1. Inventory Management
Chapter 13

2. Learning Objectives Define the term inventory
List the different types of inventory
Describe the main functions of inventory
Discuss the main requirements for effective inventory management
Describe the A-B-C approach and explain how it is useful
Describe the basic EOQ model and its assumptions and solve typical problems.
Describe the economic production quantity model and solve typical problems
Describe the quantity discount model and solve typical problems
Describe reorder point models and solve typical problems.

3. Inventory Management at Cox Hardware
From the video, what are the elements relevant to inventory management?

4. Inventory Definition Inventories are a vital part of business:
A stock or store of goods
Dependent demand items
Items that are subassemblies or component parts to be used in the production of finished goods.
Independent demand items
Items that are ready to be sold or used
Inventories are a vital part of business:
necessary for operations
contribute to customer satisfaction

5. Types of Inventory Raw materials and purchased parts
Work-in-process (WIP)
Finished goods inventories or merchandise
Tools and supplies
Maintenance and repairs (MRO) inventory
Goods-in-transit to warehouses or customers (pipeline inventory)

6. Discussion
Which of them are dependent demand items and independent demand items?
Raw materials and purchased parts
Work-in-process (WIP)
Finished goods inventories or merchandise
Tools and supplies
Maintenance and repairs (MRO) inventory
Goods-in-transit to warehouses or customers (pipeline inventory)

7. Inventory Functions Inventories serve a number of functions such as:
To meet anticipated customer demand
To smooth production requirements
Firms that experience seasonal patterns in demand often build up inventories during preseason periods to meet overly high requirements during seasonal periods.
To decouple operations
Buffers between operations
To protect against stockouts
Delayed deliveries and unexpected increases in demand increase the risk of shortages.

8. Inventory Functions Inventories serve a number of functions such as:
To take advantage of order cycles
It is usually economical to produce in large rather than small quantities. The excess output must be stored for later use.
To hedge against price increases
Occasionally a firm will suspect that a substantial price increase is about to occur and purchase larger-than-normal amounts to beat the increase
To permit operations
The fact that production operations take a certain amount of time (i.e., they are not instantaneous) means that there will generally be some work-in-process inventory.
To take advantage of quantity discounts
Suppliers may give discounts on large orders.

9. Objectives of Inventory Control
Inventory management has two main concerns:
Satisfactory Level of customer service
Having the right goods available in the right quantity in the right place at the right time
Costs of ordering and carrying inventories
The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds

10. MIS 373: Basic Operations Management
Inventory Management
Management has two basic functions concerning inventory:
Establish a system for tracking items in inventory
Make decisions about
When to order
How much to order
MIS 373: Basic Operations Management

11. Effective Inventory Management
Requires:
A system keep track of inventory
A reliable forecast of demand
Knowledge of lead time and lead time variability
Reasonable estimates of
holding costs
ordering costs
shortage costs
A classification system for inventory items
MIS 373: Basic Operations Management

12. Measures of performance
Customer satisfaction
Number and quantity of backorders
Customer complaints
Inventory turnover = a ratio of
during a period
(average) cost of goods sold
(average) inventory investment
MIS 373: Basic Operations Management

13. Inventory Counting Systems
Periodic System
Physical count of items in inventory made at periodic intervals
Perpetual Inventory System
System that keeps track of removals from inventory continuously, thus monitoring current levels of each item
Point-of-sale (POS) systems
A system that electronically records actual sales
Radio Frequency Identification (RFID)
MIS 373: Basic Operations Management

14. MIS 373: Basic Operations Management
Inventory Costs
Purchase cost
The amount paid to buy the inventory
Holding (carrying) costs
Cost to carry an item in inventory for a length of time, usually a year
Interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security).
Ordering costs
Costs of ordering and receiving inventory
determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage.
Shortage costs
Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit
MIS 373: Basic Operations Management

15. ABC Classification System
A-B-C approach
Classifying inventory according to some measure of importance, and allocating control efforts accordingly
A items (very important)
10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value
B items (moderately important)
C items (least important)
50 to 60 percent of the number
of items in inventory but only
about 10 to 15 percent of the
annual dollar value
MIS 373: Basic Operations Management

16. ABC Classification System
How to classify?
For each item, multiply annual volume by unit price to get the annual dollar value.
Arrange annual values in descending order.
A items: the few with the highest annual dollar value
C items: the most with the lowest dollar value.
B items: those in
between #
Annual demand
Unit
price
Annual value
Class
% of items
% of value 8
1,000
4,000
4,000,000 A
5.3
52.7 3
2,400
500
1,200,000 B
31.4
40.8 6
1,000,000 1
2,500
360
900,000 4
1,500
100
150,000 C
63.3
6.5 10
200
100,000 9
8,000
80,000 2 70
70,000 5
700
49,000 7
210
42,000
18,800
7,591,000
MIS 373: Basic Operations Management

17. ABC Classification: Cycle Counting
A physical count of items in inventory
Cycle counting management
How much accuracy is needed?
A items: ± 0.2 percent
B items: ± 1 percent
C items: ± 5 percent
When should cycle counting be performed?
Who should do it?
MIS 373: Basic Operations Management

18. Inventory Models Economic Order Quantity models:
identify the optimal order quantity
by minimizing total annual costs that vary with order size and frequency
The basic Economic Order Quantity model (EOQ)
The Quantity Discount model
The Economic Production Quantity model (EPQ)
Reorder Point Ordering (uncertainty, when to order)
Fixed-Order-Interval model
Single Period model (perishable items)

19. MIS 373: Basic Operations Management
Basic EOQ Model
The basic EOQ model:
used to find a fixed order quantity that will minimize total annual inventory costs
continuous monitoring system
Assumptions:
Only one product is involved
Annual demand requirements are 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
MIS 373: Basic Operations Management

20. 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
MIS 373: Basic Operations Management

21. Discussion What costs are associated with this model?
(Hint: Recall the 5 types of costs)
Purchase cost
Holding (carrying) cost
Ordering cost
Setup cost
Shortage cost (Backorder/Backlog cost)
Instructor Slides

22. MIS 373: Basic Operations Management
Total Annual Cost
Total Cost = Annual Holding Cost + Annual Ordering Cost
(TC)
where
Q = order quantity in units
H = holding (carrying) cost per unit, usually per year
D = demand, usually in units per year
S = ordering cost per order = Q H + D S 2
Average number of units in inventory
Number of orders
MIS 373: Basic Operations Management

23. Goal: Total Cost Minimization
The Total-Cost Curve is U-Shaped
There is a tradeoff between holding costs and ordering costs
Order Quantity (Q)
Ordering Costs Q*
Annual Cost
(optimal order quantity)
Holding Costs
MIS 373: Basic Operations Management

24. MIS 373: Basic Operations Management
Deriving EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
𝑇 𝐶 ′ = 𝐻 2 + −1 𝐷𝑆 𝑄 2 =0 → 𝐷𝑆 𝑄 2 = 𝐻 → 𝐷𝑆 𝑄 = 𝐻𝑄 2
𝑄 ∗ = 2𝐷𝑆 𝐻 = 2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
MIS 373: Basic Operations Management

25. MIS 373: Basic Operations Management
Example: Deriving EOQ
Tire distributer
D (Demand)=9,600 tires per year
H (Holding cost)=$16 per unit per year
S (Ordering cost) = $75 per order
𝑄 ∗ = 2𝐷𝑆 𝐻 = 2∗9,600∗ =300 𝑡𝑖𝑟𝑒𝑠
𝑇𝐶= 𝑄 2 𝐻+ 𝐷 𝑄 𝑆= ∗16+ 9, ∗75=2,400+2,400=4,800
MIS 373: Basic Operations Management

26. Let’s verify whether the Q* indeed gives the lowest cost.
Example: Deriving EOQ
D (Demand)=9,600 tires per year
H (Holding cost)=$16 per unit per year
S (Ordering cost) = $75 per order
Q*=300 tires
TCmin = 4,800
Let’s verify whether the Q* indeed gives the lowest cost.
MIS 373: Basic Operations Management

27. Exercise
A local distributor for a national tire company expects to sell approximately 9,600 tires per year. Annual carrying cost is $16 per tire, and ordering cost is $75 per order. The distributor operates 288 working days a year.
a. What is the optimal order size?
b. How many times per year the store reorder?
c. What is the length of an order cycle?
d. What is the total annual cost if EOQ is placed?
Instructor Slides

28. Solution a b c d
Instructor Slides

29. Economic Production Quantity (EPQ)
The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate)
Assumptions
Only one item is involved
Annual demand requirements are known
Usage rate is constant (= even demand throughout the year)
Usage occurs continually, but production occurs periodically (batch production)
The production rate is constant
Production rate is greater than usage rater
Lead time does not vary
There are no quantity discounts
13-29
Instructor Slides

30. EPQ: Inventory Cycle Q Qp Imax 13-30 Time Production and usage Usage
only
Cumulative
production
Amount
on hand
Time
13-30
Instructor Slides

31. Discussion What costs are associated with this model?
(Hint: Recall the 5 types of costs)
Purchase cost
Holding (carrying) cost
Ordering cost
Setup cost
Shortage cost (Backorder/Backlog cost)
Our decision making in EPQ model is to determine the size of order (Q) each time. Why?
Instructor Slides

32. EPQ Model
Instructor Slides

33. EPQ – Total Cost
13-33
Instructor Slides

34. EPQ Optimal Batch size a.k.a Economic Produciton Quantity (EPQ) 13-34
Instructor Slides

35. Exercise
A toy manufacturer uses 48,000 wheels per year for toy trucks. The firm produces 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 is $45 per production run. The firm operates 240 days per year.
a. What is the optimal batch size?
b. What is the total annual cost if EPQ is produced each run?
c. What is cycle time (production stage + usage stage)?
d. What is the production cycle time?
Instructor Slides

36. Solution a b
Instructor Slides

37. Solution c d
Instructor Slides

38. Quantity Discount Model
Price reduction for larger orders offered to customers to induce them to buy in large quantities
13-38
Instructor Slides

39. MIS 373: Basic Operations Management
When to Reorder
If delivery is not instantaneous, but there is a lead time: When to order?
Order
Quantity Q
Inventory
Lead Time
Time
Place
order
Receive order
MIS 373: Basic Operations Management

40. MIS 373: Basic Operations Management
When to Reorder
EOQ answers the “how much” question
The reorder-point (ROP) tells “when” to order
Reorder-Point
When the quantity on hand of an item drops to this amount (quantity-trigger), the item is reordered.
Determinants of the Reorder-Point
The rate of demand
The lead time
The extent of demand and/or lead time variability
The degree of stockout risk acceptable to management
MIS 373: Basic Operations Management

41. MIS 373: Basic Operations Management
Reorder-Point
ROP = (Demand per day) * (Lead time for a new order in days)
= d * L
where
d = (Demand per year) / (Number of working days in a year)
Example:
Demand = 12,000 iPads per year
300 working day year
Lead time for orders is 3 working days
In other words, the manager should place the order when only 120 units left in the inventory.
d = 12,000 / 300 = 40 units
ROP = d * L = 40 units per day * 3 days of leading time = 120 units
MIS 373: Basic Operations Management

42. Profile of Inventory Level Over Time
The Inventory Cycle
Q: When shall we order?
A: When inventory = ROP
Q: How much shall we order?
A: Q = EOQ
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time
ROP = LxD
D: demand per period
L: Lead time in periods
MIS 373: Basic Operations Management

43. Exercise: EOQ & ROP
Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? (Assuming that the lead time to receive cars is 10 days and that there are 365 working days in a year)
Recall:
𝑄 ∗ = 2𝐷𝑆 𝐻 = 2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
EOQ =
ROP = (Demand per day) * (Lead time for a new order in days)
= d * L
where
d = (Demand per year) / (Number of working days in a year)

44. Exercise: EOQ & ROP
Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size?
Since d is given in years, first convert: 5000/365 =13.7 cars per working day
So, ROP = 13.7 * 10 = 137
So, when the number of cars on the lot reaches 137, order 548 more cars.

45. But demand is rarely predictable!
Inventory
Level
When Actual Demand < Expected Demand
Order
Quantity
Lead Time Demand
ROP
Inventory at time of receipt
Time
Place
order
Receive order
Lead Time
MIS 373: Basic Operations Management

46. But demand is rarely predictable!
Inventory
Level
When Actual Demand > Expected Demand
Order
Quantity
Unfilled demand
Stockout Point
ROP
Time
Place
order
Lead Time
Receive order
MIS 373: Basic Operations Management

47. But demand is rarely predictable!
Inventory
Level
If ROP = expected demand,
inventory left 50% of the time, stock outs 50% of the time.
Order
Quantity
ROP = Expected Demand
Average
Uncertain Demand
Time
MIS 373: Basic Operations Management

48. MIS 373: Basic Operations Management
Safety Stock
Inventory
Level
To reduce stockouts we add safety stock
Order
Quantity
Order Quantity
Q = EOQ
ROP =
Safety
Stock +
Expected LT
Demand
Expected
Lead-time
Demand
Expected
LT Demand
Safety Stock
Place
order
Time
Lead Time
Receive order
MIS 373: Basic Operations Management

49. How Much Safety Stock?
The amount of safety stock that is appropriate for a given situation depends upon:
The average demand rate and average lead time
Demand and lead time variability
The desired service level
Service level = probability of NOT stocking out
Reorder point (ROP) =
Expected demand during lead time + z*σdLT
Where
z = number of standard deviations
σdLT = the standard deviation of lead time demand
MIS 373: Basic Operations Management

50. (probability of not stockout)
Reorder Point
The ROP based on a normal distribution of lead time demand
Risk of stockout
Service level
(probability of not stockout)
Quantity
Safety
Stock
Expected
demand
ROP
MIS 373: Basic Operations Management
Z scale Z

51. Recap