IE528 Lec 4
1. (Bertsimas 10.6) A company produces a set of K products at I plants. It then ships these
products to J market zones. For k = 1, ., K i = 1, ., I and j = 1, ., J the following data is
gi
IE528 Mathematical Programming and Modeling
HW1
Due March 18 (midnight)
Spring 2012
1. (Bertsimas 10.1) Suppose that we are given m constraints ai x bi for all i = 1.m,
but without the restriction ai
Advanced Linear Programming, May 18, 2009, 10:00 - 13.00
Please notice my mistake in Exercise 5 for which my sincere
apologises
(1) (1 pt.) Formulate Farkas Lemma.
Answer.
Theorem. Given m n matrix A
Sensitivity Analysis and Duality
Two of the most important topics in linear programming are sensitivity analysis and duality. After studying these important topics, the reader will have an appreciatio
Sensitivity Analysis: An Applied Approach
In this chapter, we discuss how changes in an LPs parameters affect the optimal solution. This is called sensitivity analysis. We also explain how to use the
Network Models
Many important optimization problems can best be analyzed by means of a graphical or network representation. In this chapter, we consider four specic network modelsshortest-path problem
Integer Programming
Recall that we dened integer programming problems in our discussion of the Divisibility Assumption in Section 3.1. Simply stated, an integer programming problem (IP) is an LP in wh
APPENDIX 2
Cases
Jeffrey B. Goldberg
UNIVERSITY OF ARIZONA
CASE
1 2 3 4 5 6 7 8 9 10 11
Help, Im Not Getting Any Younger! Solar Energy for Your Home
1351
1351
CASE
CASE
Golf-Sport: Managing Operations
APPENDIX 1
@Risk Crib Sheet
@Risk Icons Once you are familiar with the function of the @Risk icons, you will nd @Risk easy to learn. Here is a description of the icons.
Opening an @Risk Simulation
Thi
Simulation with Process Model
In Chapter 21, we learned how to build simulation models of many different situations. In this chapter, we will explain how the powerful, user-friendly simulation package
Simulation
Simulation is a very powerful and widely used management science technique for the analysis and study of complex systems. In previous chapters, we were concerned with the formulation of mod
Probabilistic Dynamic Programming
Recall from our study of deterministic dynamic programming that many recursions were of the following form: ft (current state) min
all feasible decisions
(or max)cfw_
Deterministic Dynamic Programming
Dynamic programming is a technique that can be used to solve many optimization problems. In most applications, dynamic programming obtains solutions by working backwa
Markov Chains
Sometimes we are interested in how a random variable changes over time. For example, we may want to know how the price of a share of stock or a rms market share evolves. The study of how
Deterministic EOQ Inventory Models
In this chapter, we begin our formal study of inventory modeling. In earlier chapters, we described how linear programming can be used to solve certain inventory pro
Game Theory
In previous chapters, we have encountered many situations in which a single decision maker chooses an optimal decision without reference to the effect that the decision has on other decisi
Decision Making under Uncertainty
We have all had to make important decisions where we were uncertain about factors that were relevant to the decisions. In this chapter, we study situations in which d
Review of Calculus and Probability
We review in this chapter some basic topics in calculus and probability, which will be useful in later chapters.
12.1
Review of Integral Calculus
In our study of ran
Nonlinear Programming
In previous chapters, we have studied linear programming problems. For an LP, our goal was to maximize or minimize a linear function subject to linear constraints. But in many in
Advanced Topics in Linear Programming
In this chapter, we discuss six advanced linear programming topics: the revised simplex method, the product form of the inverse, column generation, the DantzigWol
Transportation, Assignment, and Transshipment Problems
In this chapter, we discuss three special types of linear programming problems: transportation, assignment, and transshipment. Each of these can
Introduction to Linear Programming
Linear programming (LP) is a tool for solving optimization problems. In 1947, George Dantzig developed an efcient method, the simplex algorithm, for solving linear p
Basic Linear Algebra
In this chapter, we study the topics in linear algebra that will be needed in the rest of the book. We begin by discussing the building blocks of linear algebra: matrices and vect
An Introduction to Model Building
1.1
An Introduction to Modeling
Operations research (often referred to as management science) is simply a scientific approach to decision making that seeks to best de
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
15.053 Introduction to Optimization (Spring 2005)
Recitation 8, March 8th 2005
Problem 1 Formulating a Piece Wise Linear IP
Formulate the following as an IP. Do n
Manufacturing Planning and Control
Stephen C. Graves
Massachusetts Institute of Technology
November 1999
Manufacturing planning and control entails the acquisition and allocation of limited
resources
Advanced Linear Programming: The Exercises
The answers are sometimes not written out completely.
1.5 a)
min cT x + dT y
s.t. Ax + By b
y = |x|
(1)
First reformulation, using z smallest number satisfyi
IE528 Mathematical Programming and
Modeling
Lecture 7
Dr. Zeliha Akca
April 2012
1 / 24
Reading
Finish the Lecture 6.
Read Production Planning Chapter submitted to moodle.
Read scheduling and sequenci
IE528 Mathematical Programming and
Modeling
Lecture 6
Dr. Zeliha Akca
March 2012
1 / 21
Production Planning Problems in General
Production planning problems are the problems focused on
allocation of l
IE528 Mathematical Programming and
Modeling
Lecture 5
Dr. Zeliha Akca
March 2012
1 / 12
General Case of Disjunctive Constraints
Let a x b and d x f be two constraints.
a x and d x are not necessarily