1. Chapter 12
Inventory Management

2. Independent demand is uncertain. Dependent demand is certain.
B(4)
C(2)
D(2)
E(1)
D(3)
F(2)
Topics in this chapter apply to independent demand items.
Independent demand is uncertain. Dependent demand is certain.

3. Types of Inventories Raw materials & purchased parts
Partially completed goods called work in progress (WIP)
Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)

4. Types of Inventories (Cont’d)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers

5. Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple components of the production-distribution
To protect against stock-outs

6. Functions of Inventory (Cont’d)
To take advantage of order cycles
To help hedge against price increases or to take advantage of quantity discounts
To permit operations
The last item is critical for the smooth running of a production line. Machines between work stations usually do operations at different rates, leading to inventory between the work stations.

7. 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

8. 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

9. 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
Note that the idea of the perpetual inventory system is that we assume it goes on forever. This is the type of system that we will discuss in this chapter.

10. 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
RFID System – Tags attached to products that transmit product data to readers via radio waves
RFID is catching on. The readers do not have to be positioned as the scanners that are used to read the universal bar code.

11. 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
$ volume
of items A B C
High
Low
Few
Many
Number of Items
This is another application of the pareto principle, or pareto phenomenon, which you read about in chapter 1.

12. The above illustrates that in most companies, keeping close track of 10% to 40% of the inventory is all that is required. Hence, we say that nature has been good to inventory managers.

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 (H)
Ordering costs: costs of ordering and receiving inventory (S)
Shortage costs: costs when demand exceeds supply
When we do problems in this chapter, H will be the carrying cost (in dollars per unit per period) and S will be the cost of a single order (in dollars for a single order).

14. Profile of Inventory Level Over Time
The Inventory Cycle
Profile of Inventory Level Over Time Q
Usage
rate
Quantity
on hand
Reorder
point
Assume a bar manager always orders enough beer (Q barrels of beer) which is consumed by her customers over one week. A one day lead time means she might order the beer on Thursday morning to get a shipment (of quantity Q) on Friday morning, in order to have her full weekly supply of beer just prior to the Friday “Happy Hour.” We assume the beer is held in refrigeration storage units (which contributes to the holding or carrying cost of the beer) until needed. After the beer comes in on Friday morning, the refrigeration units are filled up to Q, and are drawn down at a usage rate until the beer is gone (being consumed by customers) on Thursday evening at closing time on the following week. However, the beer would be ordered for the next cycle on that Thursday morning. Hence, we have a perpetual inventory system that we assume goes on forever, with orders of size Q always being ordered every Thursday morning and delivered to the bar every Friday morning.
Time
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time

15. The above diagrams, the top figure indicates high inventory costs when compared to the bottom figure. Why? Which of the above (top or bottom figure) indicates high ordering costs?

16. Cost Minimization Goal
The Total Annual Carrying (Holding) Cost
Annual Cost Q H 2
Note that the carrying (or holding) cost in the above graph is a straight line passing through the origin. The (Q/2)H is the average inventory in units multiplied by the carrying cost (or holding cost) as dollars per unit per year, which gives the annual carrying (holding) cost.
Carrying Cost
Order Quantity (Q)

17. Cost Minimization Goal
The Total Annual Ordering Cost
Annual Cost D S Q
Note that as Q is small, the annual ordering cost is large. When Q is large, the annual ordering cost is small. This happens because we are dividing by Q. Also, if D is annual demand, then (D/Q) is the number of orders per year. Hence, (D/Q)S is the annual ordering cost.
Ordering Cost
Order Quantity (Q)

18. Cost Minimization Goal
The Total-Cost Curve is U-Shaped
Annual Cost
Now we add the annual carrying cost to the annual ordering cost, giving us a total cost curve for carrying inventory and for ordering inventory. NOTE THAT WE ARE NOT INCLUDING THE PURCHASE COST OF THE ITEMS AS CHARGED BY THE VENDOR (OR SELLER).
Carrying Cost
Ordering Cost QO
Order Quantity (Q)
(QO = optimal order quantity)

19. Total Cost Annual carrying cost ordering Total cost = + Q 2 H D S TC =
As shown in the previous slide, all we do to get the above formula is add the curves for annual carrying cost and annual ordering cost, giving us the total cost of carrying inventory and ordering items. Note that from the previous slide, we get the minimum total cost when the annual carrying cost is equal to the annual ordering cost.

20. Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal. Note that Qopt below is sometimes written as Q0 or EOQ (for Economic Order Quantity)
This formula comes from applying calculus, a topic in mathematics, to the equation in the previous slide. Since most students in the class are unfamiliar with calculus, we simply give you the formula without deriving it. You will not be tested on using calculus in this course.
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

21. Economic Order Quantity (EOQ) or Q0
Economic order quantity (EOQ) model
The order size that minimizes total annual cost

22. We will discuss this curve in class
We will discuss this curve in class. However, can you figure out why this curve indicates that nature has been good to inventory managers?

23. 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
EOQ is simply one of many mathematical model used in inventory management. It was developed in Bell Labs in the 1920’s, and was also known as the “Wilson Square Root Formula.”

24. Homework Problems
Do problems 3 and 5 on p While the solutions are given in the following slides, be sure that you take the time to try to solve these problems prior to looking at the solutions.

27. End of Slides for Inventory Management