The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM301016
Tutorial 9
Nov. 23
1. The ToysR4U Company has developed two new toys for possible inclusion
in its product line for the upcoming Christmas season. Setting up the production
facilities to begin production would cost $50,000 for toy 1 and $80,
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM3010
HW1_Solution
1.
The decision variables are defined as follows:
xm1s1 : number of units (tons) shipped from Mine 1 to Storage Facility 1,
xm1s2 : number of units (tons) shipped from Mine 1 to Storage Facility 2,
xm2s1 : number of units (tons) s
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW2_Solution
1.
Since there is no positive coefficient in X5 column so we get a conclusion that
Z is unbounded
2.
Solve the following LP by simplex method (use tableaux):
Maximize Z=W= X 1 4 X
3X
3
4X1 X
2
2
Subject to
X1 X
2
X1 0 X
X
2X
2
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM3010
Fall15
HW1
IELM 3010 Operations Research I
Homework 1 (Due in class on September 17th)
1. The Fagersta Steelworks currently is working two mines to obtain its iron ore. This
iron ore is shipped to either of two storage facilities. When needed, it
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW3
1. Using the bigM method to solve the problem
Minimize W= 3 X 1 2 X 2 7 X 3
Subject to
X1 X
2X1 X
10
2
X
2
X 1, X 2 , X
3
10
3
0
2. Using the bigM method to solve the problem
Maximize Z= 4 X 1 5 X 2 3 X 3
Subject to
X1 X
2
2X
15 X 1
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW4
Due in class on Oct. 13
1. (10 points) Consider the following problem
Maximize Z= 5 X 1 X 2 3 X 3 4 X 4
Subject to
X 1 2 X 2 4 X 3 3 X 4 20
4X1 6X
2X 1 3X
2
5X
3
4X
3X
3
8X
X 1, X 2 , X 3, X
4
4
40
0
2
4
50
(a) Construct the dual pr
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW4_Solution
1.
(a)
2.
(b)
The same way as shown in tutorial 5 and you will get the dual optimal solution:
(Y1, Y2, Y3, Y4)= (0, 0, 0.5, 0.5) and W=31
IELM301015
HW4_Solution
Comments:
For problem 2(b) , first you need to check the strong duali
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM%3010%
Opera.ons%Research%I%
Lecture%Note%14%
!
Xiaowei%Zhang%
Department%of%Industrial%Engineering%and%Logis.cs%Management%
HKUST%
1%
chapter in your OR Courseware. However, because the Excel approach now is someIELM%3010%
what different from what yo
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM301016
HW3
Due on Oct. 11
FINAL VERSION, RESUBMISSION, IVAN MEDNIKOV
IELM 3010 Operations Research I
Homework 3 (Due by 12:00pm on October 11)
Total 30 points
1. (10 points) Using the bigM method to solve the problem
Maximize Z= 4 X + 5 X + 3 X
1
Su
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM301016
Tutorial 6
Nov. 2nd
1.
Consider the following problem:
Max C1 x1 2x 2
S.t.
2 x1 x 2 x3 30
x1 x 2 x3 10
x1 , x 2 , x3 0
Let x 4 , x5 denote the slack variables for the respective functional constraints. When
C1 =3, the simplex method yields the
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM301016
HW3
Due on Oct. 11
IELM 3010 Operations Research I
Homework 3 (Due by 12:00pm on October 11)
Total 30 points
1. (10 points) Using the bigM method to solve the problem
Maximize Z= 4 X + 5 X + 3 X
1
Subject to
2
3
X 1 + X 2 + 2 X 3 >= 20
15 X 1
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM301016
Tutorial 10
Nov. 30th
s
Notice that the nodes of the network may be divided in layers: the nodes in the nth layer are accessible
from the origin only through nodes in the (n1)th layer(i.e., the columns of nodes in the figure constitute the
lay
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
Wyndor Glass Co. Production Planning
Profit per Batch
Product 1 Product 2 Total Profit
$3,000
$5,000
0
Plant 1
Plant 2
Plant 3
Hours Used per Batch Hours Used
Available Hours
1
0
0 <=
4
0
2
0 <=
12
3
2
0 <=
18
Batches Produced
Range Name
Plant_1
Plant_2
P
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2014
IELM 3010
Operations Research I
Lecture Note 19
Xiaowei Zhang
Department of Industrial Engineering and Logistics Management
HKUST
1
IELM 3010
Operations Research I
Lecture Note 19
Introduction
Natural solutions for IP problems include
1. Solve LP rel
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW5_Solution
1.
(a) 2.4 C1 4.8
(b)
20
If new b , then
20
1 1
3 3 20 0
new b =B1b= 1 2 20 4
5 5
0
= CBB1b= 3,4 16
4
*
*
*
New Z*=16 and (x 1, x 2, x 3)=(0, 0, 4)
new
z
2.
(a)
*
*
*
*
*
New Z*=90 and ( X 1 , X 2 , X 3 , X 4 , X 5 ) (0,5,
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW5
Due in class on Oct. 27th
1. (10 Points)
.
Now you are to conduct sensitivity analysis by independently investigating each of
the following changes in the original model.
(a) Determine the allowable range to stay optimal for C1?
(b) Find th
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2015
IELM301015
HW6
Due in class on Nov. 17
1. (20points) The Energetic Company needs to make plans for the energy systems for a new building. The energy
needs in the building fall into three categories: (1) electricity, (2) heating water, and (3) heating spac
The Hong Kong University of Science and Technology
operations research
IELM 3010

Spring 2014
IELM301014
Due in Class on Nov. 26th
HW7
1.The FlyRight Airplane Company builds small jet airplanes to sell to corporations for
the use of their executives. To meet the needs of these executives, the companys
customers sometimes order a custom design of
The Hong Kong University of Science and Technology
operations research
IELM 3010

Fall 2016
IELM301015
Tutorial 9
Nov. 20th
1. You need to take a trip by car to another town that you have never visited before.
Therefore, you are studying a map to determine the shortest route to your destination.
Depending on which route you choose, there are fiv