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Materials for Lecture 19

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- Topics for this lecture
- 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

- 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

- 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

- 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

- 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

- 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

Inventory Management Model

- The model would have 40 to 50 weeks so the startup conditions do not dictate the results for the inventory management rule being analyzed

- 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

- Scenario reorder points of: 50, 60, 70, 80, 90

- 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

- 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

- 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

High Demand

- A startup business faces decision to expansion has four options to consider

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

P(High) = .25

- Assign probabilities to each decision point and PDFs of net returns for each choice

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

- 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

- Price projections for ag. commodities
- USDA Domestic Baseline at
- http://www.ers.usda.gov/publications/oce071/

- FAPRI- Missouri Domestic Baseline at
- http://www.fapri.missouri.edu/

- FAPRI- Iowa State International Baseline at
- http://www.fapri.iastate.edu/

- USDA Domestic Baseline at
- Projection of Annual Inflation rates
- AFPC Baseline Working Paper
- http://www.afpc.tamu.edu/pubs/

- 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

- National, State and County level Data
- USDA-ERS at
- http://www.ers.usda.gov/Browse/FarmEconomy/
- Provides data for costs of production, commodity outlook

- USDA-NASS
- http://www.nass.usda.gov/
- Data for crops and plants, livestock and animals
- Planted and harvested acres
- Yield and production

- State and national season average prices for ag commodities

- USDA-ERS at
- This is where you get the historical data behind the FAPRI Baseline forecasts, used to estimate the parameters for stochastic variables

- Data at the farm level
- http://www.ers.usda.gov/Browse/FarmPracticesManagement/
- 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

- 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

- 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

- 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

- 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

- 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 www.simetar.com

- If you do not have Simetar, you can use @Risk
=NORM() same as =RISKNORMAL()

=UNIFORM() same as =RISKUNIFORM()