
The ROP based on a normal
Distribution of lead time demand

45. Fixed-Order-Interval Model
Orders are placed at fixed time intervals
Order quantity for next interval?
Suppliers might encourage fixed intervals
May require only periodic checks of inventory levels
Risk of stockout
Fill rate – the percentage of demand filled by the stock on hand

46. Fixed-Interval Benefits
Tight control of inventory items
Items from same supplier may yield savings in:
Ordering
Packing
Shipping costs
May be practical when inventories cannot be closely monitored

47. Fixed-Interval Disadvantages
Requires a larger safety stock
Increases carrying cost
Costs of periodic reviews

48. Single Period Model
Single period model: model for ordering of perishables and other items with limited useful lives
Shortage cost: generally the unrealized profits per unit
Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

49. Optimal Stocking Level
Service level = Cs
Cs + Ce
Cs = Shortage cost per unit Ce = Excess cost per unit
Service Level So
Quantity Ce Cs
Balance point

50. Example Ce = $0.20 per unit Cs = $0.60 per unit
Service level = Cs/(Cs+Ce) = .6/(.6+.2)
Service level = .75
Service Level = 75%
Quantity Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25

51. Operations Strategy Too much inventory Wise strategy
Tends to hide problems
Easier to live with problems than to eliminate them
Costly to maintain
Wise strategy
Reduce lot sizes
Reduce safety stock