OR/ISE501 In Class Exercise
Suppose a fair coin is thrown twice.
Event A: head occurs on the first throw
Event B: head occurs on the second throw.
Are these two events independent?
What is probcfw_AB?
Prob(A)= and prob(B) = . The event AB is th
6.2 Some Important Formulas
An LPs optimal tableau can be expressed in terms of the LPs parameters. The
formulas developed in this section are used in the study of sensitivity analysis,
duality, and advanced LP topics. Lets begin with a familiar max probl
Homework Set 1
Problem 1) As objective function=
z 4 x1 x2 moves to the right, it increases. True/False
Problem 2) As objective function z =
x1 + 2 x2 moves to the right, it increases. True/False
Problem 3) As objective function z =
x1 3x2 moves to the
ISE/OR501 Homework # 7 Statement
Solve each problem in detail and submit your entire work. The T/F questions are included for purpose
of providing a template for possible questions on the Test 2.
Problem 1: Use Djikstras shortest path algorithm to find th
Instructor: Javad Taheri; [email protected]
Course Scope and Objectives
To build a general understanding of the field of Operations Research (OR)
and become familiar with the OR methodologies as well as the application
areas where OR has
ISE/OR501 Homework Set 4
For the following LPs, the set of BV are given. Use the important formulas (included in this
statement) to answer the following questions showing your work in detail, that is:
1. Write the formula you are using in its gen
z 4 x1 x2
z x1 2 x2
z x1 3x2
max z 200 xw
m ax z 4 x1 3 x 2
s .t .
3 x1 2 x 2 18
x1 2 x 2 10
x1 , x 2 0
Introduction to Integer Programming
An IP problem in which all variables
are required to be integers is call a
pure integer programming
An IP problem in which only some of
the variables are required to be
integers is called a mixed integer
Introduction to Basic Inventory
The purpose of inventory theory is to
determine rules that management can use to
minimize the costs associated with maintaining
inventory and meeting customer demand.
Inventory models answer the following
A network is defined by two sets of symbols:
nodes and arcs.
An arc consists of an ordered pair of nodes
that represents a possible direction of motion
that may occur between the nodes.
A sequence of arcs such that every arc has
4.10 The Big M Method
The Dakota Furniture company
manufactures desk, tables, and
chairs. The manufacturer of
each type of furniture requires
lumber and two types of skilled
labor: finishing and carpentry.
x1 = number of desks produced
x2 = number
OR501 In class Exercise
Part A) Reconstruct the optimal tableau by using Important Formulas for the following LP:
z 4 x1 + 3 x2
x1 + x2 + s1 =
2 x1 + x2 + s2 =
x1 , x2 , s1 , s2 0
Vector of Basic Variables in Optimal solution:c
Shortest Path Problem- a review from chapter 8
Shortest Path Problem
At node 3
At node 1
At node 3
The shortest path to 3 is (1>3): $3
5.1 A Graphical Approach to Sensitivity Analysis
Sensitivity analysis is concerned with how changes in an LPs
parameters affect the optimal solution.
max z = 3x1 + 2x2
2 x1 + x2 100 (finishing constraint)
x1 + x2 80 (carpentry constraint)
40 (demand c
Input Modeling- Summary
Launch Input Analyzer
New File> Data File > Existing
Load an exiting data file
Window > Input Data
View raw data
Fit > Fit All
Fit distributions to data
: Square error, p-value of Chi-Square Test, p-value of Ko
Chapter 17: Markov Chains
Study of how a random variable changes over time.
What is a Markov Chain?
Interested in observing some characteristic of a
system at discrete points in time (labeled 0, 1, 2,).
Let Xt be the value of system characteristic at
Review of probability Distributions
Generating random numbers using Inverse Transform
Monte Carlo Simulation
Estimate the area under the for a quadratic function
Project Management (PERT)
6.3 Sensitivity Analysis
How do changes in an LPs parameters (objective function coefficients,
right-hand sides, and technological coefficients) change the optimal
solution? Let BV be the set of basic variables in the optimal tableau.
Given a change in an
Problem 1) The following constraint set does not make a feasible region:
Problem 2) From the following tableau of a maximization problem, the next simplex iteration will
pivot on the third column and first r