


Cost Matrix:

Define:

min: 1x_{11} + 4x_{12} + 5x_{13} + 5x_{21} + 7x_{22} + 6x_{23} + 5x_{31} + 8x_{32} + 8x_{33} s.t.: x_{11} + x_{12} + x_{13} = 1 // Worker 1 gets 1 job x_{21} + x_{22} + x_{23} = 1 x_{31} + x_{32} + x_{33} = 1 x_{11} + x_{21} + x_{31} = 1 // Job 1 assigned to 1 worker x_{12} + x_{22} + x_{32} = 1 x_{13} + x_{23} + x_{33} = 1 x_{ij} = 0, or 1 
Solution:
Value of objective function: 15.00 Actual values of the variables: x11 0 x12 1 x13 0 x21 0 x22 0 x23 1 x31 1 x32 0 x33 0 

We can exploit the structure to improve the performance of the Simplex Algorithm for some special type of problem.
