MS&E 121

Introduction to Stochastic Modeling

General Information

This is a fast-paced course that is intended to help students develop an understanding of the basic principles underlying how one can approach management science problems in which uncertainty plays a major role. Students should leave the course with the ability to formulate and analyze stochastic models, and interpret the results of their analysis.

After taking this course, you should:

· Understand the role of statistics and probability in answering a range of questions that arise in the management science setting, and to be an educated consumer of these methodologies

· Have a basic understanding of Markov chain modeling, including the ability to formulate such models, compute various performance measures either analytically or numerically, and interpret the solutions.

Course Description (Stanford Bulletin)

Stochastic processes and models in operations research. Discrete and continuous time parameter Markov chains. Queuing theory, inventory theory, simulation. Prerequisite: MS&E 120 or Statistics 116.

Course Topics

Review of Basic Probability and Statistics Concepts using Problem-based Focus

Applications from: Health, Environment, Finance, Risk Assessment, Insurance

Managing Inventory

Newsvendor model for perishable inventory

Inventory systems with carry-over

"Exploitation" vs "exploration"

Modeling Evolution of Uncertainty over Time (Markov Chains)

Applications from: Queueing, biology, internet search, finance, physics

Formulation

Connection of Markov chain theory to linear algebra

First-step analysis

Equilibrium calculations

Dynamic programming

Managing Congestion and Capacity
Motivation
The Poisson Process
The M/M/1 Queue (M/M/s; M/M/infinity)
The M/G/1 Queue
Superposition Theorem
Modeling abandonment and balking
Customer vs System Performance Measures
Little's Law
Networks of Queues (Open and Closed)
Kingman's Approximation for G/G/s Queues

Financial Forecasting
Prediction
Linear regression
Autoregressive modeling
In-sample vs out-of-sample testing

Pitfalls of statistical modeling

Prerequisites

Students should have a working knowledge of calculus at the level of Math 51, including differentiation and integration of functions of a single variable. Students are also expected to have had previous exposure to basic probability (at the level of either MS&E 120 or Stat 116). Exposure to matrix notation and basic linear algebra is also important.

Remark: Please see the Assignments section of the website to find a "pre-quiz" that you should take before starting MS&E 121. This "pre-quiz" is worth 0 points, and is intended only to help students assess skills in which they may have become "rusty". Also, you can find the topics you should know entering MS&E 121 is available here.

Contact Information
Instructor

Peter Glynn

Huang Engineering Center, Room 326

Tel: 650-725-0554

Email: glynn@stanford.edu

Note: If you wish to see Professor Glynn outside of his regularly scheduled office hours, please email him directly to set up a time.

Teaching Assistants

Mohammad Mousavi	mousavi@stanford.edu
Danielle Davidian	davidian@stanford.edu
Riley Matthews	rileym1@stanford.edu

Lectures, Problem Sessions and Office hours

Lectures:

Tuesday	1:30 PM - 3:05 PM	Location: Hewlett Teaching Center 200
Thursday	1:30 PM - 3:05 PM	Location: Hewlett Teaching Center 200

There is no formal requirement to attend the lectures. However, attendance will give you the opportunity to hear the instructor’s perspective on the material. In addition, students are responsible for everything that is covered in class.

Problem Sessions:

Thursday

5:00PM -6:00PM

Location: Hewlett 102

Office Hours:

Professor Glynn:

Monday	1:30 to 2:30 PM	Location: HEC 326
Wednesday	3 PM to 4 PM	Location: HEC 326

Riley

Monday

4:00 PM to 6:00 PM

Location: Huang 203

Friday

3:00 PM to 5:00 PM

Location: Huang 203

Mohammad

Sunday

4:00 to 6:00 PM

Location: Huang 203

Tuesday

11 AM to 1 PM

Location: Huang B007

Danielle

Monday

10 Am to 12 PM

Location: Huang 203

Course Website

We will make frequent use of our coursework website, so please register and choose a section at http://coursework.stanford.edu as soon as possible. All problem sets, answer keys and handouts will be available on coursework.

Recommended Text

A useful resource for this course is the text by Sheldon M. Ross, Introduction to Probability Models, Academic Press, 2010 (10th Edition). This book is especially good at reinforcing the mechanics of how to do probability calculations, and includes lots of problems that focus on this aspect of the course.

Software Requirements

Every student is expected to have access to Matlab (This access can be through clusters on campus or by acquiring a student version of the software. Please see http://www.stanford.edu/class/msande121/matlab.html). This software is widely used, both at Stanford, and by many industrial users of stochastic modeling techniques.

Homework

Solving problems is the best way to learn this material and prepare for the examination and take home assignments. The assignments will be due on: Tuesdays, by 5 PM.

The assignment grade will be based on your best five assignments (so your lowest assignment grade will be dropped). Come see us, early and often, if you have questions. It is important to keep up and we cannot help you unless you help yourself first. We would prefer you stay current and not fall behind. Therefore, we will penalize late homeworks –homeworks submitted upto 2 days late will get 20% less credit per day of lateness, and no homeworks will be accepted more than 2 days late (i.e. after 5pm on Thursdays).

You are welcome to work with others to master the principles and approaches used to solve homework problems. However, the work that you turn in should be your own. In the spirit of academic integrity and the Honor Code, you must acknowledge all of the people and materials you have consulted, including course staff and handouts, in preparing your solution sets. Note that using solutions, in any manner, to assignments given in previous years to prepare solutions for current assignments is a violation of the student Honor Code for this course

Examinations

There will be two take-home midterm examinations and one in class final exam. Midterm 1 will take place over the weekend of January 26-27, and Midterm 2 over the weekend of February 23-24.

The final exam will be on Thursday, March 21, 2013 at 7:00 p.m. to 10 p.m.

Please note: All students are responsible for ensuring that they can attend the regularly scheduled final exam. If a student is unable to make the regularly scheduled time for the final exam, a student (with the prior permission of the teaching staff) may write the final exam in an alternate time (9 AM to noon on Friday, March 22). If unusual circumstances are present that preclude writing the final exam in either the regular or alternate time slots, you should let the teaching staff know immediately.

The Honor Code places the responsibility for ensuring honest behavior on the students rather than the course staff, and violations should not be tolerated. The midterm and final examinations are strictly individual work and you are not permitted to consult on them with others. You can consult with others on the homework assignments but you must acknowledge their assistance. Please contact the teaching staff if you have any questions about the Honor Code or the requirements for any assignment or exam.

Please contact the teaching staff if you have any questions about the Honor Code or the requirements for any assignment.

Grading

The course grade will be based on six homework assignments, two take home midterm examinations, and a final examination, with the following weights and with borderline decisions affected by class participation:

· 20%: Homework

· 40%: Two Take Home Midterm Examinations

· 40%: Final Examination