# Job Assignment Problem Using Branch And Bound Algorithm

January 21st, 2017, 10:35 AM#1

## Job assignment problem solve with Branch and Bound algorithm

I started doing Branch and Bound Algorithm for assignment problem in C++ and i can't find the right solution. First of all assignment problem example:

Ok so each person can be assigned to one job, and the idea is to assign each job to one of the person so that all the jobs are done in the quickest way.

Here is my code so far:I know i might be out of track. I didn't use lower bound in the beginning, i'm actually a little confused how this algorithm exactly works. So even step by step walktrough through the algorithm would be helpful.Code:

#include "Matrix.h" // Program to solve Job Assignment problem // using Branch and Bound #include <limits.h> #include <vector> #include <algorithm> using namespace std; template<class T> NUM getCost(Matrix& matrix, size_t x, size_t y, vector<bool>& colUsed); void run(Matrix& matrix, vector<size_t>& assignedJobs); int main() { Matrix matrix; matrix.setMatrix(N); matrix.print(); vector<size_t> assignedJobs; run(matrix, assignedJobs); cout << assignedJobs[0]; /* cout << "size:E " << v.size() << endl; for (vector<NUM>::iterator i = v.begin(); i != v.end(); i++) { cout << *i << endl; } */ return 0; } // remember to use x only LOCALLY!!! NUM getCost(Matrix& matrix, size_t x, size_t y, vector<bool>& colUsed) { // pathCost NUM pathCost = matrix.matrix[x++][y]; for (size_t col = 0; col < matrix.size(); col++) { if (!colUsed.at(col)) { NUM min = #if defined NUM_INT INT_MAX; #endif #if defined NUM_DBL DBL_MAX; #endif size_t row = x; for (; row < matrix.size(); row++) { if (min > matrix.matrix[row][col]) { min = matrix.matrix[row][col]; } } pathCost += min; } } return pathCost; } void run(Matrix& matrix, vector<size_t>& assignedJobs) { // array of used columns vector<bool> colUsed; for (size_t i = 0; i < matrix.size(); i++) { colUsed.push_back(false); } for (size_t row = 0; row < matrix.size(); row++) { size_t col = 0; // bombona while (colUsed.at(col++)); col--; // choose the best job for the current worker vector<NUM> jobs; // get all the job costs from which to choose the smallest // row++ jobs.push_back(getCost(matrix, col, row, colUsed)); // iterator at the position of the smallest element of jobs vector<NUM>::iterator i_min = min_element(jobs.begin(), jobs.end()); // index of the smallest element in jobs size_t index = (size_t)distance(jobs.begin(), i_min); colUsed.at(index) = true; assignedJobs.push_back(index); } }

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