Operation and Management Assignment 4
111340
lec_07_online.pptxOperations and Supply Chain Management
MGMT 3306
Lecture 07
Outline – Inventory Management
What is Inventory?
Why hold Inventory?
ABC Analysis
Common inventory control systems
Economic Order Quantity (EOQ) Model
Continuous Review Model
Periodic Review Model
Types of Inventories
Inventory can appear in many places in a Supply Chain, and in several forms:
Raw material inventory;
Work-In-Process (WIP) inventory
Maintenance/repair/operating (MRO)
Finished good inventory.
Why do we hold inventory?
To protect a firm from demand uncertainties
Customer demand is usually hard to predict. The uncertainty in customer demand may increase due to the short life cycle of a product and the existence of competing products in the market.
While it is relatively easy to estimate the size of a particular market, it is much more difficult to estimate the demand for individual competing products in the market.
Why do we hold inventory?
To cover the demand in lead times
Even if there is no uncertainty in demand or supply, which is quite unlikely, there is a need to hold inventory due to delivery lead times.
Economies of scale offered by suppliers or transportation companies
Many of the transportation providers try to encourage large-size shipment by offering all sorts of discounts to shippers. Shippers, therefore, have to hold large inventories to take advantage of the savings.
Why do we hold inventory?
To protect a firm from unexpected interruptions in supply due to factors such as custom delays, quality issues on the supplier’s side, natural disasters, and etc.
Key Issue: Although it is clear why inventory is held, holding the right amount at the right place at the right time is difficult.
Examples of Ineffective Practices
In 1993, Liz Claiborne experienced an unexpected earnings decline as a consequence of higher-than-expected excess inventories;
In 1994, IBM struggled with shortages in the ThinkPad line due to ineffective inventory management;
In 2001, Cisco took a $2.25 billion excess inventory charge due to declining sales.
ABC Analysis
Divides inventory into three classes based on annual dollar volume
Class A - high annual dollar volume
Class B - medium annual dollar volume
Class C - low annual dollar volume
Used to establish policies that focus on the few critical parts and not the many trivial ones
Example: ABC Analysis
| Item Stock Number | Percent of Number of Items Stocked | Annual Volume (units) | x | Unit Cost | = | Annual Dollar Volume | Percent of Annual Dollar Volume | Class | |
| #10286 | 20% | 1,000 | $ 90.00 | $ 90,000 | 38.8% | A | |||
| #11526 | 500 | 154.00 | 77,000 | 33.2% | A | ||||
| #12760 | 1,550 | 17.00 | 26,350 | 11.3% | B | ||||
| #10867 | 30% | 350 | 42.86 | 15,001 | 6.4% | B | |||
| #10500 | 1,000 | 12.50 | 12,500 | 5.4% | B |
72%
23%
Example: ABC Analysis (Cont.)
| Item Stock Number | Percent of Number of Items Stocked | Annual Volume (units) | x | Unit Cost | = | Annual Dollar Volume | Percent of Annual Dollar Volume | Class | |
| #12572 | 600 | $ 14.17 | $ 8,502 | 3.7% | C | ||||
| #14075 | 2,000 | .60 | 1,200 | .5% | C | ||||
| #01036 | 50% | 100 | 8.50 | 850 | .4% | C | |||
| #01307 | 1,200 | .42 | 504 | .2% | C | ||||
| #10572 | 250 | .60 | 150 | .1% | C | ||||
| 8,550 | $232,057 | 100.0% |
5%
Example: ABC Analysis (Cont.)
C Items
A Items
B Items
Percent of annual dollar usage
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | |
10 20 30 40 50 60 70 80 90 100
Percent of inventory items
Common Inventory Control Systems
Two questions to answer by designing an inventory control system:
How much to order?
When to order
To design an effective inventory control system, managers have to take many characteristics of a Supply Chain into consideration:
Level of Uncertainty in Customer Demand
Order Lead Time: the amount of time between when an order is placed and when the order is received.
Common Inventory Control Systems
Number of Different Products Being Considered
Objective of the company, whether it is to minimize the total cost or to maximize the service level.
In situations where customer demand is uncertain, it is often impossible to meet customer orders 100% of the time and managers have to decide on a particular service level.
Costs, including setup cost, purchasing cost, and inventory holding cost
Let’s start with the simplest situation…
Suppose (1) there is no uncertainty in demand and (2) order lead time is zero.
That is, demand is known ahead of the selling season. The minute you place an order, the minute you receive the order.
For effective inventory control in this overly simplified situation, Ford W. Harris introduced the Economic Lot Size model, or Economic Order Quantity (EOQ) model, in 1915.
The EOQ model illustrates the tradeoff between the setup cost and inventory holding cost.
EOQ Model
Three types of costs are considered in the EOQ model:
Purchasing cost per unit, that is, selling price, denoted as P
Setup cost, denoted as S
Inventory holding cost per unit per year, denoted as H
The objective is to minimize the sum of the three types of costs on an annual basis.
EOQ Model (Cont.)
Let D denote the annual demand and Q denote the order quantity. Then the total annual cost can be expressed as
Annual Purchasing Cost
Annual Setup cost
S is the fixed setup cost per order. And is the number of orders to place in a year if Q units are ordered each time.
Annual Inventory holding cost
The average inventory level is Q/2 since demand is constant and the minimum inventory level is 0 and the maximum is Q. The notation H is the inventory holding cost per unit per day.
EOQ Model (Cont.)
Using a little calculus, which won’t be discussed in this class , the order quantity that minimizes the total annual cost is
Note that:
The optimal order quantity, aka economic order quantity, increases as the setup cost K increases. That is, a larger order will be placed when it is expensive to place an order.
The optimal order quantity decreases as the inventory holding cost increases so as to reduce average inventory level.
Example: EOQ
Consider a hardware supply warehouse that is contractually obligated to deliver 50,000 units of a fastener to a local manufacturer in a year. Each time the warehouse places an order from its suppliers, an ordering and transportation fee of $20 is charged. The warehouse pays $1 per each fastener. Annual inventory holding cost is 25% of the unit inventory value, or $0.25 per year.
The warehouse manager would like to know how much to order each time when the inventory gets to zero.
Example: Solution
To summarize the information given in the example,
P
S
Therefore, using the formula for EOQ,
Now a more realistic situation…
You now have an idea of the inventory control model you can use when there is no uncertainty in demand and no order lead time.
But in reality, there is always some extent of demand uncertainty and it always takes time to deliver an order.
So what can we do?
We will then discuss two inventory control models that are used widely in practice, the continuous review model and the periodic review model.
Continuous Review Model
A continuous review model is sometimes called a (Q, R) model, where Q refers to the order quantity each time you place an order and R refers to the re-order level.
Under a continuous review model,
Inventory is reviewed continuously;
An order of Q units is placed whenever the inventory position reaches the re-order level of R units;
Demand is uncertain;
It takes time to deliver an order.
Continuous Review Model (Cont.)
Notation to be used later:
D: Annual demand
S: Setup cost
: Average daily/weekly demand
: Standard deviation of the average daily/weekly demand
L: Order lead time (in days or weeks)
H: Inventory holding cost per unit per year
: Service level, the probability of satisfying demand immediately
(1- α) : Probability of stock-out
More information about Standard deviation: http :// en.wikipedia.org/wiki/Standard_deviation
Continuous Review Model (Cont.)
Then the optimal order quantity and the re-order point can be expressed as:
, which is just the EOQ
The value of z is determined by the desired service level of α.
Average demand during the lead time
It is just average daily demand * lead time
Safety stock
This is the amount of inventory to hold to protect the firm against the demand uncertainty.
Value of z
Consider a standard normal distribution, the value of z is the number of standard deviations required to the right of the mean of the standard normal distribution to ensure a certain service
The shaded area refers to the service level of α. Suppose
The corresponding z = 1.65
Mean
Service level and z value
| Service level | Corresponding z |
| 90% | 1.29 |
| 91% | 1.34 |
| 92% | 1.41 |
| 93% | 1.48 |
| 94% | 1.56 |
| 95% | 1.65 |
| 96% | 1.75 |
| 97% | 1.88 |
| 98% | 2.05 |
| 99% | 2.33 |
| 99.9% | 3.08 |
Example: Continuous Review Model
Consider a distributor of TV sets that orders from a manufacturer and sells to retailers. The distributor decides to use a continuous review model to control inventory.
There is a fixed ordering cost of $4,500, independent of the order size. The cost of a TV set to the distributor is $250 and the annual inventory holding cost is about 18% of the product cost. The order lead time is about 2 weeks.
Suppose the demand follows a normal distribution and there are 50 weeks a year. The average weekly demand is 44 units and the standard deviation of the weekly demand is 32 units. The distributor wants to ensure a service level of 97%.
What is the optimal order quantity and the re-order level?
Example: Solution
To summarize the information given in the problem,
D = 44 units per week * 50 weeks = 2,200 units
S = $4,500
= 44 units per week
L = 2 weeks
H = 18% * unit product cost = 18% * $250 = $45
= 97%
Example: Solution
Then
units
That is, the distributor should order 663 units each time the inventory position reaches 173 units.
Periodic Review Model
It is sometimes called a Q model, where Q refers to the order quantity each time you place an order.
Referred to as Fixed-period in the textbook
Under a periodic review model,
Inventory is reviewed periodically, like once every r periods;
An order of Q units is placed when the inventory is reviewed;
Demand is uncertain;
It takes time to deliver an order.
Periodic Review Model (Cont.)
Since the inventory is reviewed once every r periods, all we need to decide is the order size when the inventory is reviewed.
Using the same notation as in the continuous review model,
where is the standard deviation of the demand over the review and lead time.
Safety Stock
Example: Periodic Review Model
Suppose you are given the following information and are required to design a periodic review model:
D = 2,200 units
S = $4,500
= 44 units per week
L = 2 weeks
H = $45 per unit per year
= 97%
r = 2 weeks
Example: Solution
Then, by using the formula, we can get
