Pertemuan Minggu ke 10 Part 1 Mencari Tabel Optimal Metode MODI

Introduction

This tutorial will guide you through the process of finding the optimal table using the MODI method, a technique commonly used in operations research for solving transportation problems. Understanding this method can enhance your problem-solving skills in logistics and resource allocation.

Step 1: Understand the Transportation Problem

• Familiarize yourself with the transportation problem framework, which involves minimizing shipping costs while satisfying supply and demand constraints.
• Identify the basic components:
  • Supply: The total amount of goods available from sources.
  • Demand: The total amount of goods required at destinations.
  • Costs: The shipping costs between each source and destination.

Step 2: Set Up the Initial Transportation Table

• Create a matrix that represents your supply and demand:
  • List sources in rows and destinations in columns.
  • Fill in the costs of shipping from each source to each destination.
  • Indicate supply values at the end of each row and demand values at the end of each column.

Step 3: Find an Initial Basic Feasible Solution

• Use methods such as the Northwest Corner Rule, Least Cost Method, or Vogel's Approximation Method to determine initial allocations.
  • Northwest Corner Rule: Start at the top-left corner of the table and allocate as much as possible to the first cell, then move right or down.
  • Least Cost Method: Allocate to the cell with the lowest cost first.
  • Vogel's Approximation Method: Calculate penalties for not using the lowest cost routes and allocate accordingly.

Step 4: Calculate the Initial Cost

• After filling the initial allocations, calculate the total cost by summing the products of the allocated amounts and their respective costs.
• Ensure that the total supply equals total demand to validate the solution.

Step 5: Apply the MODI Method

• Calculate the opportunity costs for each cell:

  • Assign a variable to each basic cell (allocated cell) and denote them.
  • Use the values from allocated cells to calculate the opportunity cost for each unallocated cell.

• Update the table:

  • Identify the cell with the most negative opportunity cost and prepare to adjust allocations.

Step 6: Determine the New Allocations

• Create a closed loop to adjust the allocations:
  • Identify a path through the table using the selected cell and alternate between adding and subtracting values.
  • Reallocate until no further improvements can be made.

Step 7: Check for Optimality

• Reassess the opportunity costs:
  • If all opportunity costs are non-negative, the current solution is optimal.
  • If negative costs remain, repeat Step 5 and Step 6.

Conclusion

In this tutorial, you learned how to effectively use the MODI method to find optimal solutions for transportation problems. By following these steps, you can streamline resource allocation and minimize costs. As a next step, consider applying this method to real-world logistics problems or exploring advanced optimization techniques for complex scenarios.