Business & Technology

'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:

Why a negative coefficient of variable means it is not optimal in Simplex method? Which means why we should make all coefficient non-negative(positive) for optimization of MAX linear programming problem? When we have the following MAX problem. MAX 3x + 5y This can be transformed to the Standard form: z - 3x - 5y As long as we have a negative coefficient in this standard form equation then there is still a way to increase 'z' value by increasing 'x', 'y' as well. However, when having positive one : z + 3x +5y then there is no way to increase 'z' value unless 'x' or 'y' has a negative value. Which is not available by the condition: S.T. x, y >0 Therefore, in order to find the optimum solution of MAX problem, we only need to make sure all coefficients are positive of Objective Function equation.