How does MODI algorithm find the optimal solution?

'MODI' algorithm' figures out the opportunity cost which cost can be saved if we were choose that option. So when we know the opportunity cost that is larger than the cost of chosen cells, then we can instead assign the item, for instance, into the cells having lower cost than the opportunity cost and can save the delivery cost from.


Improvement indices: l
l = cost (of cell) - u - v

In a matrix, when it comes to the optimal solution, each unoccupied cell should have non-negative 'l' improvement indices. Which means that the cost of the unoccupied cells is large enough with the opportunity cost (u, v) so that we do not have to assign items into that cell instead.

Great youtube video:

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