MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONSECONDLIVEMEETING
Example1:LPFormulation
Manpower Planning: Certain types of facilities operate seven days each week and face the problem of allocating manpower
during the week as staf
MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONLIVEMEETING7
Example1:
Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following
payofftable:
Stateofnature
Alternative
S1
S2
A1
4323X_21_ch21_p001-029.qxd
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9:16 PM
Page 21-1
CHAPTER
Dynamic Programming
CONTENTS
21.1 A SHORTEST-ROUTE PROBLEM
21.2 DYNAMIC PROGRAMMING
NOTATION
21.3 THE KNAPSACK PROBLEM
21.4 A PRODUCTION AND
INVENTORY CONTROL
PROBLEM
21
4323X_21_ch21_p001-029.
MSci603 Week2
LPFORMULATION
1
LP Formulation: Manpower Planning
Certain types of facilities operate seven days
each week and face the problem of allocating
person power during the week as staffing
requirements change as a function of the day of
the week.
Name: _ Class: _ Date: _
ID: A
Review Problems with Solutions
Problem
1. Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are
given below.
Plastic
Ink Assembly
Molding Time
Fliptop Model
3
5
5
Tiptop Model
Principles of Operations Research
Week 2:
Graphical Sensitivity Analysis
and
Applications of Linear Programming
Problems Modeling and Analysis
Instructor: A. Obeidi
Sensitivity Analysis
Used to test the operational validity of an LP model.
How variation i
Masters in Management Science Online
Department of Management Sciences
Faculty of Engineering
University of Waterloo
MSCI 603Z Principles of Operations Research
Fall 2012
Assignment 1
Due by October 2, 2012
General Guidelines for Assignment
This is an in
Masters in Management Science Online
Department of Management Sciences
Faculty of Engineering
University of Waterloo
MSCI 603Z Principles of Operations Research
Fall 2012
Assignment 1
Due by October 2, 2012
General Guidelines for Assignment
This is an in
Masters in Management Science Online
Department of Management Sciences
Faculty of Engineering
University of Waterloo
MSCI 603Z Principles of Operations Research
Fall 2012
Assignment 4
Due by November 20, 2012
General Guidelines for Assignment
This is an
Linear Optimization
1 of 32
http:/home.ubalt.edu/ntsbarsh/opre640a/partviii.htm
Deterministic Modeling:
Linear Optimization with Applications
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Solutions to Problems in Assignment 1
Problem 1:
1)
The optimal solution is
2,
6. Note that the feasible should be shaded, not just labeled.
which is calculated by the coefficient
2) The slope of the objective function can be shown to be
of X over the coe
5/31/2011
MSci603Spring2011
Week4
DUALITY
1
Duality: Learning Objectives
1. Understand the concepts of duality and the relationship between
the primal and dual linear programming problems.
2. Know the economic interpretation of the dual variables.
3. Be a
6/15/2011
MSci603Spring2011
Week6
IPPROGRAM
1
Integer Program: Learning Objectives
1. Be able to recognize the types of situations where integer linear
programming problem formulations are desirable.
2. Know the difference between all-integer and mixed i
5/10/2011
MSci603Spring2011
Week1
LPFORMULATION
1
Understand the following concepts
mathematical model
problem formulation
linear program
feasible region
function
linear functions
objective function
constraint
nonnegativity constraints
slack variable
surp
MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONFIRSTLIVEMEETING
Example1:LPFormulation
Papa Louis manufactures wooden tables and chairs for small kids. Each "table" built: Sells for $27 and uses $10 worth of raw
materials, increase
MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONLIVEMEETING4
Iwillreviewanewdualityconceptcalledcomplementaryslacknessandanswerquestionsaboutthisimportant
topic.ThenIwilldiscussthefollowingexamples.
Example 1:
The following table ex
MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONLIVEMEETING6
Example1:Basketball
Coach Jack is trying to choose the starting line-up for the basketball team. The team consists of seven players who
have been rated (on a scale of 1=po
MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONLIVEMEETING7
Example1:
Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following
payofftable:
Stateofnature
Alternative
S1
S2
A1
4323X_17_ch17_p001-047.qxd
11/16/09
6:34 PM
Page 17-1
CHAPTER
17
Linear Programming:
Simplex Method
CONTENTS
17.1 AN ALGEBRAIC OVERVIEW
OF THE SIMPLEX METHOD
Algebraic Properties of the
Simplex Method
Determining a Basic Solution
Basic Feasible Solution
1
4323X_20_ch20_p001-008.qxd
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8:36 PM
Page 20-1
CHAPTER 20
Minimal Spanning Tree
4323X_20_ch20_p001-008.qxd
11/16/09
20-2
8:36 PM
Chapter 20
Page 20-2
Minimal Spanning Tree
In network terminology, the minimal spanning tree problem involves using the
MSCI603
PrinciplesofOperationsResearch
A.Obeidi
PROBLEMSTOBEDISCUSSEDONFIRSTLIVEMEETING
LPFORMULATION
Example1:Manufacturing
Papa Louis manufactures wooden tables and chairs for small kids. Each "table" built: Sells for $27 and uses $10 worth of raw
mater