ISE 204/IE 252 - HOMEWORK 3
Due: 11.05.2015 16:00
Work individually! Any detection of copying will cause you to get 0 points!
(1) State University of Urla has decided to reconstruct the sidewalks throughout the east side of its campus to provide
wheelchair access. However, upgrading sidewalks is a very expensive undertaking, so for the first phase of this project,
university administrators want to make sure they connect all buildings with wheelchair access with the minimum total length
of refurbished sidewalks possible. Following is a network of the existing sidewalk on the east side of campus, with the feet
between each building shown on the branches:
130
130
130
Determine a minimum spanning tree that will connect all the buildings on campus with wheelchair access sidewalks and
indicate the total length of sidewalk.
(2) An emergency planning team has identified five sites (A to E) for basing paramedic teams and has broken the area into six
demand regions. There are two major goals:
1. To have at least one paramedic team based at most 4 minutes away from each demand region,
2. To have at least two paramedic teams at most 6 minutes away from regions 2 and 3.
Travel time in minutes and the costs of the proposed bases are shown in the table below.
(a) Formulate an IP model to select the cities that will satisfy the team’s goals at a minimum cost.
(b) Solve the IP model by using GAMS. Submit also your GAMS input and output with your homework.
(3) A fertilizer plant can make a product by any of 3 processes. The unit production cost for each process is $15, $7, and $11
respectively. One raw material, whose availability is limited to 415 units is needed for the production process. The amount of
raw material used in each process per unit product is 2, 4, and 3 respectively. Top management wants process 1 to be used
for at least production of one unit (Any solution, where process 1 is not used at all isn’t acceptable). Time available for
production is 450 minutes, and the respective production time per unit is 4, 3, and 2 minutes. The total amount of production
should be 150 units. A fixed setup cost of $300 charged for all processes.
(a) Set up an IP model to determine how many units should be produced in each process such that the total variable
production cost is minimized.
(b) Solve the IP model by using GAMS. Submit also your GAMS input and output with your homework.
ISE 204/IE 252, Spring 2014-2015
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(4) You have been assigned to arrange the songs on the cassette version of Madonna’s latest album. A cassette tape has two
sides (1 and 2). The songs on each side of the cassette must total between 14 and 16 minutes in length. The length and type
of each song are given in table below.
Song
1
2
3
4
5
6
7
8
Type
Ballad
Hit
Ballad
Hit
Ballad
Hit and Ballad
Pop and Ballad
Ballad and hit
Length
(in
minutes)
4
5
3
2
4
3
5
4
The assignment of songs to the tape must satisfy the following conditions:
 Each side must have exactly three ballads.
 Side 1 must have at least two hit songs.
 Either song 5 or song 7 must be on side 1 (or both).
 Exactly one of songs 7 and 8 must be on side 1.
 If song 5 is on side 1, then songs 2 and 4 must be on side 2.
Construct an IP formulation to determine the arrangement of the minimum number of the songs on the tape. Do not forget to
assign each song to one and only one side of the tape.
ISE 204/IE 252, Spring 2014-2015
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