Stepping stone method

Definition

The stepping stone method is an iterative algorithm used to find an optimal solution for the transportation problem by adjusting the distribution of goods from multiple suppliers to multiple consumers. This method identifies a series of improvements that can be made to the current solution by analyzing potential routes, moving along a 'stepping stone' path, and adjusting quantities accordingly until the optimal distribution is achieved. The process helps identify if any unused routes can lead to a lower cost solution, emphasizing cost efficiency and optimal allocation.

5 Must Know Facts For Your Next Test

1. The stepping stone method relies on the concept of 'stepping stones' that represent potential improvements in routing that could reduce transportation costs.
2. In this method, unused routes are evaluated to determine if they can provide a lower-cost option by reallocating shipments between sources and destinations.
3. The stepping stone method is often used after finding an initial basic feasible solution using other methods like the northwest corner rule or the least cost method.
4. It provides a systematic way to explore different shipping paths, allowing for continuous improvement of the initial solution until no further reductions in cost are possible.
5. This method is especially useful when dealing with large-scale transportation problems where visualizing all potential routes can be complex.

Review Questions

• How does the stepping stone method improve upon an initial basic feasible solution in solving transportation problems?
  • The stepping stone method improves upon an initial basic feasible solution by systematically evaluating unused routes to see if reallocating shipments can lower overall transportation costs. By tracing potential 'stepping stones', it identifies opportunities for redistributing shipments along different paths. This iterative process continues until no further cost reductions are achievable, leading to an optimal solution that maximizes efficiency.
• Discuss the steps involved in applying the stepping stone method and how they contribute to finding an optimal solution.
  • Applying the stepping stone method involves several key steps: first, identify the basic feasible solution; then, select unused routes and calculate potential costs for each. Next, analyze these routes using a matrix to find 'stepping stones' that represent possible adjustments. The adjustments are made based on the cost implications until no further improvements are found. This structured approach allows users to systematically optimize their distribution strategy.
• Evaluate the effectiveness of the stepping stone method compared to other methods for solving transportation problems and discuss potential limitations.
  • The stepping stone method is effective in refining initial solutions and identifying optimal distributions due to its systematic evaluation of unused routes. Compared to methods like the simplex or transportation simplex methods, it is often more intuitive and easier for beginners to grasp. However, one limitation is that it may require multiple iterations, which can be time-consuming for very large problems. Additionally, it may not always guarantee finding an optimal solution if initial conditions are not favorable.

Related terms

Transportation problem: A type of linear programming problem that focuses on finding the most cost-effective way to distribute goods from several suppliers to several consumers.

Basic feasible solution: A solution that meets all supply and demand constraints in a transportation problem, using the minimum number of routes required for distribution.

Optimal solution: The best possible outcome in a linear programming problem, where the objective function is maximized or minimized while satisfying all constraints.