Mathematical formulation of a operations research problem

How can I implement this objective function and its constraints in Matlab (p-median problem)?

Thank you very much!

[darova]

I can give you a start

y = zeros(1,10);
y = facility == candidate;

Answer 1

[Hasan Cosgun]

nNodes = 52; % no of nodes (customers)
nP = 6; % No of Warehouses/Facilities
% dist: nNodes x nNodes distance matrix

% decision variables
x = optimvar('x',1,nNodes,'Type','integer','LowerBound',0,'UpperBound',1);
y = optimvar('y',nNodes,nNodes,'Type','integer','LowerBound',0,'UpperBound',1);

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

prob.Objective = sum(sum(dist .* y)); 

onesum = sum(y,2) == 1;

vertxy = optimconstr(nNodes,nNodes);

for i=1:nNodes
    for j=1:nNodes
        vertxy(i,j) = y(i,j) <= x(j);
    end
end

depsum = sum(x) == nP;

prob.Constraints.onesum = onesum;
prob.Constraints.vertxy = vertxy;
prob.Constraints.depsum = depsum;

nSolution  = solve(prob);

Just a full start...

[David Franco]

Thank you very much @Hasan Cosgun!!! I updated your code with an example:

% P-Median Problem (PMP)

rng default

nNodes = 32; % No of Customers
nP = 6; % No of Facilities

xx = randi(20,nNodes,2);

dist = pdist2(xx,xx,'euclidean');

% decision variables
y = optimvar('y',1,nNodes,'Type','integer','LowerBound',0,'UpperBound',1);
x = optimvar('x',nNodes,nNodes,'Type','continuous','LowerBound',0);

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

prob.Objective = sum(sum(dist .* x));

onesum = sum(x,2) == 1; % Restriction 1

depsum = sum(y) <= nP; % Restriction 2

vertxy = optimconstr(nNodes,nNodes);

for i = 1:nNodes
    for j = 1:nNodes
        vertxy(i,j) = x(i,j) <= y(j); % Restriction 3
    end
end

prob.Constraints.onesum = onesum;
prob.Constraints.depsum = depsum;
prob.Constraints.vertxy = vertxy;

[sol,fval,exitflag,output]  = solve(prob);

Solving problem using intlinprog.
LP:                Optimal objective value is 82.069171.                                            


Optimal solution found.

Intlinprog stopped at the root node because the objective value is within a gap tolerance of the optimal value, options.AbsoluteGapTolerance = 0 (the default value). The intcon variables are integer within tolerance,
options.IntegerTolerance = 1e-05 (the default value).

z = 1:nNodes;

idx = sum(sol.x .* z(ones(nNodes,1),:),2);

h1 = gscatter(xx(:,1),xx(:,2),idx);
hold on
h2 = plot(xx(sol.y == 1,1),xx(sol.y == 1,2),'ko');
legend('Location','eastoutside')

h2.Annotation.LegendInformation.IconDisplayStyle = 'off';

Answer 2

[Matt J]

Should be very easy with the Problem-Based Optimization Workflow.

[David Franco]

Thank you Matt, I will try this.