Discrete Time Markov Chains (1/3)
Stochastic processes
A stochastic (random) process, Xt, t T, is a collection
(family) of random variables, where T is an index set.
A stochastic process is a representation of a system that
evolves over time in a proba
Discrete Time Markov Chains (2/3)
Chapman-Kolmogorov (C-K) Equations
(n)
Consider a MC, Xn with state space cfw_0,1, 2, . Let pij be
the n-step transition probability from state i to state j. I.e.,
pij( n) Pcfw_X nk j | X k i .
(n)
( n)
Let P [ pij ] b
Probability and Random Variable (4)
Discrete Random Variables
The Uniform Random Variable
A rv X that is equally like to be near any point of an
interval (a, b) is said to have a uniform distribution.
The pdf of X is
1
, if a x b
f X ( x) b a
0 ,
othe
Unit B - Probability and Random Variable (1)
Sample space and Events
Suppose that an experiment with an uncertain outcome is
performed (e.g., rolling a die).
While the outcome of the experiment is not known in
advance, the set of all possible outcomes
Probability and Random Variable (3)
Discrete Random Variables
The Bernoulli Random Variable
Suppose an experiment can result in success with probability
p and failure with probability (w.p.) 1p.
We define a Bernoulli random variable X as X =1 if the
ex
Probability and Random Variable (2)
Random Variables
Consider a function that assigns real numbers to events
(outcomes) in . Such real-valued function is a random
variable.
E.g., when rolling two fair dice, define X as the sum of the
two dice. Then, X
Unit B-5
Probability and Random Variable
Lognormal random variable A stock price model
A rv Y is said to be lognormal if X = ln(Y) is a normal
random variable.
Alternatively, Y is a lognormal rv if Y = eX, where X is a
normal rv.
If X = ln(Y) is norma
On Theoretical Probability Models
Ready-made theoretical models save us from
having to build probability distributions from
scratch for each new uncertainty scenario.
We find a theoretical model that closely matches the
probability assessments of the un
Review of Basic Inventory
Models
The single-period newsvendor model
Consider a newsvendor, who, at the start of each day,
must decide the amount of newspapers to stock, S.
Placing an order has a negligible cost.
Daily demand for the newspaper is D (a r
Location and Distribution
Decisions in Supply Chains
How the decision makers actually decide on
the location of the facilities in the network
and the assignment of those facilities to the
customers they serve?
In this chapter we focus our attention to
l
Review of Basic Inventory
Models
Introduction
Most industries have to deal with inventories. E.g., shelf and warehouse
(back room) inventory in retail, and raw material, work in process and
finished product inventory in manufacturing.
Proper inventory m
Supply Chain Contracts
Contracts
Supply Contract can include the following:
Pricing and volume discounts.
Minimum and maximum purchase quantities.
Delivery lead times.
Product or material quality.
Product return policies.
2-Stage Sequential Supply Ch
Supplier Selection Models and
Methods
Introduction
Supplier selection process is difficult because the criteria for selecting suppliers
could be conflicting
Supplier selection is a multiple criteria optimization problem that requires tradeoff
among differ
Transportation Decisions in
Supply Chain Management
Suppose you are the manager of regional
distribution center, located in Atlanta.
Suppose your company agreed to assumed
responsibility for hiring the carrier that will
move the goods from Oakland to At
Aggregate Planning
Definition
Given a demand forecast over a planning
horizon, develop a plan for production and
allocation of resources by making appropriate
trade off among capacity, inventory and
backlogs.
The aggregate planning problem is basically a
Overview of Chapter 7
We will review the basics of probability theory.
Since uncertainty is a typical aspect of problems,
rigorous and accurate problem solving requires
using probability theory (i.e., math and logic).
Specifically, we want you to:
Under
Overview of Chapter 11
In this chapter, we will cover Monte Carlo simulation:
A different approach than those already discussed to
dealing with uncertainty in a decision situation
Constructing a model that captures all of the relevant
aspects of the unc
Bullwhip effect
Definition
The increase in demand variability as we move up in
the supply chain is referred to as the bullwhip effect.
Causes
Lack of information: In the beergame no information except for the order amount
is perpetuated up the supply cha
Overview of Chapter 10
In this lecture, we will cover:
Constructing probability distributions from data
Fitting data to theoretical probability
distributions
Modeling relationships with data
Regression analysis
Differences between decision analysis a
Overview of Chapter 14
In this lecture, we will cover:
The preference side of decision analysis
How can we model a decision makers
preferences?
Introduce an approach called utility theory that
allows us to incorporate riskiness
Develop the basic tools
Probability and Decision Analysis
Sensitivity Analysis
Chapter 5
ENGM 603
Overview of Chapter 5
In this lecture, we will cover sensitivity analysis and several tools
for performing sensitivity analysis.
A modeling approach to sensitivity analysis
Identi
Value of Information: Some Basics
An investor has some funds available to invest in one of three
choices: a high-risk stock, a low-risk stock, or a savings account
that pays a sure $500.
If he invests in the stocks, he must pay a brokerage fee of $200.
Hi
The Management Theory - ENMG 601
Faculty Of Engineering & Architecture
(Engineering Management Program)
PART II
Methodologies For Strategy
Formulation
(Introduction)
ENMG 601
By: Nader M. Ghazal (Ph.D.)
Management Theory ENMG 601 Part II
Definition of
S
The Management Theory - ENMG 601
Faculty Of Engineering & Architecture
(Engineering Management Program)
PART III
Intro to
Organizations Dynamics (OB)
ENMG 601
By: Nader M. Ghazal (Ph.D.)
Management Theory ENMG 601 Part I
11
Outline
Organizations Dynami