PROGLIN - Transportasi part 5 (optimasi dengan metode Modified Distribution/MoDi)

Summary

This video explains the Modified Distribution Method (MODI) for optimizing transportation costs. The process involves calculating UI (row values) and VC (column values) for each matrix cell, followed by determining the cost changes (Cij) for non-basis variables. The method proceeds through iterations, selecting negative Cij values and reallocating goods until the solution becomes optimal. The video provides step-by-step instructions, illustrating each calculation, looping process, and the final optimal solution. The total transportation cost is calculated based on the optimized allocations, with a preview of how to handle imbalanced supply and demand in future videos.

Takeaways

• 😀 The video explains the Modified Distribution Method (MODI) for solving transportation problems in operations research.
• 😀 The method involves finding values for UI (row values) and VC (column values), which are then used to determine the cost for each non-basic variable.
• 😀 The first step in MODI is to assign values for UI and VC, with U1 set to 0 and the other values calculated based on a given cost matrix.
• 😀 Once the UI and VC values are determined, the Cij (cost) for each non-basic variable is calculated using the formula Cij = Cij - UI - VC.
• 😀 If there are any negative Cij values, the solution is not optimal, and the most negative Cij is selected as the entering variable.
• 😀 The stepping stone method is employed to update the values and allocate goods to the entering variable, following a loop method.
• 😀 The process is iterative, with each iteration checking if any Cij values are still negative. If so, the loop continues with new allocations.
• 😀 After each iteration, new tables are created, adjusting the allocation and recalculating UI and VC values until no negative Cij values remain.
• 😀 When all Cij values are non-negative, the solution is considered optimal, and the total cost (TC) is calculated by multiplying the quantities with their respective costs.
• 😀 If supply and demand are not balanced, the video suggests additional techniques to handle such imbalances, which will be discussed in a subsequent video.
• 😀 The video also demonstrates step-by-step examples, using specific numbers, to show how the MODI method leads to an optimal solution for transportation problems.

Q & A

What is the Modi Method (Modified Distribution Method)?

The Modi Method is a technique used to optimize transportation problems by finding the best distribution of goods. It involves calculating UI (row values) and VC (column values), and using these to find the transportation cost for each non-basic variable.

How are UI and VC values determined in the Modi Method?

UI values are determined for each row, and VC values are determined for each column. The relationship used is: Cij = UI + VC, where Cij is the transportation cost. UI for the first row is set to 0, and other values are derived based on the transportation cost matrix.

What is the purpose of calculating Cij in the Modi Method?

Cij (cost per unit of transportation) is calculated for every non-basic variable. It helps in determining the optimal allocation by checking if any Cij is negative, indicating that the solution is not optimal.

What action is taken if Cij values are negative?

If any Cij value is negative, the solution is not optimal. The non-basic variable with the most negative Cij is chosen as the entering variable, and the allocation process is adjusted accordingly.

What is the significance of the 'loop' in the Modi Method?

The 'loop' in the Modi Method is used to adjust the allocations of goods. It follows a sequence of positive and negative steps to ensure the optimal allocation, moving from one variable to another based on the current solution.

How do you allocate goods to the entering variable?

Goods are allocated to the entering variable according to the looping process. The minimal value between the current allocation and the new potential allocation is selected, and the corresponding cells are updated.

What happens after the first iteration in the Modi Method?

After the first iteration, the new allocation is checked again for negative Cij values. If there are still negative Cij values, further iterations are conducted by choosing the next entering variable and adjusting the allocation until all Cij values are non-negative.

How is the optimal solution identified in the Modi Method?

The optimal solution is identified when there are no negative Cij values after completing an iteration. At this point, the current allocation represents the best distribution of goods at the lowest cost.

What is the process for calculating the total transportation cost?

The total transportation cost (TC) is calculated by multiplying each allocation (xij) by its respective transportation cost (Cij) and then summing up all these values.

What should be done if the supply and demand are not balanced in the transportation problem?

If the supply and demand are not balanced, a dummy variable or a balancing technique is introduced to adjust the supply or demand so that the total supply equals the total demand. This ensures the transportation problem can still be solved effectively.