Understanding Transportation Problems

Transportation problems are a category of linear programming problems. They need to be solved in a process known as optimisation.
The goal of solving transportation problems is to identify the best or most efficient way to transport goods or services from several sources (like factories) to several destinations (like warehouses or customers), while attempting to minimise cost or time.
These problems regularly involve minimising cost, but they may also involve maximising an aspect like profit, depending on the context.

Formulating Transportation Problems

A transportation problem’s objective function seeks to minimise total transportation costs while meeting the constraints of supply and demand.
In these problems, origin points or sources represent locations where goods are produced, stored, or supplied.
Destination points or sinks represent locations where goods are needed or demand must be met.
Problems use variables to denote the quantity of the goods being transported from each source to each sink.
Equations are then used to represent the aggregate supply available at each source and the required demand at each sink.

The first step in solving transportation problems is to create a transportation table to organise and represent all data.
The North-West Corner Method, Least Cost Method, or Vogel’s Approximation Method are initial allocation approaches that can be used to generate an initial feasible solution.
Once an initial feasible solution is found, it is optimised using the Stepping Stone Method or the Modified Distribution Method (MODI).
The Row Minima Method and the Column Minima Method are reduction methods employed when finding optimal solutions.

Transportation problems have applications across various industries such as logistics, manufacturing, transportation, military logistics and supply chain management.
It’s essential for understanding and practising how to model and solve specific transportation problems, as real-world cases might not be ‘textbook’ examples and may require adjusting the model or applying different techniques.