SIE 321 - Spring 2014
Midterm #1
SIE 321: Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Midterm #1 Solution
Problem #1 (40pt) (Markov chain modeling)
Daves Photography Store stocks a particular model camera that can be ordered weekl

SIE 321 - Probabilistic Models in Operations Research
Dr. Ruiwei Jiang
Department of Systems and Industrial Engineering
University of Arizona
Jiang (UA)
PMOR
Spring 2014
1 / 93
Outline
1
Introduction
2
class Info
3
Probability Theory Review
4
Poisson Proc

SIE 321 - Probabilistic Models in Operations Research
Dr. Ruiwei Jiang
Department of Systems and Industrial Engineering
University of Arizona
Jiang (UA)
PMOR
Spring 2014
1 / 154
Outline
1
Introduction
2
Probability Theory Review
3
Poisson Processes
4
Mark

Birth-and-Death Processes: Definition
Definition: a birth-and-death process is a stochastic process, with
nonnegative integer states N(t), that satisfies the following assumptions:
Assumption 1: Given N(t) = n, the current probability distribution of
the

SIE 321 - Probabilistic Models in Operations Research
Dr. Ruiwei Jiang
Department of Systems and Industrial Engineering
University of Arizona
Jiang (UA)
PMOR
Spring 2014
1 / 119
Outline
1
Introduction
2
class Info
3
Probability Theory Review
4
Poisson Pro

Transition probabilities and diagram: example 3
Example:
A department store classifies the balance of a customers bill as fully
paid (status 0), 1 to 30 days in arrears (status 1), 31 to 60 days in
arrears (status 2), or bad debt (status 3).
The accounts

A shop has two identical machines that are operated continuously except when they break down.
Suppose that if the machine is up on clay in. it is up on the (n + 1)" day with probability 0.9.
independent of the past. On the other hand. if it is down on the

Huy Ho
Michael Rojano
SIE 370 Lab 7
Lab 7: Intro to Sequential Circuits
Purpose:
The purpose of this lab is to introduce and get familiar with sequential circuits. The 555
timer will be used to generate a clock pulse. The 555 timer is a very cheap and use

Huy Ho
Michael Rojano
SIE 370 Lab 2
Lab 1: Serial Communication Protocols
Purpose:
The purpose of this lab is to introduce and provide hands on experience with serial
communication. The familiarization of basic computer hardware dealing with serial
commun

Huy Ho
Michael Rojano
SIE 370 Lab 8
Lab 8: High Level Language Controller
Purpose:
The purpose of this lab is to design and program a code to control the speed of two trains
enabling them to not crash on a figure eight course. They are 4 inputs and 2 outp

Huy Ho
Michael Rojano
SIE 370 Lab 5
Lab 5: COMBINATION LOGIC CIRCUITS II
Purpose:
The purpose of the combination logic circuit lab is to create a circuit from scratch beginning with
a design based on a truth table. The design is based on a simple security

Huy Ho
Michael Rojano
SIE 370 Lab 1
Lab 1: Serial Communication Protocols
Purpose:
The purpose of this lab is to introduce and provide hands on experience with serial
communication. The familiarization of basic computer hardware dealing with serial
commun

Huy Ho
Michael Rojano
PreLab3 Microprocessor Introduction
1) Install Arduino IDE
2) The Arduino has a debugging LED on pin 13. Use the tutorial code \Blink" on
ttp:/arduino.cc/en/Tutorial/Sketch. Write the code in the IDE and run the program on
the Arduin

Huy Ho
Michael Rojano
SIE 370 Lab 2
Lab 3: MICROPROCESSOR INTRODUCTION
Purpose:
The purpose of the microprocessor introduction lab is to introduce to basic use of the Ardunio
Uno Microprocessor. The lab also incorporates the programing language C+ in comb

Huy Ho
Michael Rojano
SIE 370 Lab 4
Lab 4: COMBINATION LOGIC CIRCUITS I
Purpose:
The purpose of the combination logic circuit lab is to create a circuit from scratch beginning with
a design based on a truth table. The Boolean Algebra laws and theorem is u

Huy Ho
Michael Rojano
SIE 370 Lab 6
Lab 6: Adaptive Cruise Control Micro Processor Project
Purpose:
The Purpose for this lab is to design a program that will control the speed of a remote
control car using a microprocessor. The microprocessor will control

SIE 321 - Probabilistic Models in Operations Research
Dr. Ruiwei Jiang
Department of Systems and Industrial Engineering
University of Arizona
Jiang (UA)
PMOR
Spring 2014
1 / 75
Outline
1
Introduction
2
class Info
3
Probability Theory Review
4
Poisson Proc

Expected costs per unit of time: motivation
Example:
Consider the inventory example.
Assume that the owner, Dave, incurs
inventory.
0
2
C (xt ) =
8
18
the following cost based on his
if
if
if
if
xt
xt
xt
xt
= 0,
= 1,
= 2,
= 3.
How would you compute the ex

Continuous-Time Markov Chains
Definition:
Intuitively, continuous-time Markov chains (CTMC) are DTMCs with
a random amount of time for staying in each state.
Motivation:
In previous discussion of DTMCs, we assume that time was discrete,
i.e., t = 1, 2, .

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 1, due in class at 1:00pm on Monday Feb. 3rd, 2014
To receive full credit, you should make sure you follow the following guidelines.
Questions:
There are 7 questions

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 2, due in class at 1:00pm on Monday Feb. 24th, 2014
To receive full credit, you should make sure you follow the following guidelines.
Questions:
There are 7 questions

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 3, due in class at 1:00pm on Wednesday Apr. 2nd, 2014
To receive full credit, you should make sure you follow the following guidelines.
Questions:
There are 7 questio

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 4, due in class at 1:00pm on Friday Apr. 11th, 2014
To receive full credit, you should make sure you follow the following guidelines.
Questions:
There are 4 questions

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 5, due in class at 1:00pm on Monday Apr. 28th, 2014
To receive full credit, you should make sure you follow the following guidelines.
Questions:
There are 4 questions

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 6, due in class at 1:00pm on Wednesday May 7th, 2014
To receive full credit, you should make sure you follow the following guidelines.
Questions:
There are 4 question

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 2 Solution
Problem #1 (15pt)
A shop has two identical machines that are operated continuously except when they break down.
Suppose that if the machine is up on day n,

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 1 Solution
Problem #1 (13pt)
A gambler is rolling a pair of fair dice. What is the probability that
1. (3pt) the sum of the dots on the dice is 7?
2. (2pt) the sum of

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 3 Solution
Problem #1
Hearts Dog Food and Corporal Dog Food are battling tooth and nail for the nations dog biscuit
market. A dog owner buys one box of dog biscuits pe

SIE 321 - Probabilistic Models in Operations Research
Ruiwei Jiang
Spring 2014
Homework 4 Solution
Problem #1
A post oce has two customer service clerks. Suppose you arrive at the post oce at 1 pm and
nd that both of the clerks are busy but there is no on