1. Materials for Lecture 19 Topics for this lecture Read Chapter 14
Setting up an internet business
Inventory management models
Decision tree models
Data, where is it?
Read Chapter 14
Lecture 19 Inventory Management.XLSX
Lecture 19 Decision Tree.XLSX

2. Inventory Management & Data Sources
Inventory management is about
When to re-order
How much to order
Factors to consider
Cost of storage
Cost of placing an order
Cost of lost sales due to shortage
Stochastic demand
Delivery time from time order is placed
Can you backlog demand

3. Inventory Management
Simulate the inventory management problem as a stochastic problem
Simulate N periods to test impacts of alternative inventory management schemes
Period -- length of time for the problem – week, month
Based on the time period for the demand data
Also based on order/delivery time

4. Inventory Management Example of a weekly Inv. Management Problem
Cost to place an order $200
Cost of a unit purchased $4
Cost of storage for 1 week $3
Cost of each lost sale $10
Price of product sold $25
Weekly demand PDF ~ N(40,6)
2 week delivery time; could be stochastic
Beginning inventory 100
Inventory management rule to test:
Place order if inventory on hand <= 50 units
Amount to order = 150 – inventory on hand
KOV = average weekly profit, cost, inventory, revenue

5. Rules for Simulating Inventory
Demandt is stochastic
Beginning inventoryt = ending inventoryt-1
Supplyt = beginning inventoryt + quantity receivedt
Salest = Minimum (demandt or supplyt)
Ending Inventoryt = supplyt – salest
Quantity receivedt = quantity orderedt-n
if it takes “n” periods for the delivery
Lost salest = 0.0 If(supplyt > demandt) else Lost salest = demandt – supplyt

6. Calculating Inventory Costs
Purchase costst = cost per unit paid for product
Order costst = fixed cost to place an order (shipping costs, office expense, delivery processing costs, Fed Ex rush delivery fee, etc.)
Storage costst = cost per unit * beginning inventoryt
Penalty costst = cost to the business for lost sales or
lost salest * cost for perceived lost goodwill

7. Inventory Management Model
Week 1 2 3 4
Beginning inventory
100 60
Quantity Ordered
150
Quantity Received
Supply
Demand 40 70 30 50
Sales
Ending Inventory
Lost Sales 10
Costs
Storage
300
180
Order
200
Purchase
600
Penalty
TOTAL
280
1100
800
Revenue
900
1350
1125
Profit
1070
-1100
325
The model would have 40 to 50 weeks so the startup conditions do not dictate the results for the inventory management rule being analyzed

8. Inventory Management Scenarios
Reorder Point
Should firm reorder when inventory < 50?
Scenario 40, 50, 60, 70, 80, 90 for the reorder point
Order up to amount
Should firm reorder a larger amount
Scenario 140, 150, 160, 170, 190
Would it be more profitable to pay more (or less) to get the order delivered faster (slower)?
Pay $300/order to get delivery in 1 week
Pay $100/order to get delivery in 3 weeks
Each question is a PDF, use simulation to estimate the unknown PDF

9. Inventory Management.XLS
Scenario reorder points of: 50, 60, 70, 80, 90

10. Decision Trees
Many textbooks are available to discuss decision trees and their application to decision making
Decision trees are a simple way to organize decisions and outcomes
Decision trees do not use simulation
Decision trees could be used to construct simulation models
Outline for this section of the lecture
Demonstrate a simplified decision tree
Demonstrate its use for decision making
Demonstrate how a decision tree can be used to formulate a simulation model

11. Decision Tree Terminology
Box represents a decision
Circle denotes an outcome
Decision tree organizes decisions and outcomes
Stay in Houston 45% chance Die
Run
Stay in College Station 0% chance Die
Hurricane coming to Galveston
Stay and Die

12. Decision Tree for Business
A startup business faces decision to expand or exit
Franchise Business, rich beyond belief
Continue Development
Business Fails, dog dies, spouse leaves with an employee, you become a street person
Business breaks even for years, no big profits earned
Sell business

13. Decision Tree for Business
A startup business faces decision to expansion has four options to consider
High Demand
Moderate Demand
Franchise Business
Low Demand
Continue Development
Fails to take off
Franchise Business Fails
Business breaks even for years, no big profits earned
Sell business at a loss

14. Decision Tree to Simulation
Assign probabilities to each decision point and PDFs of net returns for each choice
P(High) = .25
P(Mod) = .30
Franchise Business
Invest $1million
P(Success) = 0.75
P(Low) = .40
Continue Development
P(Near Fail) =0.05
Start
Franchise Business Fails P(F) = .25
Business breaks even for years, no big profits earned P(breakeven) = 0.25
Sell business at a loss of 50% of the initial investment

15. Decision Model with Risk

16. Decision Model with Risk

17. Decision Model with Risk

18. Decision Model with Risk

19. Decision Trees Summary
Useful concept
Maybe most useful in structuring our thinking about the options and the probabilities for each possible outcome
When combined with a risk model it can add value to the simulation model results
Is applicable to branch type decisions

20. Data, Where Do You Find It?
Price projections for ag. commodities
USDA Domestic Baseline at
FAPRI- Missouri Domestic Baseline at
FAPRI- Iowa State International Baseline at
Projection of Annual Inflation rates
AFPC Baseline Working Paper
Definition of a Baseline
Continue the current policies for 10 years
Assume average weather
Simulate demand and supply forces for 10 years using econometric models
Baselines are great source for point forecasts to use as your means

21. Data, Where Do You Find It?
National, State and County level Data
USDA-ERS at
Provides data for costs of production, commodity outlook
USDA-NASS
Data for crops and plants, livestock and animals
Planted and harvested acres
Yield and production
State and national season average prices for ag commodities
This is where you get the historical data behind the FAPRI Baseline forecasts, used to estimate the parameters for stochastic variables

22. Data, Where Do You Find It?
Data at the farm level
NASS surveys farmers and ERS tabulates the surveys, interactive web forms allow you to query the survey data base to calculate averages for questions asked in the surveys
Survey farmers yourself
That is what AFPC does and it works, its just costly
This is where we get historical production data and local prices so we can make the local wedges

23. Data, Where Do You Find It?
More about farmers production data
You must use actual yield data at the farm level to reflect the producer’s actual risk
Farmer yield data has more risk than county or state data because the latter is averaged over all farms in the region
If you must use county yield data, at least increase relative risk to account for difference
Use an EMP distribution with an Expansion factor
Ỹt = Ŷt *(1+(EMP(Si , F(Si)) * Et)
where Et is a fraction such as 1.3 to increase the relative risk 30%, and
Si is a fraction of mean or trend

24. Data, Where Do You Find It?
Some data series you have to purchase because it is cost effective or proprietary
Examples of data that can be purchased:
Weekly prices for grain in foreign countries
Monthly ethanol prices
Monthly ocean freight rates for shipping grain
Daily futures and options prices
Daily prices for stocks and mutual funds
Where do you find data that is for sale?
Look for trade publications that report weekly or monthly prices or quantities
They usually offer to sell the historical data

25. Data, Where Do You Find It?
Data for unobserved variables
Yields for a farm you want to buy may not be available, and it they are your yield will likely be higher
Yields for a crop that has never been grown
Only have experiment station test plot yields
Demand for a product that does not exist
But there is one like it
Customer acceptance for a new product
Life cycle of the introduction adoption of a new seed
Interview experts and simulate different aspects of the business based on their knowledge
Rely on best guess parameters for simple distributions such as Uniform or GRKS

26. Summary of AGEC 622 Linear programming – what ought to be
Probabilistic forecasting – capabilities of forecasting with multiple regression, exponential smoothing, seasonal analysis, and time series analysis
Monte Carlo simulation – what could be ….
Frame your problem in a systems framework
Model design and development
Parameter estimation for stochastic variables and deterministic component of a forecast
Validate simulated variables
Univariate and MV distributions
Apply these tools for business decision making using stochastic efficiency

27. What can you take to the job?
Improved Excel skills
Applied econometrics
Ability to organize & build a business model
Make any business model a risk analysis tool
Rank risky alternatives
Deterministic and probabilistic forecasting
Simetar
Available as long as you are a fulltime student
After you graduate, buy it at
If you do not have Simetar, you can
=NORM() same as =RISKNORMAL()
=UNIFORM() same as =RISKUNIFORM()