Maximization Transportation Problem

The maximization transportation problem is similar to the minimization transportation problem, but with the objective of maximizing the total profit or revenue rather than minimizing the total cost. The goal is to determine the optimal shipment quantities from each source to each destination that maximize the total profit, subject to supply and demand constraints.

The formulation of the maximization transportation problem is as follows:

Objective function: Maximize Z = ∑∑cijxij

Subject to:

∑xij ≤ si, for i = 1, 2, …, m

∑xij ≥ dj, for j = 1, 2, …, n

xij ≥ 0, for i = 1, 2, …, m and j = 1, 2, …, n

where:

xij is the quantity of shipment from source i to destination j

cij is the profit per unit of shipment from source i to destination j

si is the supply capacity of source i

dj is the demand requirement of destination j

m is the number of sources

n is the number of destinations

To solve the maximization transportation problem, the same methods as for the minimization transportation problem can be used, such as the North-West Corner Method, Least Cost Method, Vogel’s Approximation Method, Stepping Stone Method, and Modified Distribution Method. However, the objective is to maximize the profit or revenue, so the optimal solution will be the one that maximizes the objective function Z.