1. Chapter 9
Inventory Management

2. Objectives
After reading the chapter and reviewing the materials presented the students will be able to:
Explain inventory systems and ordering policies
Describe the different types of inventory, their uses, and costs.
Identify and compute order quantities, reorder points, and safety stock.
Explain ABC inventory classification and vendor managed inventory.

3. Basics of Inventory Management
Inventory is quantities of goods in stock.
They cost money to purchase.
In manufacturing inventory can take a variety of forms, such as raw materials and component parts, which are delivered from suppliers.
Once the items enter the production process, they become work-in-process (WIP) inventory.
When the production process is completed, inventory is classified as finished goods.
Inventory also includes supplies and equipment.
Inventory policy addresses the basic question of when and how much to order.

4. Reasons for Carrying Inventory
1. Protect Against Lead Time Demand: Goods cannot arrive immediately when we run out of stock. Even in lean systems, where inventory is delivered in predicted intervals, there is still a certain amount of inventory that must be held in stock.
2. Maintain Independence of Operations: Inventory is typically placed between workstations to decrease their interdependence, so that work stoppage at one station does not shut down the entire assembly line.
3. Balance Supply and Demand: Holding extra inventory enables an organization to meet unexpected surges in demand. Not having extra inventory may mean missed sales.
4. Buffer Uncertainty: A batch of damaged goods, delay due to weather, or a strike at a supplier plant can cause delays.
5. Economic Purchase Orders: Buying in large quantities may result in savings associated with transporting larger quantities at one time.

5. Types of Inventory
1. Cycle Stock: This is a quantity or the batch that is produced during the production cycle.
2. Safety Stock: It is the extra inventory that we carry to serve as a cushion for uncertainties in supply and demand.
3. Anticipation Inventory: Their one purpose is to compensate for differences in the timing of supply and demand or in anticipation of a price increase or a shortage of products.
4. Pipeline Inventory: this is the inventory that is simply in transit (barge, truck, or rail).
5. Maintenance, Repair and Operating Items (MRO): Office supplies, forms, toilet paper, cleaning supplies, and tools and parts needed to repair machines.

6. Inventory Costs
1. Holding Cost: This includes storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capital.
2. Ordering Cost: This cost includes all the costs involved in placing an order and procuring the item.
3. Shortage Costs: Potentially there is a loss of sale. Also there can be a loss of goodwill and reputation with customers.

7. Inventory Systems
Every inventory system must answer two questions: when to order and how much to order.
1. Fixed Order Quantity Systems: The quantity that is ordered with this system is constant or fixed. An order is placed when the inventory point drops to a predetermined level, noted as the reorder point (ROP).
2. Fixed Time Period System: here the inventory levels are checked in fixed time periods, T, and the quantity that is ordered varies. The system sets a target inventory level T to be maintained. The amount of inventory that needs to be ordered will be some quantity Q, is the difference between the target inventory R and how much inventory is in stock, the inventory position (IP) at time T: Q = R – IP.

8. Comparing Fixed Order Quantity Versus Fixed Time Period Systems
The biggest difference between the two systems is the timing and quantities of the orders placed.
With the fixed order quantity system inventory is checked on a continuous basis and the system is prepared to place an order multiple times a year on a random basis.
With the fixed time period system inventory levels are checked in set time intervals. The orders for all items can be bundled.
Fixed order quantity systems are more appropriate for high value items as average inventory carried is lower. Also it is more appropriate when stock outs are less desirable, as inventory is monitored on a continuous basis. However the system is more costly to maintain.

9. Fixed Order Quantity Systems
The first decision in the fixed order quantity model is to select the order quantity Q.
The total annual cost (TC) comprises annual purchase cost, annual ordering cost, and annual holding cost.
TC = DC + (D/Q)S + (Q/2)H
where TC = Total Cost; D = Annual demand; C = Unit Cost; Q = Order Quantity; S = Ordering cost; and H = Holding cost.
Inventory holding costs increase with order quantity.
A smaller order quantity results in lower holding costs, but a higher ordering cost.
The objective is to pick an order quantity that minimizes the sum of both the holding and ordering cost, which is the minimum point on the total cost curve (see figure in text). This is the best or optimal order quantity.
Q opt = EOQ = √(2DS)/H
where Q opt = EOQ = Economic Order Quantity; D = Annual demand; S = Ordering cost; and H = Holding cost.

10. Reorder Point
Assume that the demand rate, d, and the lead time (L) are constant and known with certainty.
The reorder point (ROP) would be enough inventory to ensure demand is covered during the length of lead time.
ROP = demand during lead time = d L

11. Safety Stock
Unfortunately, d and L are rarely fixed, and demand is often higher than expected.
So, we have to carry a bit more inventory called safety stock or buffer stock.
ROP = demand during lead time + safety stock = d l + SS = d l + Zk σL
Where k is the service level, such as 95% service level
Z is obtained from the standard normal table for a particular value of k
σL is the standard deviation of demand over the lead time L. The standard deviation is the square root of the variance.
See example in text.

12. Fixed Time Period Systems
The quantity ordered at time interval T is:
Q = R – IP
Where Q = order quantity
R = target inventory level
IP = inventory position at time T
The time interval T is typically set for organizational convenience.
The quantity Q that is ordered is the amount that will restore inventory levels back to R, the target inventory level.

13. Computing Target Inventory
The target inventory level needs to be large enough to cover three types of demand:
1. Demand during the length of lead time L.
2. Demand during the length of the review period T.
3. Safety stock, SS, to guard against uncertainty.

14. Independent Versus Dependent Demand
Independent demand is demand for a finished product, such as a computer or a bicycle.
Dependent demand is demand for component parts or subassemblies.
The inventory systems we discussed thus far are for independent demand.

15. ABC Inventory Classification
The first step in managing inventory is to classify inventory based on its degree of importance in order to manage it properly.
ABC classification is based on Pareto’s Law , which states that a small percentage of items account for a large percentage of value.
Roughly 10% to 20% of inventory items account for 70% to 80% of inventory value. These highly valued items are classified as A inventory items.
Moderate value items account for approximately 30% of inventory items and contribute to roughly 35% of the total. They are called B items.
Approximately 50% of the items only contribute to roughly 10% of the total inventory value. These are called C items and are of least importance.
The most sophisticated inventory systems should be used for A items. By contrast C items are typically left for automated ordering systems.

16. Practical Considerations of EOQ
1. Lumpy demand: A more practical option is to use something called a periodic order quantity (POQ). If weekly demand is 120 units with an EOQ of 350 units. This means that EOQ covers an average of 350/120 = 2.9 weeks of demand. This rounds to an economic order period of three weeks. This is the POQ. We order three weeks of demand at a time.
2. EOQ Adjustments: Managers can increase or decrease the EOQ within reason to accommodate container size, truck loads, and various types of discounts.
3. Capacity Constraints: Ordering extra inventory to hedge against a price increase may result in unanticipated expenses if additional storage space is needed to be leased.

17. Measuring Inventory Performance
The most common metrics to measure inventory are: units, dollars, weeks of supply, and inventory turns.
The first two measures address the number of units available and the dollars tied up in inventory.
Weeks of supply = Average on hand inventory/Average weekly usage.
Inventory turnover = Cost of goods sold/ Average inventory value

18. Vendor Managed Inventory (VMI)
With vendor managed inventory (VMI) the vendor is responsible for managing the inventory located at the customer’s facility.
The vendor stocks the inventory, places replenishment orders, and arranges the display.
The vendor typically owns the inventory until it is purchased by the customer.

19. Summary Inventory is quantities of goods in stock.
Inventory policy addresses the basic question of when and how much to order.
Reasons for Carrying Inventory: 1. Protect Against Lead Time Demand. 2. Maintain Independence of Operations. 3. Balance Supply and Demand. 4. Buffer Uncertainty. 5. Economic Purchase Orders.
Types of Inventory: 1. Cycle Stock. 2. Safety Stock. 3. Anticipation Inventory. 4. Pipeline Inventor. 5. Maintenance, Repair and Operating Items (MRO).
Inventory Costs: 1. Holding Cost. 2. Ordering Cost. 3. Shortage Costs.
Every inventory system must answer two questions: when to order and how much to order.
Fixed Order Quantity Systems: The quantity that is ordered with this system is constant or fixed. An order is placed when the inventory point drops to a predetermined level, noted as the reorder point (ROP).
Fixed Time Period System: here the inventory levels are checked in fixed time periods, T, and the quantity that is ordered varies.
The objective is to pick an order quantity that minimizes the sum of both the holding and ordering cost, which is the minimum point on the total cost curve. This is the best or optimal order quantity Q opt = EOQ = √(2DS)/H where Q opt = EOQ = Economic Order Quantity; D = Annual demand; S = Ordering cost; and H = Holding cost.
Reorder Point ROP = demand during lead time = d L where d = demand rate and L = lead time
The target inventory level needs to be large enough to cover three types of demand: 1. Demand during the length of lead time L. 2. Demand during the length of the review period T. 3. Safety stock, SS, to guard against uncertainty.
Independent demand is demand for a finished product, such as a computer or a bicycle.
Dependent demand is demand for component parts or subassemblies.
ABC classification is based on Pareto’s Law , which states that a small percentage of items account for a large percentage of value. Roughly 10% to 20% of inventory items account for 70% to 80% of inventory value. These highly valued items are classified as A inventory items. Moderate value items account for approximately 30% of inventory items and contribute to roughly 35% of the total. They are called B items. Approximately 50% of the items only contribute to roughly 10% of the total inventory value. These are called C items and are of least importance.
With vendor managed inventory (VMI) the vendor is responsible for managing the inventory located at the customer’s facility.

20. Home Work 1. Name 5 reasons for carrying excess inventory.
2. What are the two questions inventory systems must answer?
3. What is the objective of picking an order quantity?
4. What are the 3 types of demand that a target inventory level needs to cover?
5. Explain the ABC classification system of inventory items.