Methods for Forecasting Seasonal Items With Intermittent Demand Chris Harvey University of Portland.

Slides:

Advertisements

Similar presentations

Data Analysis Class 4: Probability distributions and densities.

Advertisements

Chapter 3 Some Special Distributions Math 6203 Fall 2009 Instructor: Ayona Chatterjee.

Discrete Uniform Distribution

1 Methods of Experimental Particle Physics Alexei Safonov Lecture #21.

Sample size optimization in BA and BE trials using a Bayesian decision theoretic framework Paul Meyvisch – An Vandebosch BAYES London 13 June 2014.

Chapter 1 Probability Theory (i) : One Random Variable

Binomial Random Variables. Binomial experiment A sequence of n trials (called Bernoulli trials), each of which results in either a “success” or a “failure”.

CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Moments and transforms of special distributions (Sec ,4.5.3,4.5.4,4.5.5,4.5.6)

Estimation of parameters. Maximum likelihood What has happened was most likely.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference (Sec. )

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference.

A random variable that has the following pmf is said to be a binomial random variable with parameters n, p The Binomial random variable.

Statistical analysis and modeling of neural data Lecture 4 Bijan Pesaran 17 Sept, 2007.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Special discrete distributions Sec

Stat 321- Day 13. Last Time – Binomial vs. Negative Binomial Binomial random variable P(X=x)=C(n,x)p x (1-p) n-x  X = number of successes in n independent.

Review of important distributions Another randomized algorithm

Discrete Probability Distributions

A Review of Probability Models

Discrete Probability Distributions

LECTURE 14 SIMULATION AND MODELING Md. Tanvir Al Amin, Lecturer, Dept. of CSE, BUET CSE 411.

Likelihood probability of observing the data given a model with certain parameters Maximum Likelihood Estimation (MLE) –find the parameter combination.

Chapter 5 Statistical Models in Simulation

Modeling and Simulation CS 313

The Negative Binomial Distribution An experiment is called a negative binomial experiment if it satisfies the following conditions: 1.The experiment of.

Inventory Guru Introduction

Random Variables. A random variable X is a real valued function defined on the sample space, X : S  R. The set { s  S : X ( s )  [ a, b ] is an event}.

1 The Base Stock Model. 2 Assumptions  Demand occurs continuously over time  Times between consecutive orders are stochastic but independent and identically.

Week 21 Conditional Probability Idea – have performed a chance experiment but don’t know the outcome (ω), but have some partial information (event A) about.

1 Managing Flow Variability: Safety Inventory Operations Management Session 23: Newsvendor Model.

Mixture of Gaussians This is a probability distribution for random variables or N-D vectors such as… –intensity of an object in a gray scale image –color.

Methodology Solving problems with known distributions 1.

Probability Refresher COMP5416 Advanced Network Technologies.

8.2 The Geometric Distribution. Definition: “The Geometric Setting” : Definition: “The Geometric Setting” : A situation is said to be a “GEOMETRIC SETTING”,

Exam 2: Rules Section 2.1 Bring a cheat sheet. One page 2 sides. Bring a calculator. Bring your book to use the tables in the back.

4.3 More Discrete Probability Distributions NOTES Coach Bridges.

Random Variables Example:

1 Optimizing Decisions over the Long-term in the Presence of Uncertain Response Edward Kambour.

Ch 2. Probability Distributions (1/2) Pattern Recognition and Machine Learning, C. M. Bishop, Summarized by Joo-kyung Kim Biointelligence Laboratory,

Probability Generating Functions Suppose a RV X can take on values in the set of non-negative integers: {0, 1, 2, …}. Definition: The probability generating.

Recoverable Service Parts Inventory Problems -Ibrahim Mohammed IE 2079.

AP Statistics Chapter 8 Section 2. If you want to know the number of successes in a fixed number of trials, then we have a binomial setting. If you want.

Bayesian Estimation and Confidence Intervals Lecture XXII.

Normal Vector. The vector Normal Vector Definition is a normal vector to the plane, that is to say, perpendicular to the plane. If P(x0, y0, z0) is a.

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

Ch3.5 Hypergeometric Distribution

Math 4030 – 4a More Discrete Distributions

Bayesian Estimation and Confidence Intervals

Random Variables and Their Distributions

Random variables (r.v.) Random variable

Discrete Probability Distributions

The Impact of Replacement Granularity on Video Caching

Traffic Simulator Calibration

Production Scheduling: Mel’s Burger Bar

The Bernoulli distribution

Chapter 5 Statistical Models in Simulation

Maximum Likelihood Find the parameters of a model that best fit the data… Forms the foundation of Bayesian inference Slide 1.

Probability & Statistics Probability Theory Mathematical Probability Models Event Relationships Distributions of Random Variables Continuous Random.

Some Discrete Probability Distributions

Statistical NLP: Lecture 4

Chernoff bounds The Chernoff bound for a random variable X is

HKN ECE 313 Exam 1 Review Session

Useful Discrete Random Variable

L16 Cost Functions.

8.2 The Geometric Distribution

L16 Cost Functions.

Each Distribution for Random Variables Has:

Geometric Poisson Negative Binomial Gamma

Geometric Distribution

IE 360: Design and Control of Industrial Systems I

Presentation transcript:

Methods for Forecasting Seasonal Items With Intermittent Demand Chris Harvey University of Portland

Overview What are seasonal items? Assumptions The (π,p,P) policy Software Architecture Simulation Results Further work

Seasonal Items Many items are not demanded year round – Christmas ornaments – Flip flop sandals Demand is sporadic – Intermittent Evaluate policies that minimize overstock, while maximizing the ability to meet demand.

Demand Quantity of a Representative Seasonal Item

Assumptions Time till demand event is r.v. T, has Geometric distribution – T ~ Geometric(p i ) where p i = Pr(demand event in season) – T ~ Geometric(p o ) where p o = Pr(demand out of season) Geometric distribution defined for n = 0,1,2,3… where r.v. X is defined as the number (n) of Bernoulli trials until a success. pmf

Assumptions Size of demand event is r.v. D, has a shifted Poisson distribution – D ~ Poisson( λ i )+1 where λ i + 1 = E(demand size in season) – D ~ Poisson( λ o )+1 where λ o +1 = E(demand out of season) Poisson distribution defined as Where r.v. X is number of successes (n) in a time period. Pmf

Histogram and Distribution Fitting of Non-Zero Demand Quantities

The (π, p, P) policy Order When Order Quantity

New Simulation Structure Organization – Modular – Interchangeable – Bottom up debugging Global Data Structure – Very fast runtime – [[lists]] nested in [lists] Lists may contain many types: vectors, strings, floats, functions… Main simulation: Data structure aware Main simulation: Data structure aware Director for Each Method: Data Structure ignorant Director for Each Method: Data Structure ignorant Generic Function definitions Generic call args Generic return args Specific call args Specifc return args

Performance

P p ROII for π =.9

Future Work Bayesian Updating – Geometric and Poisson parameters are not fixed – Parameters have a probability distribution based on observed data – Parameters are continuously updated with new information Modular nature of new simulation allows fast testing of new updating methods

Giving Thanks Dr. Meike Niederhausen Dr. Gary Mitchell R