What are the three methods of solving transportation problems?

Kickstarting the Logistics: Three Methods to Solve Transportation Problems

Transportation problems, at their core, deal with finding the most efficient and cost-effective way to distribute goods from various sources (factories, warehouses) to different destinations (markets, retailers). Solving these problems can significantly impact profitability and operational efficiency, making the initial approach critical. Before diving into optimization techniques, we need a starting point – an initial basic feasible solution. This is where methods like the North West Corner Method, the Least Cost Method, and Vogel’s Approximation Method (VAM) come into play. Each offers a distinct strategy to get the ball rolling, offering different levels of sophistication in their approach.

1. The North West Corner Method (NWCM): Simplicity at its Finest

The North West Corner Method is arguably the simplest to understand and implement. It’s a straightforward allocation strategy that focuses on starting at the “northwest” (top-left) cell of the transportation table. The principle is to allocate as much as possible to this cell, satisfying either the supply constraint of the source or the demand requirement of the destination, or both.

• How it works: Start by comparing the supply of the first source and the demand of the first destination. Allocate the minimum of these two values to the NW cell.
• Adjust: If the supply is exhausted, move down to the next row. If the demand is satisfied, move to the right to the next column. If both are satisfied, move diagonally to the next cell.
• Repeat: Continue this process of allocating and adjusting, moving east or south until all supply and demand constraints are met.

While incredibly easy to use, the NWCM doesn’t consider transportation costs. This means the initial solution it provides can often be far from optimal. It’s essentially a ‘fill-as-you-go’ approach without considering economic factors.

2. The Least Cost Method (LCM): Considering the Price Tag

Unlike the NWCM, the Least Cost Method (also sometimes called the Minimum Cost Method) considers the cost of transportation when making initial allocations. This method aims to prioritize routes with lower costs, potentially leading to a more efficient initial solution.

• How it works: Identify the cell in the entire transportation table with the lowest transportation cost.
• Allocate: Allocate as much as possible to this cell, satisfying either the supply constraint of its source or the demand requirement of its destination, or both.
• Adjust: Eliminate the row or column that is fully satisfied. If both supply and demand are met simultaneously, eliminate only one and assign zero to the remaining cell.
• Repeat: Repeat the process, always selecting the cell with the next lowest cost from the remaining unallocated cells until all supply and demand are met.

The LCM is generally considered to be better than the NWCM because it incorporates cost information, leading to a more cost-conscious initial solution. However, it only considers the immediate cost of a single allocation and may not consider the overall impact on the entire transportation plan.

3. Vogel’s Approximation Method (VAM): A Smarter Initial Guess

Vogel’s Approximation Method (VAM) takes a more sophisticated approach to finding an initial basic feasible solution. It focuses on identifying the opportunity cost associated with not using the cheapest route in each row and column. These “penalty” costs help prioritize allocations that minimize regret.

• How it works: Calculate the penalty for each row and each column by finding the difference between the two smallest costs in that row or column.
• Identify: Select the row or column with the largest penalty.
• Allocate: Allocate as much as possible to the cell with the lowest cost within the selected row or column, satisfying either supply or demand.
• Adjust: Eliminate the row or column that is fully satisfied.
• Repeat: Re-calculate the penalties for the remaining rows and columns, and repeat the allocation process until all supply and demand are met.

VAM is generally considered the most accurate of the three methods for finding a good initial solution. It considers the relative costs of different transportation routes more comprehensively than the NWCM or LCM, often resulting in an initial solution closer to the optimal one. This, in turn, can significantly reduce the number of iterations required in subsequent optimization steps.

In Conclusion: Starting Strong for Optimization Success

While the North West Corner Method, the Least Cost Method, and Vogel’s Approximation Method each provide a way to establish an initial basic feasible solution for transportation problems, they differ significantly in their complexity and effectiveness. The NWCM offers simplicity, the LCM adds cost considerations, and VAM introduces a more strategic, opportunity-cost driven approach. The choice of method depends on the specific needs and resources available, but remember, a good starting point can drastically reduce the effort required to reach an optimal transportation plan, ultimately leading to significant cost savings and improved logistics efficiency. The initial solution, regardless of how it is found, will always be subjected to a more rigorous optimization method such as the stepping stone method, or the MODI method, to arrive at the very best and most economical outcome possible.