There has been a lot of improvements about the healthcare for last years. The most
important and crowd-pulling invention about healthcare is adopting additive manufacturing
techniques to the system. These additive manufacturing processes enable healthcare
IE 305 Simulation
In-class Quiz
15 November 2016
1. We are interested in seeing if the number of
minor accidents occurring each day at a
construction project is Poisson distributed. The
statistics for a 100-day period is shown on the right.
For example, t
IE 305 Simulation
In-class Quiz
21 November 2016
1. We are interested in seeing if the number of flu cases occurring each day
at the Sabanci University Health Center (SUHC) is Binomial(l; 5, 0.5). On the
right are the results for a 200-day period. For exa
IE 305 Simulation
This quiz is not graded.
1.
In-class Quiz
7 November 2016
2. Ten percent (10%) of computer parts produced by a certain supplier are defective.
What is the probability that a sample of 10 (ten) parts contains more than 3 (three)
defective
IE 305 Simulation
In-class Quiz
(Not graded)
1.
The distribution you see is a standardized
normal distribution with random variable
Z. We use the letter P for the probability
and F for the cumulative distribution
function. Which expressions describe the
t
IE 305 Simulation
In-class Quiz
18 October 2016
1. Generate 1000 (thousand) random numbers with standard normal
distribution.
2. Use Arenas Input Analyzer to construct the probability distribution.
3. Use the fit in the menu to see if you replicate the di
IE 305 Simulation
In-class Quiz
25 October 2016
Two different part types arrive at a facility for processing. Parts of Type 1 arrive with
interarrival times following a normal distribution with mean of 11.5 hours and standard
deviation of 2.0 hours. The f
IE 305 Simulation
In-class Quiz
1 November 2016
1. We have data that follows a normal distribution of unknown mean and variance.
Suppose we collect the following data: 1, 2, 3, 6, -1.
Let the null hypothesis be that mean = 0 and the alternative hypothesis
IE 305 Simulation
In-class Quiz
31 October 2016
1. If we have a fair coin what is the probability that we will decide incorrectly it is unfair?
We sum up the probabilities associated with the red boxes, namely,
0.001*2 + 0.01*2 + 0.044*2 = 0.11
IE 305 Simulation
In-class Quiz
11 October 2016
1. On average there are 2 hits per minute on a specific web page. How long do we have to
wait at most to observe a first hit with a probability of 0.9? (Please provide the
numerical answer in seconds.)
IE 305 Simulation
In-class Quiz
17 October 2016
1.
What is the total number of parts processed in a specialized serial processing when the
service time is constant 1 (one) hour?
1) Suppose the final tableau of a maximization problem is given as below where s1 and s2
are the slack variables associated with the first and second constraints respectively.
Z
x1
x2
x3
s1
s2
1
6
0
0
3
6
45
0
-2/3
1
0
1/3
1/3
4
0
1/3
0
1
1/3
-1/3
2
a) Wr
IE 301
Week 3
The Gauss-Jordan Method
Using the Gauss-Jordan method, we can show that any system of
linear equations must satisfy one of the following three cases:
Case 1 The system has no solution.
Case 2 The system has a unique solution.
Case 3 The syst
8) Suppose the final tableau of a maximization problem is given as below where x4 and x5
are the slack variables.
Z
1
0
0
x1
0
0
1
x2
4
-1
2
x3
0
1
0
x4
2
1/2
1/2
x5
4
1/2
-1/2
RHS
20
4
2
All parts of the question are independent of each other. The requir
IE 301 Deterministic Models in
Operations Research
)
Week 1
Origins
World War II
Allocate scarce resources to military
operations and to the activities within each
operation
Organize logistics
Rapid spread of OR started after 1950s to all
sorts of org
IE 301
Week 2
Financial Planning
Suppose you have the following investment
alternatives for the coming 3 years. The cash
flows are given per unit TL.
All cash flows are assumed to be at the end of
the associated year.
End of year
A1
A2
A3
0
-1
-1
1
0,2
IE 301
Week 5
Sensitivity Analysis and Duality
Since all the parameters of an LP model are
estimates, it is essential to check the
robustness of the optimal solution/value with
respect to changes in the parameters.
We will first go through a graphical e
IE 301
Deterministic Models in
Operations Research
Six types of changes in an LPs parameters change the optimal
solution.
Changing the objective function coefficient of a nonbasic variable.
Changing the objective function coefficient of a basic variable.
IE 430 - HW #2 (due 2 November 2016 @ 11 PM)
SOLUTIONS
1-a)
cfw_
1,
Define: =
if facility is opened
0,
otherwise
xij number of units transported from facility i to customer j.
5
Min
6
=1
5=
s.t.
5
+
=1
1
6
=1
6=1
1
=
0
,
cfw_0, 1
The CPLEX model i
IE 430 - HW #3 (due 8 November 2016 @ 11 PM)
SOLUTIONS
1. The model was given in HW #2 Solutions.
a) x12 x21 x25 x26 x 43 1,
x14 0.125, x44 0.875 , y1 y 2 y 4 1 ,
Z 220500
b) Define x decision variables boolean instead of float+
x12 x21 x 23 x25 x26 x44 1
IE 430 - HW #4 (due 7 December 2016 @ 11 PM)
SOLUTIONS
1.
CPLEX .mod file:
/sets
range terminals= 1.7;
/parameters
int SupDem[terminals]=.;
/ Create a record to hold information about each arc
tuple arc cfw_
key int fromnode;
key int tonode;
foat cost;
c
IE 430 - HW #3
(due 8 November 2016 @ 11 PM)
1. Repeat Part 1.d and 1.e of HW2 by reducing the capacity of facility 4 from 9000 to 5500.
Locations
2. A fire brigade wants to determine the optimal locations of fire stations. The region can be
divided into
How to compute dual variables from primal simplex tableau
Let;
cB: objective coefficients of the basic variables
B: matrix formed by the columns of A that belong to (are under) the basic variables.
Dual variables can be computed using the following formul
MS 301 SPRING 2014 RECITATION 2 SOLUTIONS
1. The below table summarizes Crimevilles requirements for on-duty police officers by the time of day.
Time of Day
Number of Officers Required
2:00 a.m. - 6:00 a.m.
2
6:00 a.m. - 10:00 a.m.
6
10:00 a.m. - 2:00 p.m
MS 301 SPRING 2014 RECITATION 9 SOLUTIONS
These questions are from Operations Research: Applications and Algorithms by Wayne L. Winston 4th Ed.
1. Section 9.2 Question 1
2. Section 9.2 Question 3
Let x1 = Units of Product 1 produced
x2 = Units of Product
MS 301 SPRING 2014 RECITATION 6 SOLUTIONS
These questions are from Operations Research: Applications and Algorithms by Wayne L. Winston 4th Ed.
1) Page 313 Section 6.7 Problem 3
5) Page 322 Section 6.8 Problem 8
The dual objective function is w = .5y1 + .
MS 301 SPRING 2014 RECITATION 4 QUESTIONS
These questions are from the textbook Operations Research: Applications and Algorithms by Wayne L.
Winston 4th Ed.
1) Page 154 (Section 4.7) Question 2
Then the simplex tableau is:
Row
0
1
2
X2 enters the basis in