Practice: Programaci on Linear. Heuristic and Optimizaci on
Ingeniera degree in Inform Attica. Course 2019-2020. Department Inform Attica
An important museum has contacted students in the course of heuristic and Optimizaci several interviews you have selected your compa~ nero and you to give soluci tECHNICAL of Programaci on Linear.
2.1. Part 1: Model B ASICO in Calc
1. Objective
The objective of this pr
resolve two types of tools: Cleaves computation and algorithms resoluci modelizaci on.
2. Problem Statement
Actica is that students learn to model problems programaci
on linear and ECHNICAL of
The museum that now work explains that est to in the process of renovaci on and wants acquire new equipment in the market to improve its facilities. One of the main reasons for preocupaci
on the museum is the gesti on their tickets. In this sense, the museum describes it has three
inputs: the main located on the east side, and two secondary located on the north side and west respectively (Figure 1 (a)).
Figure 1: (a) View of the ground and each of the inputs and (b) view of the first floor of the museum.
Currently, each entry is serviced by a only person responsible for the sale of tickets, you give her-
cripci on the premises, and access control. However, these three are insufficient to handle the volume of visitors, and each access da huge queues that make many visitors leave the hold or pre fi were visiting other places are formed. In this sense, the museum gives us the waiting time currently employs every visitor to enter the museum each entry (Table 1). Adem
on using t
on. After on several issues through
reports that each of these entries remain open for 8 hours da.
To solve this problem, the museum wants to acquire m aquinas vending tickets, turnstiles,
and hire m staff as to expedite the entry of visitors to the museum. Each of these elements allow one
as we
Input Input East West North
Standby time / visitor (min.)
130
100
90
Table 1: Timeout every visitor at every entrance.
reduce waiting each visitor to enter the museum differently. In Table 2, in the first row, it is shown reducci on in minutes per visitor. Applying these reductions, tendramos that if you install a
mAquina vending at the main entrance, the waiting time for visitors pasara 130 to 128 minutes. However, if two are installed m aquinas vending and a new person is hired for this entry, the
pasara timeout visitor to 130-122 minutes. In the second row of Table 2 the hourly cost of service of each of the elements shown.
Table 2: Informaci on on the reducci on the time and cost of m aquinas vending machines, lathes, and people you want to place the museum at each entrance.
The museum imposes some restrictions when solving the problem:
First, total spending generated by m aquinas vending machines, lathes and people Museum You want to make the da for all your entries must not exceed 1000 and.
Adem as the main entry should not exceed m 10% as expenditure for each other two tickets.
On the other hand, the sum of n umber of m aquinas vending secondary winches each entry must
be less than the same amount of the main entrance, and n umber of winches north entrance should be lower than in the west entrance. Adem
as well as mnimo, there must be two m Vending aquinas, two winches and two at the entrance principal and m Vending Aquina, a lathe and a person in each of the secondary entrances.
By Finally, it is expected that reducci on timeout per visitor at the main entrance is greater
in each of the other two inputs, since it is where they receive m as visitors.
In this part, the aim is to determine cu Al is the n umber of m aquinas vending machines, lathes and new
the museum staff should be located at each entrance to minimize the average waiting time for visitors considering all entries, and taking into account the restrictions.
It asks:
1. Model the problem as a problem of Programaci on Linear whole. 2. To implement the model on a sheet of C computation (LibreOf fi ce).
2.2. Part 2: Model advanced GLPK
The museum est very satisfied with the results we have obtained in the first part, and now poses another problem you want to solve. In particular, the museum tells us that it has acquired 8 robots (Figure 2).
These robots are able to present each of the 17 rooms that the museum is on the first floor on two wings, west and east, and est an named with a letter (Figure 1 (b)). The specifications
of each of the robots acquired by the museum are detailed in Table 3.
In the first row of Table 3 describes the time it takes for each robot to present the visitor an object of the room in which it is located.
Vending Torno Person
Reducci on hold (min./visitante)
2
3
4
cost ( and/ hour)
4
5
8
You can see, in this case, the robot R 5 is the M
as RApido to present
2
Figure 2: Example of robot acquired by the museum.
Table 3: Informaci on on each of the robots acquired by the museum.
each of these objects, and R 2 the M as slow. In the second row of Table 3 units described
energa consumed by the robot to present an object in the room, and Finally, the He describes the last row of lmite energa that the robot can consume before running out batera. The museum wants us to take care of asignaci
these robots on each of the museum. Table 4 shows the n
umber of objects containing each of these rooms. As, you can see that
rooms A, B Y C containing five items each, room D Y AND each containing six objects, and as on. A room is considerar to presented if the robot has been assigned presenting all objects of the same.
Table 4: N umber of objects in each room of the museum.
R1 R2 R3 R4
R5 R6
R7 R8
Presentaci on (min./objeto)
4
6
5
3
2
3
4
5
Energa (unid./objeto)
7
5
3
one
2
4
4
5
Lmite Energa (pcs.)
90 95 40 45 100 75 8
5 60
A, B, CD, EF, G, HI, JK, L, MN, O, P, Q
Objects
5
6
4
7
3
2
To make the asignaci Salas on robots, we must consider the following restrictions. In first
Instead, there can be m as a robot in a room, and all rooms must be assigned a robot. Adem
a robot can not be assigned less than two yam rooms as three. The museum informs us, adem
the robots R 3, R 5 Y R 6 They can not be assigned to rooms belonging to the West Wing and robots R 2 Y R 4 They can not be assigned to rooms in the east wing. On the other hand, s olo robots est rooms assigned to an A, B or
both may be assigned to C, D or both rooms. As energa consumption, a robot can not be assigned to rooms whose presentations require energa lmite than you can consume before running out batera. By
Finally, since the West Wing rooms are m great as it is required that the time presentations of the rooms in this wing is 10% greater than the time of the presentations of the rooms in the east wing.
The aim in this part is to minimize the average waiting time for visitors to access the museum by purchasing m aquinas vending machines, lathes, and staff and time presentaci
museum halls. To do this, we must take into account the restrictions imposed by the museum. It asks:
1. Model the problem as a problem of programaci linear on whole.
2. To implement the model in a modeling language m so as sticado fi (MathProg).
2.3. Part 3: An Result Alisis
on all
This section should analyze all the results obtained, describing the soluci
proving that meets the constraints of this statement) and analyze qu and est restrictions limiting an soluci on the problem.
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on obtained (com-
ace, as that
An Alisis the complexity of the problem: cu Antas variables and constraints you have de fi ned ?, amending pro- Blema, varying par ameter oa~ by adding / removing robots and explains c omo this affects the difficulty of resoluci on the resulting problem. Adem
as, you should answer the following questions: cu to is the waiting time visitor access
to enter through the main entrance? And for each of the secondary entrances? cu anto time you llevar all rooms of the museum? qu and robots encargar an to make the presentaci on in each of these rooms? It also discusses the advantages and disadvantages of the two tools used in the course: LibreOf fi ce and GLPK.
2.4. Extra part: Problem Programaci on Din Amica
to visit
Given the success that has seen the model proposed for the museum, after about das contacts
us again to solve other problems: the distribution of some of his artworks to other museums that perform temporary exhibitions. To make the deal, the museum has a only cami on, which has the capacity to meet all orders received.
Before you start with the cast should develop a road map. The goal is to define a delivery route so that it begins at the museum home visit every destination a only once and return to the starting point. Assuming that the deal can be done in working hours without refueling, you are asked: carry out a program to decide the itinerary using
programaci
to receive a plain text fi le that contendr Museum origin, which are identified car fi input file:
on din amica to minimize path length. The program
the distance matrix between all destinations, including the
to with the string MO. A continuaci
M1 M2 M3 M4 MO MO 0
24 16 2. 3 24
M1 16 0 27 14 eleven M2 fifteen 14 0 16 27 M3 14 22 19 0 2. 3 M4 13 eleven 26 18 0
on an example shown
For testing purposes, it is recommended to randomly generate fi les with different n
destination, assuming uniform distributions between 10 and 30 kil ometros for distances. It should be that the distance of a localizaci on as same must be zero, so the main diagonal of the
matrix must be 0.
Should to surrender the program in the language desired by a bash script to run it:
itinerario.sh. This script recibir as an argument to the le fi distances and imprimir 2 lneas: the first indicates the total distance of the route and the second route formed. A continuaci shows an example of output fi le:
Total distance: 78 Itinerary: MO, M2, M3, M1, M4, MO
As you can see the routes begin and fi nalizan in the museum home, passing a each museum. Memory deber documented an programaci equations
as possible additional optimizations that help make the program m
answered the following questions:
Whether to make deliveries to 100 different museums, cu Al is the n umber of combinations hara one brute force algorithm ?. cu Al is the n umber of combinations to consider your soluci on?
umber of museums
to the screen on it
only once Amica employed, as
on din
as efficient. Adem as should
Sera m efficient as the ejecuci on the algorithm if the museums were ordered in funci criterion?
on the alg a
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Now imagine that instead of wanting to calculate the route m as short, ie, a path whose length was the mnima possible, I would get all routes mnima length. Possible Sera by programaci
on din Amica? Justifies reply 3. Guidelines for Memory
Memory must be submitted in .pdf format and have a m cover andndice. At least, must contain:
1. Brief introducci on explaining the contents of the document. 2. Descripci on models, arguing decisions.
3. An parsing the results.
4. Conclusions on the pr Actica.
The memory should not include C Odigo source in ning A case. 4. Evaluaci on
the evaluaci on the pr Actica is realizar to about 10 points. For the pr
at least paragraph 1 and memory. the distribuci 1. Part 1 (3 points)
Modelizaci on the problem (1 point) Implementaci on the model (2 points)
2. Part 2 (5 points)
Modelizaci on the problem (3 points) Implementaci on the model (2 points)
3. Part 3 (2 points)
4. Extra Part: Programaci on Din amica (1 point)
on points it is as follows:
aximum of 15 sheets in total, including the cover,
Actica be evaluated deber
to be held
In evaluaci on the modelizaci on the problem, a correct model supondr To give the other points, the modelizaci on the deber problem to:
It is formalized in the memory correctly. Preferably be simple and concise. Be well explained (it must be made
half of the points.
clear cu
Justi fi ed in memory all decisions dise~
In evaluaci on the implementaci To give the other points, the implementaci
to is the utility of each variable / restricci untaken.
on the model, a correct model supondr on the deber problem to:
on).
half of the points.
on) capabilities that provide the tools to do / actua-
as simple as possible (for example, use SUMPRODUCT if possible in the
computation or use of sets in MathProg).
Keep c Odigo (sheet c computation of fi les MathProg) properly organized and commented.
Use (in implementaci Lizar the model as m If the sheet c
Names should be descriptive. Should to understand it. In
scoring An parsing results is valorar personal tions about the difficulty of pr
Ana nadirse comments in cases where necessary
positively the fact to include in the memory conclusions Actica and what they learned during their elaboraci on.
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Important: the models implemented in sheet C computation and GLPK must be correct. That is, they must operate and obtain solutions optimas the problem that is requested. in ning one case obtendr to qualify caci 1 point higher than a model that is not correct. Therefore, if no est Part 1 correctly completed,
the mnote axima ser at 1 point and, if not part 2 est correctly completed, as much obtendr
caci qualify on 4 points.
5. Delivery
You have the deadline to deliver the pr Actica until October 27 at 23:55. The deadline is fi rm and not to extend to.
Solo one member of each pair of students must rise:
A only file fi. zip the secci on the pr Global Classroom That Work called delivery Pr Actica 1 .
The fi le should be appointed p1-NIA1-NIA2.zip, where nia1 Y nia2 are the dgitos the last 6 NIA (filling with 0 s on the left if necessary) of each partner. Example: p1-054000-671342.zip.
In pdf format memory must be delivered to trav Turnitin is the link called delivery Report Pr Actica 1 .
The report must be delivered in pdf format and must be named Nia1-NIA2.pdf -despu NIA conveniently each student. Example: 054000-671342.pdf.
the descompresi on the le fi delivered must first create a directory called Nia1-nia2,
where nia1 Y nia2 are the last 6 dgitos NIA (filling with 0 s on the left if necessary)
of each partner. This directory should contain: first, the same memory in pdf format that has been given to trav
on a
Turnitin is, and must be called Nia1-NIA2.pdf -despu It is to replace expediently NIA mind of every student; Second, a fi le called AUTHORS.txt to identify that each author of the pr
Actica in each lnea in the format: NIA Last Name, First Name. For example:
Von Neumann 054000, 671342 John Turing, Alan
Adem ace, this directory must produce at least two directories named exactly Part 1 Y part 2 . If extra part (of Programaci surrender on Din Amica), then you must include a third
directory part 3 That contains it.
It shows continuaci on one distribuci possible on the fi le resulting from descompresi on:
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It is to replace
p1-054000-671342 /
054000-671342.pdf
AUTHORS.txt
part-1 /
part-1.ods
part-2 /
part-2.dat
part-2.mod
part-3 /
part-3.cc
itinerario.sh
Important: Failure to follow the rules of delivery can be a p the end of the pr Actica.
oss of up to 1 point in the qualify caci on
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