IE 301 - Assignment 2
Due: Friday, November 11, 2016 at 12.00
(Papers will be collected before the midterm)
Question 1
Suppose that a new car costs $10,000 and that the annual operating cost and resale value of
the car are as shown in the following table.
NLPs with One Variable
One Variable Unconstrained
Optimization
Consider f(x) defined from R to R
Lets assume we are trying to find the
maximum value f(x) can take
max f ( x)
s.t.
x
If f(x) is concave, any local maximum is also
a global maximum
One Var
Quadratic Programming
1
Quadratic Programming
A quadratic programming problem (QPP) is an
NLP in which each term in the objective
function is of degree 2, 1, or 0 and all
constraints are linear
max f ( x1 , x2 ) 15 x1 30 x2 4 x1 x2 2 x12 4 x22
s.t.
x1 2
ShawIaIfurS=Rixhxmx=x +x+21xix2xg3 xlx1isanumnex
flmctinn.
Slhiiln 'l'heHessaanis-giwnby
2 l 1
HII],I2EXJ=[l 2 l.]
l l it
Bydnhngmsiiandmhlmm] 1 andEafHassiamwpubtainlemt-m'dpmi
pal mier 4 3:- 1]. y deleting rm [and claims] 1 and 3 of Haasian. we obtain H
Dynamic Programming
1
Description
Dynamic Programming (DP) is a technique that
can be used to solve many optimization
problems.
It provides a systematic procedure for
determining the optimal combination of
decisions.
In most applications, dynamic progr
Unconstrained Maximization and
Minimization with Several Variables
Consider this unconstrained NLP
max (or min) f ( x1 , x2 ,.xn )
s.t.
( x1 , x2 ,., xn ) R n
1
Unconstrained Maximization and
Minimization with Several Variables
A necessary condition for
IE301 Operations Research II
Fall 2016
Course Description
The aim of this course is to introduce the most widely used nonlinear mathematical programming
and dynamic programming methods and Markov chains. Topics covered in this course include
nonlinear opt
Probabilistic Dynamic
Programming
1
Probabilistic Dynamic Programming
In deterministic dynamic programming, a
specification of the current state and current
decision was enough to tell us with certainty the new
state and the costs/rewards during the curr
IE301 Operations Research II
Fall 2015
Instructor: Ali Ekici
The OR World You Know
Linear Programming
minimize or maximize a linear objective
subject to linear equalities and inequalities
maximize 3x + 4y
subject to
5x + 8y 24
x, y 0
A feasible solutio
IE 302 Production Systems Analysis
INVENTORY CONTROL STOCHASTIC
DEMAND
O.rsan zener
1
Quote of the day
The only thing that makes life possible is permanent,
intolerable uncertainty; not knowing what comes next.
Ursula K. LeGuin
2
Deterministic vs Stocha
IE 302 Production Systems Analysis
INVENTORY CONTROL DETERMINISTIC
DEMAND
O.rsan zener
1
Quote of the day
The mind is like an iceberg, it floats with one-seventh of its
bulk above water.
Sigmund Freud
2
Inventory
Inventory management: Inventory managemen
IE 302 Production Systems Analysis
FORECASTING
O.rsan zener
1
Quote of the day
God does not play dice with the universe.
Albert Einstein
God not only plays with dice, he sometimes throws them
where they can't be seen.
Stephen Hawking
2
Forecasting
Motiva
IE 302
Instructor: O. Orsan
Ozener
Recitation 2, Fall 2016
1
October 11, 2016
EOQ & ABC Analysis
Question 1
Number 2 pencils at the campus bookstore are sold at a fairly steady rate of 60 per week. The pencils
cost the bookstore 2 cents each and sell for
IE 302 Production Systems Analysis
INTRODUCTION
O.rsan zener
1
Quote of the day
Watch the costs and the profits will take care of themselves.
Andrew Carnegie
2
Transition in Employment
Popular View: We are merely shifting to a service economy, the same
IE 302
Instructor: O. Orsan
Ozener
Recitation 2, Fall 2016
1
October 11, 2016
EOQ & ABC Analysis
Question 1
Number 2 pencils at the campus bookstore are sold at a fairly steady rate of 60 per week. The pencils
cost the bookstore 2 cents each and sell for
IE 302
Instructor: O. Orsan
Ozener
Recitation 1, Fall 2016
1
October 3, 2016
Forecasting
Question 1
Shoreline Park has the following data on the number of visitors since its opening (given in Table 1).
Table 1: Number of visitor for the past 6 months
Mont
IE 576
Sample Problems for Exam II
1. What is price differentiation?
2. What are the real-world limitations of price differentiation? Name two of them and explain
briefly.
3. Name of three of the tactics for price differentiation and explain them briefly.
IE 576 Pricing and Revenue Management
Summer 2016
Course Description
Learning
Outcomes
The aim of this course is to provide a comprehensive introduction to both the theory and the
practice of revenue management and pricing. Course objectives are: (i) to f
Capacity Allocation
Introduction
Determining how many seats (or hotel rooms) to
allow low-fare customers to book when there is
the possibility of future high-fare demand
Important because most of the airliners have
based their revenue management strateg
Pricing with Constrained
Supply
Nature of Supply Constraints
Most sellers face supply constraints at least some
of the time, such as in between replenishment
times
There are many cases in which a seller needs to
consider the constrained nature of supply
Price Differentiation
Price Differentiation
One of the most fundamental concepts in PRO
Practice of a seller charging different prices to
different customers either for
exactly the same good
slightly different versions of the same good
To extract add
Basic Price Optimization
Basic Price Optimization
We discuss
Basic elements of pricing and revenue optimization
(PRO)
How basic PRO problem can be formulated as an
optimization problem
Goal (objective function) of the optimization
problem is to maximi
Review
Calculus & Probability & Optimization
Calculus Review
Calculus
The equation
lim f ( x) c
x a
means that as x gets closer to a (but not equal to
a), the value of f(x) gets arbitrarily close to c.
A function f(x) is continuous at point a if
lim f (
Markdown Management
Introduction
Waiting for the Sale is a time-honored strategy for
savvy shoppers
Budget-minded customers know that they can
save by waiting
The longer they wait, the more they save
Many items will be marked down by 70% or more
by th
IE 576
Sample Problems for Exam I
1. What might be the reason that a seller sells a product below its cost? Give a real life
example.
2. What is a perfectly competitive market? Under which conditions, a market is called a
perfect market?
3. How are the pr
IE 576
Pricing and Revenue Management
Introduction
This course is about how to make better pricing
and revenue management decisions in order to
increase the profitability of companies
Pricing decisions are faced by almost every
company:
Commonplace
Co