MATLAB: Matrix Optimization using optimization toolbox

Question

I have a matrix with each row being a task and each column being a worker. The cells contain a performance for each worker on each task. Each worker can take up to two tasks with each task only requiring one worker. I want to alocate workers in a way that maximizes performance. How would i go about doing this?

Answer 1

Should be pretty easy with the problem-based linear program solver,

X = optimvar('X',numTasks,numWorkers,'Type','integer','LowerBound',0,'UpperBound',1);
prob = optimproblem('ObjectiveSense','maximize');
prob.Constraints.oneworker=sum(X,2)<=1;
prob.Constraints.maxTasks=sum(X,1)<=2;
prob.Objective=sum(performances(:).*X(:));
Xsolution = solve(prob);