Group Paper One
In this paper your group analyzes an industry of your choosing and identify some problems
worth solving in it. It is a precursor to the second group paper in which you will propose a
potential solution. The second paper will be much e
TERMS FOR PRIVATE PLACEMENT OF SERIES SEED PREFERRED STOCK OF
[Insert Company Name], INC.
[Date]
The following is a summary of the principal terms with respect to the proposed Series Seed Preferred
Stock financing of [_], Inc., a [Delaware] corporation (t
Today
MVP
Personas & User Stories
Lean
Specifying the product
Product Problems
What to make?
How to make it?
Is it good?
How to improve it?
Minimum Viable Product
What is the least amount of time and money you can
spend on the product to start learning?
M
Equity
Ownership of C-corporations is in the form of Shares
A corporation can have pretty much any number of
shares
Corporations can generally create and sell new shares
(primary offering) or other owners can sell their shares
(secondary offering)
Ownersh
Today
Venture capital
What they look for
How they invest
What they do
What VCs Look For
Very large markets
Scalability
Near-term commercial viability
VC Math
$10
$100
$500
$10
$80
$400
$10
$60
$240
$10
$40
$160
$10
$30
$120
$10
$20
$100
$10
$50
$10
$10
$5
Today
Financial Models
The Corporate Structure and equity
Financial Model
Shows progression over time
Used for cash planning and seeing trends
Widget Business
Why Corporations?
Limited liability
Unlimited life
Partial ownership
Equity
Ownership of C-corpo
Simulation
Lecture 21:
Statistical Validation Techniques (Goodness of Fit)
Introduction
We will test if empirical observations agree with out model distribution
Goodness of Fit tests
Discrete and Continuous Distribution cases
Model distribution parameters
Simulation
Lecture 22:
Statistical Validation Techniques (Goodness of Fit: Unknown Parameters)
Discrete RV
We know the type of distribution (e.g. Poisson) but parameter such as
rate or mean are unknown.
Example: can daily # of accidents be fit by a Poiss
Simulation
Lecture 19:
Variance Reduction Techniques (Post Stratification)
Introduction
Need to estimate []
Introduce control variable with known distribution
Proportional sampling uses n( = ) observations for each strata
We can do post-stratifying instea
The Moment Generating Function of a Normal RV
Suppose that X is normally distributed with a mean of and a variance of 2 . Show that
1 2 2
M (t) := E[etX ] = et+ 2 t .
Solution
Work directly with the denstiy and follow the algebra/calculus:
Z +
Z +
2
2
1
1
Simulation
Lecture 20:
Variance Reduction Techniques (Importance Sampling)
Introduction
Importance sampling is a technique of transforming original
distribution into a different one
Importance sampling changes the probability measure
We aim to reduce the
Tanker Scheduling
Ships have:
capacity
draught (minimum depth to float)
range of speeds and fuel consumption
location and available time
Ports have:
weight limits
draught
other physical restrications
government restrictions
Tanker Scheduling (cont
Stochastic Scheduling
Models Real World Uncertainty
processing times
arrivals
machine availability
.
Our Model:
Distribution over job data known in advance.
Realization only known when job arrives/completes or when it can be
inferred.
Example:
pj =
This Class
Very brief intro to Lean
Customer Development
Eectuation
In a sense there's just one mistake that kills
startups: not making something users want. If you
make something users want, you'll probably be fine,
whatever else you do or don't do. And
Zipcar
Market Size
Top down:
0.04% of population
66 million people in top 20 markets
26,400 members @ ~$1000 contrib/member/year
$26.4 million contribution/year
Bottom up:
Contribution in Boston =$1.3 million
16 cities
$20.7 million contribution/year
Cust
Customer Discovery, Phase One : State Your Business Model Hypotheses
71
Market Size Hypothesis
Market Size Hypothesis (Physical and Web/Mobile)
Physical
Channel
Web/Mobile
Channel
This brief is an outlier-it doesn't directly map onto the business model ca
Group Paper Two
You have explored the competitive feasibility of an industry. Now its time to come
up with an idea and describe what your company will do and how it will do it.
You should do this paper as a group. It should be about 10 pages to 15
Lifetime Value
1. Present value
A dollar today is worth more to you than a dollar a year from now. If it werent, you
could borrow a dollar from someone with a promise to repay that dollar a year from
now,
Zipcar Customer Development Script
A. Figure out some basic stuff about who youre talking to
1.
2.
3.
4.
Where do you live? Do you have a spouse/partner? Do you have kids?
Do you need to drive for any reason?
Do you own a car? Do you share it with anyone
The Business Model Canvas
Key Partners
Key Activities
Designed for:
Designed by:
Value Propositions
Key Resources
Cost Structure
Customer Relationships
Date:
Version:
Customer Segments
Channels
Revenue Streams
This work is licensed under the Creative Comm
IEOR E4600 Applied Integer Programming
Optimizing using lp files in Gurobi
Raghav Singal
January 11, 2017
In this document, we will go over how to solve the examples (discussed in 0Examples.pdf)
using lp files in Gurobi. This is a 2-in-1 document in the s
35
5.2. EXACT METHODS FOR THE TSP
5.2.1. BRANCH AND BOUND METHODS
Branch & Bound methods are normally based on some relaxation of the ILP model of TSP. The
decision variables of the model are
xij =
1 if the cycle goes along arc i j
9 0 otherwise
In the fo
IEOR E4600 Applied Integer Programming
Setting up Gurobi on a MacBook
Raghav Singal
January 11, 2017
Perform the following steps to setup Gurobi:
1. Create an account at Gurobi (click here) using your Columbia email.
2. Click here, make sure you are signe
IEOR E4600 Applied Integer Programming
Setting up Gurobi on a Windows PC
Raghav Singal
January 11, 2017
Perform the following steps to setup Gurobi:
1. Create an account at Gurobi (click here) using your Columbia email.
2. Click here, make sure you are si
IEOR E4600 Applied Integer Programming
Optimizing using Python-Gurobi
Raghav Singal
January 12, 2017
In this document, we will go over how to solve the examples (discussed in
0Examples.pdf) using Python-Gurobi.
Before getting started, you should familiari
Department of Management Engineering / Operations Research
Department of Management Engineering / Operations Research
The Symmetric TSP
Branch and Bound for TSP
Using the 1-tree relaxation
Jesper Larsen and Jens Clausen
P
min
d x
P(i,j)E ij ij
x =2
i cfw
Cutting Planes
Goal: Add inequalities to an IP so that the convex hull of the feasible
points for the IP are described by the original inequalities of the IP plus
the added inequalities.
Want to find new inequalities quickly
Want the new inequalities to
Next: Branch and Bound Up: Relaxations Previous: One-Tree Relaxation
Assignment Relaxation
Our final relaxation is based on a completely different idea. We can arbitrarily orient a tour and talk in terms
of node j following node i. Clearly each node follo
IEOR E4600 Applied Integer Programming
HW6 solution
Raghav Singal
March 11, 2017
Problem 1
(i) On solving the LP with lower bound of zero and upper bound of one, we get the
optimal objective to be 5.1667. Hence, the lower bound on the IP objective is 5.16