Operation Research Transportasi Stepping Stone Tahap-1 (www.bienecenter.com)

Introduction

This tutorial provides a step-by-step guide to solving transportation problems using the Stepping Stone method, specifically focusing on Stage 1. Transportation problems are a key aspect of operations research and involve finding the most efficient way to distribute goods from multiple suppliers to multiple consumers while minimizing costs. Understanding this method can significantly enhance your analytical skills in logistics and supply chain management.

Step 1: Understanding the Transportation Problem

• Define the problem: Identify suppliers, consumers, supply quantities, demand quantities, and transportation costs.
• Set up the cost matrix: Create a matrix that outlines the costs associated with transporting goods from each supplier to each consumer.

Step 2: Initial Feasible Solution

• Choose a method: Use methods such as the North-West Corner Rule, Least Cost Method, or Vogel's Approximation Method to find an initial basic feasible solution.
• Calculate allocations: Fill in the matrix with allocations based on your chosen method while ensuring that supply and demand constraints are met.

Step 3: Identify the Basic Feasible Solution

• Mark allocations: Identify which cells in your cost matrix have been filled based on your allocations. These are your basic variables.
• Check for optimality: Ensure that the total cost is minimized using the current allocations.

Step 4: Applying the Stepping Stone Method

• Select an unoccupied cell: Choose a cell in the cost matrix that has not been allocated.
• Create a loop: Draw a closed loop connecting the selected cell to the occupied cells. Alternate between adding and subtracting allocations along the loop.
• Calculate the opportunity cost: Determine the effect on the total cost if one unit is transported through the unoccupied cell.

Step 5: Update Allocations

• Adjust allocations: If the opportunity cost is negative, increase the allocation in the unoccupied cell and adjust the allocations in the occupied cells within the loop accordingly.
• Recalculate totals: Update the total transportation cost based on the new allocations.

Step 6: Repeat the Process

• Iterate through steps: Continue identifying unallocated cells, creating loops, and adjusting allocations until no further improvements can be made.
• Check for optimality: Ensure all opportunity costs are non-negative, indicating that the solution is optimal.

Conclusion

By following these steps, you can effectively solve transportation problems using the Stepping Stone method. This method allows for iterative improvement of your solution until you reach optimal costs. To deepen your understanding, consider applying this method to different scenarios or exploring further into operational research techniques. For more detailed examples and applications, visit www.bienecenter.com.