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

2023
Views:

484

Pages:

14
Author:

StellarStrategist

Setup AMPL Type the following commands into the console: 1. Set the solver to be CPLEX: option solver cplex; There are many solvers included with AMPL but we will mostly use CPLEX Time to solve! Type the following commands into the console: 1. Load the model: model paint.mod; 2. Solve! solve; 3. Output: CPLEX 12.7.0.0: optimal solution; objective 17433.33333 0 simplex iterations (0 in phase I) What is the solution? Display the objective function, constraint or variable: display ; For example: display totalProfit; Display all variables: display _varname, _var; Reset AMPL reset; 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 a symbolic LP to help Berkeley Paint Company maximize profit. Symbolic model n = number of paints to produce xi = Amount of paint i to produce max s.t. p1 x1 + p2 x2 + p3 x3 + ...pn xn 1 1 1 1 x + x + x + ... + x ≤t r1 1 r2 2 r3 3 rn n 0 ≤ xi ≤ ui for i = 1 ... n Or equivalently: max ∑ni=1 pi xi s.t. ∑ni=1 r1i xi ≤ t 0 ≤ xi ≤ ui for i = 1 ... n Writing a symbolic model in AMPL # parameters param n; param capacity; param profit{i in 1..n}; param r{i in 1..n}; param maxDemand{i in 1..n}; # variables var paint{i in 1..n} >= 0; # objective function maximize totalProfit: sum{i in 1..n} profit[i]*paint[i]; # constraints subject to time: sum{i in 1..n} ( 1 / r[i] ) * paint[i] <= capacity; subject to demand_limit {i in 1..n}: paint[i] <= maxDemand[i]; Save as paintSymbolic.mod Syntax comments Use more elaborate names than in your LP. param is used to define a parameter. We define an indexed variable / parameter with: { in } Typical indices are: i,j,k Range: 1..n TWO dots! Use [2] to access the second index. Summation are defined similarly: sum{ in } Indexed constraints are defined with: subject to { in }: What is missing? Data! Specifying data in AMPL param n := 2; param capacity := 40; param profit := 1 10 2 15; param r := 1 40 2 30; param maxDemand := 1 1000 2 860; Save as paintSymbolic.dat Syntax comments: Defining the value of a simple parameter: param := ; Defining the value of an indexed parameter: param := ... ; Parameters with multiple indices: Definition: { in , in } Accessing an index: [,] Example definition: var paint{i in 1..m, j in 1..n} >= 0; Example constraint: subject to demandConstraint {j in 1..n}: sum{i in 1..m} paint[i,j] = demand[j]; Data with multiple indices: param := ... ; Solving a symbolic model Load model: model paint.mod; Load data: data paintSymbolic.dat; Solve: solve; Setup AMPL - Sensitivity Analysis Type the following commands into the console: 1. Set the solver to be CPLEX: option solver cplex; 2. Enable sensitivity analysis: option cplex_options 'sensitivity'; 3. Turn off presolve (needed for sensitivity analysis): option presolve 0; 4. Load model and solve as usual. model paint.mod; solve; Sensitivity Analysis Outputs Display the objective function, constraint or variable: display ; For example: display totalProfit; Display all variables: display _varname, _var, _var.rc, _var.down, _var.current, _var.up; Display all constraints: display _conname, _con, _con.slack, _con.up, _con.current, _con.down;