How to solve Berlin Airlift Linear Optimization Problem

How to solve Berlin Airlift Linear Optimization Problem - Simplex LP - Сообщения

#1 Опубликовано: 19.12.2017 10:01:12
usamakhan

usamakhan

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How will you go about solving following problem in Smath

Problem statement is as follows:

Цитата

On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to supply food, clothing and other supplies to more than 2 million people in West Berlin. The cargo capacity was 30,000 cubic feet for an American plane and 20,000 cubic feet for a British plane. To break the Soviet blockade, the Western Allies had to maximize cargo capacity, but were subject to the following restrictions: No more than 44 planes could be used. The larger American planes required 16 personnel per flight; double that of the requirement for the British planes. The total number of personnel available could not exceed 512. The cost of an American flight was $9000 and the cost of a British flight was $5000. The total weekly costs could note exceed $300,000. Find the number of American and British planes that were used to maximize cargo capacity.



Based on this the author & using an online LP solver I have:

http://prntscr.com/hpk4j5

#2 Опубликовано: 19.12.2017 13:45:04
Martin Kraska

Martin Kraska

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You can use the "simplex" package in Maxima (linear optimization)

See page Examples> Maxima usage> Linear optimization in the interactive handbook.

Example maxima linear optimization.png
Example maxima linear optimization.sm (41 КиБ) скачан 47 раз(а).
Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
#3 Опубликовано: 19.12.2017 21:12:22
Jean Giraud

Jean Giraud

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How will you go about solving following problem in Smath



Maybe plot the problem 1rst ?
Next solve solely with Smath, whereas Maxima is not component of stable 6179.

CriticalRegion.PNG
#4 Опубликовано: 20.12.2017 10:22:16
usamakhan

usamakhan

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Thanks for the answers Jean would you be kind enough to attach the .sm file too. For field engineers like us your math skills seems rather cryptic & is digested properly after 2/3 days of experimenting
#5 Опубликовано: 20.12.2017 11:59:15
Jean Giraud

Jean Giraud

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Wrote

Thanks for the answers Jean would you be kind enough to attach the .sm file too.


Here is + some extra stuff. Maybe there is way to draw an inscribed 3D ?

Jean

Solve GivenFind Critical Region Copy.sm (39 КиБ) скачан 46 раз(а).

#6 Опубликовано: 20.12.2017 19:59:09
CBG

CBG

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Using Smath Studio with Maxima and the example of Martin Kraska.

Metodo_Simplex.png

Metodo_Simplex.sm (52 КиБ) скачан 39 раз(а).

Best Regards

Carlos


#7 Опубликовано: 21.12.2017 15:27:26
CBG

CBG

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Here is a small and simple Simplex algorithm without the use of the Maxima function.


Small_Simplex_algorithm.png

Small_Simplex_Algorithm.sm (16 КиБ) скачан 40 раз(а).

Best regards

Carlos


CAUTION: The algorithm is NOT TESTED, but it works well for this example.

It is necessary to refine it so that it work in all cases.
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frapuano 21.12.2017 18:37:00
#8 Опубликовано: 21.12.2017 16:10:07
Jean Giraud

Jean Giraud

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Thanks Carlos for the "Simplex algo"
#9 Опубликовано: 22.12.2017 01:40:32
CBG

CBG

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A little Simplex algorithm improved


Small_Simplex_Algorithm_Improved.sm (88 КиБ) скачан 42 раз(а).


Best regards

Carlos
#10 Опубликовано: 22.12.2017 02:46:37
CBG

CBG

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I'm sorry, I found a bug in the Simplex algorithm.

Now it's fixed.

Small_Simplex_Algorithm_Improved_2.sm (135 КиБ) скачан 54 раз(а).


Best regards

Carlos
#11 Опубликовано: 22.12.2017 10:12:27
Jean Giraud

Jean Giraud

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I'm sorry, I found a bug in the Simplex algorithm.



That huge number in the program, can be replaced by ∞ [Smath machine number]
RemToDo => check vs Mathcad
First A[i ... badly indexed.

Small_Simplex_Algorithm_Improved_2.sm (140 КиБ) скачан 48 раз(а).

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CBG 22.12.2017 12:54:00
#12 Опубликовано: 22.12.2017 12:57:52
CBG

CBG

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Thanks Jean, Now we just have to continue testing the Simplex algorithm, to identify possible faults.

regards

Carlos
#13 Опубликовано: 22.12.2017 13:38:07
Jean Giraud

Jean Giraud

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Thanks Jean, Now we just have to continue testing the Simplex algorithm, to identify possible faults.



I have tested only this one => 1/1 Mathcad 11
Gorgeous, hope for more good !

Jean

Undocumented Copy.sm (25 КиБ) скачан 52 раз(а).
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