Maximisation assignment problemsSome assignment problems require the maximisatio

Maximisation
assignment problemsSome assignment problems require the maximisation of profit
or effectiveness rather than the minimisation of costs. It is straightforward
to obtain an equivalent minimisation problem by converting all numbers in the
given data matrix to opportunity costs. This is done by subtracting every number in the original pay-off matrix from the
largest number in that matrix. You may in fact subtract them from any
number greater than or equal to the largest number. The arithmetic is often simplified
by choosing a larger number such as 100 or 1000.The transformed entries produced in this way are the opportunity
costs. We now apply the Hungarian algorithm to the transformed matrix.The optimal assignment obtained is the
optimal assignment for the original maximising problem. The total pay-off
or profit is then obtained by adding the original pay-offs of those cells used
in the optimal assignment.