How to solve Berlin Airlift Linear Optimization Problem

#1 Pubblicato: 19/12/2017 10:01:12

7 apprezzamenti in 97 post.

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How will you go about solving following problem in Smath

Problem statement is as follows:

Citazione
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 Pubblicato: 19/12/2017 13:45:04

Martin Kraska

1.361 apprezzamenti in 2.275 post.

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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.sm (41,89 KiB) scaricato 1210 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

#3 Pubblicato: 19/12/2017 21:12:22

Jean Giraud

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Wrote
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.

#4 Pubblicato: 20/12/2017 10:22:16

usamakhan

7 apprezzamenti in 97 post.

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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 Pubblicato: 20/12/2017 11:59:15

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 (39,35 KiB) scaricato 1238 volta(e).

#6 Pubblicato: 20/12/2017 19:59:09

CBG

78 apprezzamenti in 312 post.

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

Metodo_Simplex.sm (52,26 KiB) scaricato 1245 volta(e).

Best Regards

Carlos

#7 Pubblicato: 21/12/2017 15:27:26

CBG

78 apprezzamenti in 312 post.

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

Small_Simplex_Algorithm.sm (16,35 KiB) scaricato 1265 volta(e).

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.

1 utenti hanno apprezzato questo post

frapuano 21/12/2017 18:37:00

#8 Pubblicato: 21/12/2017 16:10:07

Jean Giraud

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Thanks Carlos for the "Simplex algo"

#9 Pubblicato: 22/12/2017 01:40:32

CBG

78 apprezzamenti in 312 post.

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A little Simplex algorithm improved

Small_Simplex_Algorithm_Improved.sm (88,5 KiB) scaricato 1215 volta(e).

Best regards

Carlos

#10 Pubblicato: 22/12/2017 02:46:37

CBG

78 apprezzamenti in 312 post.

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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 (135,66 KiB) scaricato 1242 volta(e).

Best regards

Carlos

#11 Pubblicato: 22/12/2017 10:12:27

Jean Giraud

983 apprezzamenti in 6.866 post.

Gruppo: User

Wrote
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 (140,42 KiB) scaricato 1248 volta(e).

1 utenti hanno apprezzato questo post

CBG 22/12/2017 12:54:00

#12 Pubblicato: 22/12/2017 12:57:52