operations management
jenny2000000
20_NewsvendorProblem.pptxClass 19 Managing Inventories: Newsvendor Problem
Instructor: Mani Lakshmanan
P300 Introduction to Operations Management
What is lean?
Operational processes can be described as being lean when they are very efficient and have few wasted resources.
Guiding Principles
Precisely specify value for each specific product
Identify the value stream for each product, eliminate waste
7 types of waste: overproduction, waiting, defects, etc
Make Value Flow without Interruptions
Inventory hides problems
Let the Customer Pull Value from the Producer
Pull system <-> production based on real demand but not forecast, Kanban scheduling
Pursue Perfection
Strategic Benefit of Lean Systems
Principle
Contribution Margin:
The difference between price and the firm’s direct costs (traced to specific product)
Fixed Cost:
Cost of facilities, equipment, capital, and support labor such as management and engineering
$
Production Quantity
Break-even
The amount a firms needs to sell in order to make profit
Break-even under lean production
OM Triangle
Capacity
Inventory
Variability
reduction
Capacity, inventory, and variability reduction (information) are substitute ways to satisfy customers’ demand for products/services.
Quality and Six Sigma, Chapter 6
House Building Game
Lean Operations and TPS, Chapter 8
Inventory Management: Newsvendor Problem
Chapter 7
Economic Order Quantity
Case V: Blanchard Importing and Distributing
Bear Game and Bullwhip effect
Outline
Definition
Roles of Inventory
Financial Impact of Inventory
A Single-Period Inventory Model: Newsvendor Problem
Definitions
Inventory is a supply of items held by a firm to meet demand
Inventory specific to manufacturing (items contributing or becoming a firm’s output):
Raw materials
Component parts
Work-in-Process inventory
Finished products
Inventory in all types of organizations:
MRO inventory (maintenance, repair, operating supplies)
MRO inventory: office supplies
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Roles of Inventory: 1. Balancing Supply and Demand
Batch production:
it is beneficial to produce batches of products before demand realizes.
Customers often expect products to be available at the time they decide to purchase
Seasonality of supply or demand:
Some products can only be produced at certain times of year, but have demand all year long (agriculture).
Customers may be interested in products only at certain time of year, but production runs all year.
Roles of Inventory: 2. Buffering Uncertainty in Demand or Supply
Variation in supply and demand are managed with buffer (safety) stock
Demand:
Typically, it is impossible to know exact future demand.
Supply:
How long until replenishments arrive
Roles of Inventory: 3. Enabling Economies of Buying
Demand: 1 unit per day, 100 days
What’s the cheapest way to buy finished products from a supplier to meet above demand?
Cost 1: Purchase payment
Quantity <50, $2 per unit
50<Quantity <100, $1.5 per unit
Quantity >=100, $1 per unit
Cost 2: Transportation, $100 per trip with quantity less than 200 units
Cost 3: Inventory cost
<--price discounts
<--economies of transportation
Roles of Inventory: 4. Enabling Geographic Specialization
Supply and demand locations vary
Demand for most products exists virtually everywhere.
Production locations are typically few, so larger quantities have to be produced, shipped, and stored.
Outline
Definition
Roles of Inventory
Financial Impact of Inventory
A Single-Period Inventory Model: Newsvendor Problem
Financial Impact of Inventory
Carrying (Holding) Costs
Opportunity cost (including cost of capital)
Storage and warehouse management cost
Taxes and insurance
Obsolescence, loss, spoilage, shrinkage
Material handling, tracking, and management cost
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Obsolescence, Ihpone 4
Spoilage: bread, fruit
Shrinkage, expensive eletronic units (computer processors)
Apple Inventories from Balance sheet
http://files.shareholder.com/downloads/AAPL/1719417363x0x536523/381559d7-04a1-40d5-8e2a-236e3f867158/AAPL%20Q1FY12%2010Q%2001.25.12.pdf
Either come from investment or debt, keep inventory as low as possible
Free up cash to invest in other assets, or reduce debt
Financial Impact of Inventory
Stockout Cost (Shortage cost)
Cost of lost sales or future sales
Expediting cost
Disruption of production (shortage of components on assembly line)
Ordering and Setup Cost
Purchasing items: costs incurred in placing and receiving orders
Making items: costs during change-overs between items
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Stock out
Supply chain disruption: flood/earthquake
Japan quake killing U.S. new car supply
http://www.cbsnews.com/video/watch/?id=7361499n
Outline
Definition
Roles of Inventory
Financial Impact of Inventory
A Single-Period Inventory Model: Newsvendor Problem
A Single-Period Inventory Model: Newsvendor Problem
O’Neill’s Hammer 3/2 wetsuit
15
Hammer 3/2 timeline
Determine an amount of products to stock before actual demand is known.
Products are ordered only one time, and have little value after the period is over
Marketing’s forecast for sales is about 3200 units.
16
Hammer 3/2 cost and revenue
O’Neill sells each suit for p = $190
O’Neill purchases each suit from its supplier for c = $110 per suit
Discounted suits sell for v = $90
This is also called the salvage value.
How many wetsuits should the company order?
“too much/too little problem”:
Order too much and inventory is left over at the end of the season
Order too little and sales are lost.
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“Too much” and “Too little” costs
Cos = cost of being overstocked
Cost of left over inventory.
Cos = cost of product + cost associated with disposing of the extra product – salvage value.
For the Hammer 3/2 Cos = Cost+0 – Salvage value = c+0 – v = 110 – 90 = 20
Cso = stockout cost
Cost of don’t have enough inventory
Cso = lost profit due to insufficient inventory + lost future sales + lost of customers’ good will
For the Hammer 3/2 Cso = lost profit = Price – Cost = p – c = 190 – 110 = 80
The goal is find the order quantity that minimizes the expected total cost of overstock and stockout
weighted average of all possible values
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Expected total cost of overstock and stockout
| Demand | Probability |
| 3000 | 30% |
| 3200 | 40% |
| 3500 | 30% |
O’Neill sells each suit for p = $190
O’Neill purchases each suit from its supplier for c = $110 per suit
Discounted suits sell for v = $90
If order quantity is 3300 units,
The expected total cost is
TC= 30%(3300-3000)
+40%(3300-3200)
+30%(3500-3300)
The expected total cost depends on order quantity
How many wetsuits should the company order?
The ratio Cso / (Cso + Cos) is called the critical ratio.
Choose order quantity, Q, such that the probability of satisfying all demand (i.e., demand is Q or lower) equals the critical ratio.
Let function be the c.d.f. of demand, the order quantity Q satisfies
c.d.f._Cumulative Distribution Function
Q
20
How many wetsuits should the company order?
For the Hammer 3/2 the critical ratio is (also known as TSL- Target Service Level
Demand follows a Normal distribution with mean and standard deviation
Choose Q such that the probability demand is Q or lower equals the critical ratio.
Q= 4185
c.d.f.
Excel function: =NORM.INV(0.8, 3192)
Excel Function NORMINV
NORMINV (p, mu, sigma) returns the value x such that, with probability p, a normal random variable with mean mu and standard deviation sigma takes on a value less than or equal to x.
How many wetsuits should the company order?
The critical ratio is 0.80.
Suppose the demand has
Find the critical ratio inside the Standard Normal Distribution Function Table:
If the critical ratio falls between two values in the table, choose the greater z-statistic … this is called the round-up rule.
Choose z = 0.845
Convert the z-statistic into an order quantity :
23
Newsvendor Model Solution Summary
Identify overstock cost and stockout cost
Find critical ratio
Find z by lookup the critical ratio inside the Standard Normal Distribution Function Table
Use mean and standard deviation of demand to find the order quantity,
Q=
Exercise
Suppose you open a kiosk at the mall every October to sell Halloween costumes.
For a skeleton costume, buy for $10 and sell for $30.
Any costumes not sold have to be disposed of because the design changes each year and customers will not purchase a previous year’s costume. Disposal and salvage costs are minimal and can be considered zero.
Demand for the skeleton costume follows normal distribution with mean 200 units and standard deviation 15 units.
What should be the order quantity?
Identify overstock cost and stockout cost
Cos = cost of product + cost associated with disposing of the extra product – salvage value = _____________
Cso = lost profit due to insufficient inventory + lost future sales + lost of customers’ good will =_________
Find critical ratio =_________
Find z by lookup the critical ratio inside the Standard Normal Distribution Function Table
z= ________
Use mean and standard deviation of demand to find the order quantity
Mean Standard deviation
Order quantity Q=
10
30-10 =20
2/3=0.66666..
Standard Normal Distribution Function Table
Identify overstock cost and stockout cost
Cos = cost of product + cost associated with disposing of the extra product – salvage value = _____________
Cso = lost profit due to insufficient inventory + lost future sales + lost of customers’ good will =_________
Find critical ratio =_________
Find z by lookup the critical ratio inside the Standard Normal Distribution Function Table
z= ________
Use mean and standard deviation of demand to find the order quantity
Mean Standard deviation
Order quantity Q=
10
30-10 =20
2/3=0.66666..
0.44
200
15
200+0.44*15=206.6,
rounded to 207
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Generate forecast
of demand and
submit an order
to TEC
Receive order
from TEC at the
end of the
month
Spring selling season
Left over
units are
discounted
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0.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549
0.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852
0.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.8133
0.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389
