1. Inventory Management Chapter 13
MIS 373: Basic Operations Management
Additional content from L. Beril Toktay

2. Learning Objectives After this lecture, students will be able to
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 reorder point models and solve typical problems.
Describe situations in which the fixed-order interval model is appropriate, and solve typical problems.
Describe service level and risk of stockout and use Z table to identify the z value for a service level or a risk of stockout
MIS 373: Basic Operations Management

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

4. Inventory An inventory is a stock or store of goods.
Inventories are a vital part of business:
necessary for operations
contribute to customer satisfaction
A “typical” firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory
But
Costly
May have limited shelf-life
Carrier may have limited space
MIS 373: Basic Operations Management

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)
MIS 373: Basic Operations Management

6. Costs of Inventory Physical holding costs:
out of pocket expenses for storing inventory (insurance, security, warehouse rental, cooling)
All costs that may be entailed before you sell it (obsolescence, spoilage, rework...)
Opportunity cost of inventory: foregone return on the funds invested.
MIS 373: Basic Operations Management

7. why most companies still like to hold inventories?
With all these costs,
why most companies still like to hold inventories?

8. 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.
MIS 373: Basic Operations Management

9. 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.
MIS 373: Basic Operations Management

10. Objectives of Inventory Control
Inventory management has two main concerns:
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
MIS 373: Basic Operations Management

11. 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

12. 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

13. 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

14. 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

15. One-Bind & Two-Bin Systems
One-Bin System
Two-Bin System
Bin A
Bin B
MIS 373: Basic Operations Management

16. Inventory Costs Purchase cost Holding (carrying) costs Ordering costs
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

17. 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

18. ABC Classification 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

19. 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

20. How Much to Order? Economic Order Quantity Models
Economic Order Quantity (EOQ) 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)
MIS 373: Basic Operations Management

21. Basic EOQ Model The basic EOQ model: Assumptions:
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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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)

33. 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.

34. But demand is rarely predictable!
Inventory
Level
Order
Quantity
Demand???
Time
Place
order
Receive order
Lead Time
MIS 373: Basic Operations Management

35. 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

36. 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

37. 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

38. Safety Stock To reduce stockouts we add safety stock Order Quantity
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

39. Expected demand during lead time + z*σdLT
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

40. (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

41. Z Table How to use Z table:
Other variations of Z table
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s/lesson17/TopOfNormalBTable.gif
How to use Z table:
Decide the desired service level
Look up the smallest number in the Z table that is greater than the service level
Use the row of the number to identify the first two digits of the z
Use the column of the number to identify the second decimal point
Q1: what is the z for a 99% service level?
Q2: what is the z for a 10% risk of stockout?

42. Fixed-Order-Interval Model
The fixed-order-interval (FOI) model is used when orders must be placed at fixed time intervals (weekly, twice a month, etc.): The timing of orders is set. The question, then, at each order point, is how much to order.
Fixed-interval ordering systems are widely used by retail businesses.
If demand is variable, the order size will tend to vary from cycle to cycle.
This is quite different from an EOQ/ROP approach in which the order size generally remains fixed from cycle to cycle, while the length of the cycle varies.
MIS 373: Basic Operations Management

43. Fixed-Order-Interval Model
Reasons for Using the Fixed-Order-Interval Model
A supplier's policy might encourage orders at fixed intervals.
Grouping orders for items from the same supplier can produce savings in shipping costs.
Some situations do not readily lend themselves to continuous monitoring of inventory levels.
Many retail operations (e.g., drugstores, small grocery stores) fall into this category.
The alternative for them is to use fixed-interval ordering, which requires only periodic checks of inventory levels.
MIS 373: Basic Operations Management

44. fixed-quantity ordering
The same quantity
fixed-quantity ordering
LT: Lead Time
Different quantity
fixed-interval ordering
same length
same length
LT: Lead Time
OI: Order Interval
MIS 373: Basic Operations Management

45. Fixed-Order-Interval Model
Order size in the fixed-interval model is determined by the following computation:
Amount to order
Expected demand during protection interval
Safety stock
Amount on hand at reorder time = + − Q =
𝑑 𝑂𝐼+𝐿𝑇 +
𝑧 𝜎 𝑑 𝑂𝐼+𝐿𝑇 − A
where
d = demand in a time unit, e.g., 100 units per day
OI = Order interval (length of time between orders), e.g., 10 days
LT = Lead time, e.g., 3 days
𝜎 𝑑 = the standard deviation of the demand, e.g., 20 units
z = z score for a desired service level, e.g., 2.33 for a 99% service level
A = Amount on hand at reorder time
MIS 373: Basic Operations Management

46. Example: Fixed-Order-Interval Model
Given the following information, determine the amount to order.
d = 30 units per day
OI = 7 days
LT = 2 days
𝜎 𝑑 = 3 units per day
Service level = 99%  z = 2.33 (by looking up the z table)
A = 71 units Q = +
𝑧 𝜎 𝑑 𝑂𝐼+𝐿𝑇 − A
𝑑 𝑂𝐼+𝐿𝑇 = +
30 7+2
2.33×3× 7+2 − 71
= 222 units
MIS 373: Basic Operations Management

47. Key Points
All businesses carry inventories, which are goods held for future use or potential future use.
Inventory represents money that is tied up in goods or materials.
Effective inventory decisions depend on having good inventory records, good cost information, and good estimates of demand.
The decision of how much inventory to have on hand reflects a trade-off, for example, how much money to tie up in inventory versus having it available for other uses. Factors related to the decision include purchase costs, holding costs, ordering costs, shortage and backlog costs, available space to store the inventory, and the return that can be had from other uses of the money.
As with other areas of operations, variations are present and must be taken into account. Uncertainties can be offset to some degree by holding safety stock, although that adds to the cost of holding inventory.
MIS 373: Basic Operations Management