Facilities Location Problem With MATLAB

Excellent! I solved the barebones outline for facility choice by maximizing profits.

Let us say you have three distribution businesses in three different cities: Denver, Seattle, and St. Louis. You ship the biochar from each distribution center to three other cities: LA, Topeka, and NYC. The company's demand is increasing, but the company cannot afford to build a producer and a distribution center. A new producer should be built at a currently available distribution center. Which one?

A similar question is posed by [1]. and can be answered by a Facilities Location Problem (FLP) algorithm. Here is the code, and Seattle is the winner, which matches [1].

MATLAB Code:

m = 3;  % Number of locations, producers, and distribution centers. 

n = 3;  % Number of customers

Producer = {"Denver", "Seattle", "St Louis"}; % Each Producer Ships to: LA, Topeka, and NYC.  

s = [400, 700, 600];  % Capacity, ensure this matches the number of rows of x

d = [300, 100, 500];  % Demand

c = [10, 5, 17; 11, 18, 28; 18, 3, 9];  % Variable cost like shipping.

x = optimvar('x', [m, n], 'LowerBound', 0);

maximum =[];

for i = 1:m

    prob = optimproblem('ObjectiveSense', 'maximize');

    prob.Objective = sum((100 - c(i, :)) .* x(i, :));

    % Define constraints correctly

    prob.Constraints.colsum = sum(x, 1) <= d(:').';  

    prob.Constraints.rowsum = sum(x, 2) <= s(:);  % s(:') ensures s is treated as a column vector

    % Convert problem and solve

    problemStruct = prob2struct(prob);

    [xSol, fval, exitflag, output] = intlinprog(problemStruct.f, ...

        problemStruct.intcon, problemStruct.Aineq, problemStruct.bineq, ...

        problemStruct.Aeq, problemStruct.beq, problemStruct.lb, problemStruct.ub);

    

    maximum = [maximum, abs(fval)];

    % Display results

    fprintf('The Producer is: %s\n', Producer{i});

    fprintf('The monetary value is: %.2f\n', abs(fval));

 

end

[maxValue, maxIndex] = max(maximum); 

if maxIndex == 1

    fprintf('The Producer is: %s\n', Producer{maxIndex});

    fprintf('The monetary value is: %.2f\n', maxValue); 

elseif maxIndex == 2

    fprintf('The Maximum Producer is: %s\n', Producer{maxIndex});

    fprintf('The Maximum monetary value is: %.2f\n', maxValue);

else

    fprintf('The Producer is: %s\n', Producer{maxIndex});

    fprintf('The monetary value is: %.2f\n', maxValue)

end        

End MATLAB Code.

Output:

The Maximum Producer is: Seattle

The Maximum monetary value is: 56500.00

Discussion:

The shipping costs, production values, etc are fictional and inaccurate. I am practicing and validating my code with REF [1].

References:

1. Cantlebary, Liz. Li, Lawrence. (2020). Facility location problem. Cornell University. https://optimization.cbe.cornell.edu/index.php?title=Facility_location_problem