University:
University of California, Berkeley
Course:
COMPSCI 61B | Data Structures
Academic year:

2023
Views:

35

Pages:

10
Author:

StellarStrategist

AMPL Tutorial Linear Programming n min(max) ∑i=1 ci xi ≤ n s.t. ∑i=1 a1i xi (= ) b1 ≥ ≤ n ∑i=1 a2i xi (= ) b2 ≥ ⋮ n ∑i=1 xi - decision variables, aji , ci , bj - problem data ≤ ami xi (= ) ≥ bm Installation Instructions 1. Download AMPL MacOS: http://ampl.com/demo/amplide.macosx64.tgz Windows: http://ampl.com/demo/amplide.mswin64.zip Linux: http://ampl.com/demo/amplide.linux64.tgz 2. Extract the archive. 3. In the amplide folder, you should find the amplide application. 4. Open the amplide application. 5. Type into the console: printf "Hello World!\n"; 6. Press Enter. 7. If it prints Hello World! , then you are done! Special Instrustion for Mac OSX Special note for users of macOS 10.12 Sierra: As a side-effect of a new security feature introduced with this version, you may see an error message beginning The IDE cannot find the AMPL executable... To fix this problem, quit the IDE application and then follow these steps: (1) In your amplide.macosx64 folder, find the Amplide file (with a cat's head icon). (2) Drag the Amplide file to your desktop. (3) Drag the Amplide file back into the amplide.macosx64 folder. (4) Then double-click the file icon to start the AMPL IDE again. AMPL IDE Modelling: Berkeley Paint Company Berkeley Paint Company makes two colors of paint: Blue and Gold The type of paints have the following characteristics (per gallon): Paint Profit (pi ) Production/hour (ri ) Blue Gold 10 15 40 30 Maximum demand (ui ) 1000 860 Berkeley Paint Company has 40 hours of production capacity available to produce paint. Formulate an LP to help Berkeley Paint Company maximize profit. Model x1 = Amount of Blue paint to produce x2 = Amount of Gold paint to produce max s.t. 10x1 + 15x2 (1/40)x1 + (1/30)x2 ≤ 40 x1 ≤ 1000 x2 ≤ 860 x1 ≥ 0 x2 ≥ 0 Formulating the model in AMPL # variables var PaintB; var PaintG; # objective function maximize totalProfit: 10 * PaintB + 15 * PaintG; # constraints subject to time: (1/40)*PaintB + (1/30)*PaintG <= 40; subject to blue_limit: 0 <= PaintB <= 1000; subject to gold_limit: 0 <= PaintG <= 860; Another way to write it # variables var PaintB >= 0; var PaintG >= 0; # objective function maximize totalProfit: 10 * PaintB + 15 * PaintG; # constraints subject to time: (1/40)*PaintB + (1/30)*PaintG <= 40; subject to blue_limit: PaintB <= 1000; subject to gold_limit: PaintG <= 860; Save as paint.mod Comments on Syntax # starts a comment All lines of code end with a ; Variables are declared with var The objective function has the following format: maximize : ; or minimize : ; The constraints have the following format: subject to : ; Names must be unique. Also, a variable and constraint cannot have the same name. AMPL is case sensitive. Keywords must be lower case.