Ananalysisof
The Bad Systems
Engineering
ofo Bikeshare
System
LingheZheng
UVA
ItsacaseofBadSystemEngineering,
because:
1.LackoftheWholeCitySystem
thinking.
Bikeswereusedtosolvethe
trafficproblem,butactually,theycan
onlybeusedforashortdistanceand
itsmuchs
SYS 6005  Homework Assignment 1
Due 5 September 2017
Reading
Chapter 1
All starred Problems (and Solutions) at the end of Chapter 1.
Study Problems: 14, 17, 20, 27, 31, 34 (Solutions are available on the SYS 6005 Collab site.)
Problems to Turn In
Inst
SIE6003 Linghe Zheng 09.18.2017
On my honor as a student, I have neither given nor received aid on this assignment/examination.
Linghe Zheng
1. (15 points) Show that a set is convex if and only if its intersection with any line
is convex.
Answer: First, l
Pictureretrievedfrom:http:/www.vanguardia.com.mx/articulo/uberlanzanuevosistemadepropinasen3ciudadesdeeu
LingheZheng
Uber Good
Choices
A young lady (in her early thirties) would like
to drive parttime for Uber; unfortunately,
she does not have a vehicle
SIE6003 Linghe Zheng 09.18.2017
On my honor as a student, I have neither given nor received aid on this assignment/examination.
Linghe Zheng
1. (10 points) Suppose f : R R is convex, and a, b dom f with a < b.
a) Show that
f (x)
b x
x a
f (a) +
f (b)
ba
Picture Retrieved
from
AliExpress.com
Vendor_Problem
SIE 6001
Linghe Zheng
09.19.2017
Calculate the
Expectations
Calculate the Profits
If sell by vendors,
Stencil 7500 Tshirts are recommended.
Produc
t Tshirts
Cost
($)
Sell/per
Tshirt
($)
1000 3212
0
5
ha s
g iNeBt
e
Ph lit(P
@ a
s a m le
oo
oo
l
u r c o e s
w e ct
)o s

2
b IA
4i924
p
)
d tA*octlr
) LM?
6
=
0
y n

=
x cx )
x
TdIQO&I
s $c [p a
1Pa
3 g

p (>
(
o
+ p cx
=

D
> ptl)
L f
(\ +
u
p
x 3

Tx Q P C )

3 )
W
S
X
'"
.
d
=
0
.
3
+
Surfs Up
Buying a vacation condominium in the Outer Banks
SIE6001
Linghe Zheng
Executive summary
Lease
The lease prices
changes with
seasons, but
normally a
house near the
sea can be
Leased for
$2666.7/month.
Mortgage
Repayment
$1951.775/mont
h (Loan)
+
Thus, the observation of a white cow makes the hypothesis all cows are white more
likely to be true.
Solution to Problem 1.27. Since Bob tosses one more coin that Alice, it is imu
possible that they toss both the same number of heads and the same number o
The event A ["1 B can be written as the union of two disjoint events as follows:
AHB=4AanCMAanU
so that
Pcfw_AHB=Pcfw_AHBHC]+P[AHBHCE. cfw_2]
Similarly,
P[AFIC=P(AHBHC]+Pcfw_AHHCHC]. (3]
Combining Eqs. (1)43), we obtain the desired result.
Solution to Pro
Let E (or E or E be the event that A cfw_or B or C, respectively) occurs and you first
select the envelope containing the larger amount . Let g (or E or Q) be the event
that A [or B or C, respectively) occurs and you rst select the envelope containing the
Solution to Problem 1.31. cfw_a Let A be the event that a [l is transmitted. Using
the total probability theorem, the desired probability is
Penn an + (1 Franc E11=a1 ea + (1 p1cfw_1 El)
cfw_b By independence, the probability that the string lll is recei
The term ptupd cortesponds to the win~draw outcome, the term pw ppw corre
sponds to the winulosenwin outcome, and the term cfw_1 pw p, corresponds to losenwinu
win outcome.
cfw_b If pm *5: 1,12, Boris has a greater probability of losing rather than winni
as likely if we know that B has occurred than if we know that C has occurred. Alices
reasoning corresponds to the special case where C = A U B.
Solution to Problemi 1.16. In this problem, there is a tendency to reason that since
the opposite face is eithe
and
AEHH=cfw_2, AEFIB:cfw_4,E, AHB=cfw_5.
Thus, the equality of part cfw_b is veried.
Solution to Problem 1.5. Let G and C be the events that the chosen student is
a genius and a chocolate lover, respectively. We have P09] : cfw_1.6, Pcfw_C] = DEF, and
P0
CHAPTER 1
Solution to Problem 1.1. We have
A:cfw_2,4,E, B=cfw_4,5,,
so A UB :cfw_2,1,5,, and
cfw_ALISE = cfw_1,3.
on the other hand,
A sec 2 cfw_1,3,3r1 cfw_1,2,3 2 cfw_1,3.
Similarly, we have A n B = cfw_4, 3, and
cfw_A r1 .3) = cfw_1, 2,3, 5.
on the oth
Figure 1.1: Sequential descriptions of the chess match histories under strategies
[1], (ii), and cfw_iii.
for e drew. In the case of e tied 1&1 score, we go to sudden death in the next game,
and Boris wins the match [prbbitf pm), or loses the match (proba
theorem. We have
1 1
Frimm g ' E 'Pn1.1cfw_3l=
n. 1 1 2 2
Fn1,1(3] pn,u[2) + 2 n  E pn1.1[2 + E  H 'Pna):
1 1
Pa 0(21 g ' E 'PnI 1(1):
n 1 1
pn1,1(2] 1T ' E 'Pnmil]:
1 1
Ian2.21:2] L ' Finlull:
'11.
fin1.1]: 1
Combining these equations, we obtain
SYS 6043 Applied Optimization
Day 2
Breakout #2
Problem 1:
Acme Manufacturing produces two primary types of products, anvils and cages. Anvils
come in several different shapes and sizes, but all share the characteristics of being
compact and heavy (in fac
SYS 6043 Applied Optimization
Day 2
Homework #2
Due at the start of Day 3
.
Problem 1 [Individual]
Use the BellmanFord algorithm to find the solution to find the shortest path distance
from s to t in the problem in Figure 1.
a. Show the progress of your
Directions on Loading RelaxIV into Excel
Before continuing: Make sure you have downloaded and extracted the RelaxIV zip
file you can find in the materials section on Toolkit
Method I:
1. In the extracted folder you will find a file called RelaxIV_interfac
SYS 6043 Applied Optimization
Day 2
Breakout #1
Problem 1:
Consider the shortest path problem illustrated below.
A. Compute the shortest path distances and associated shortest st path using
Dijkstras method. Write down the value of all distance labels at
Surname 1
Name
Instructor
Course
Date
Challenger and Columbia Accidents Analysis
The Challenger and the Columbia disasters are the two major tragedies in the history the
Space Shuttle Program. They posed a great challenge to the National Aeronautics and S
GLM 3
1/ 21
A. A. Flower
Agenda
Review
Generalized Linear Models 3
Model Tests
Diagnostics
Model
Selection
Abigail A. Flower
Department of Systems and Information Engineering
University of Virginia
Charlottesville, VA 22904
SYS 4021 Linear Statistical Mod
MLR5
1/ 30
L. Barnes
Review
ANCOVA
PC
Regression
Lecture 10: Multiple Linear Regression
ANCOVA and PC Regression
Overview
Laura Barnes
Department of Systems and Information Engineering
University of Virginia
Charlottesville, VA 22904
SYS 4021 Linear Stat
SYS 6003: Optimization
Fall 2016
Lecture 10
Date: Sep 26th
Instructor: Quanquan Gu
In the following, we will introduce another convexity preserving operation: composition
with scalar function.
Theorem 1 Let g : Rd R and h : R R, define f (x) = h(g(x), whe
SYS 6003: Optimization
Fall 2016
Lecture 14
Date: Oct 12th
Instructor: Quanquan Gu
Last time we introduced a class of functions which has Lipschitz continuous gradient,
and its property.
Lemma 1 Let a function f has LLipschitz continuous gradient over do
SYS 6003: Optimization
Fall 2016
Lecture 26
Date: Dec 5th
Instructor: Quanquan Gu
We continue providing examples for duality.
Example 1 (Standard Linear Programming)
min c> x
subject to
x
Ax = b, x 0.
Lagrangian function:
L(x, , ) = c> x + > (Ax b) > x,
w
PCA2
1/ 21
A. A. Flower
Correlation
Properties
Principal Components Analysis 2
Practice
Abigail A. Flower
Department of Systems and Information Engineering
University of Virginia
Charlottesville, VA 22904
SYS 4021 Linear Statistical Models
1
Agenda
PCA2
2
SYS 6003: Optimization
Fall 2016
Lecture 3
Date: August 31th , 2016
Instructor: Quanquan Gu
In this lecture, we will answer the second question raised last time (i.e., how to characterize the optimal solution) by studying the firstorder necessary conditi