Least Cost Cell Method | In case of Tie | Transportation Problem in Operations research | Kauserwise

Kauser Wise

13 Oct 202206:56

Summary

TLDRThis video tutorial focuses on solving a balanced transportation problem using the least cost cell method. The presenter guides viewers through the process of finding an initial basic feasible solution by selecting the least cost cell and allocating resources based on supply and demand. The video includes a step-by-step demonstration using a cost matrix with three sources and four destinations, and it concludes with the calculation of the total transportation cost. Viewers are encouraged to explore more videos on the topic and on handling unbalanced transportation problems.

Takeaways

🚚 The video is a tutorial on solving transportation problems using the least cost cell method.
🔍 The presenter begins by ensuring the transportation problem is balanced, confirming that the total supply equals the total demand.
📊 A cost matrix with three sources and four destinations is provided, with specific supply and demand figures.
📝 The least cost cell method involves selecting the cell with the lowest cost to start the allocation process.
✂️ After allocating, cells that are fully utilized are 'deleted' from further consideration.
🔄 In case of a tie in the lowest cost, the presenter explains how to choose the cell that allows for the maximum allocation.
🔄 The term 'Thai' is mentioned to describe a situation where the same cost value appears in multiple cells.
📉 The process is iterative, with the presenter repeatedly selecting the least cost cell and allocating resources until all cells are utilized.
📋 The video concludes with a calculation of the total transportation cost based on the allocations made.
🎥 A follow-up video is teased, which will cover solving unbalanced transportation problems using the same method.

Q & A

What is the main topic of the video?
-The main topic of the video is solving the Transportation Problem using the least cost cell method.
What is the first step in solving a Transportation Problem as described in the video?
-The first step in solving a Transportation Problem is to check whether the problem is balanced or unbalanced by comparing the total supply with the total demand.
How is a balanced Transportation Problem defined in the video?
-A balanced Transportation Problem is defined as one where the total supply equals the total demand.
What is the total supply and demand in the given problem according to the video?
-The total supply is 600 units (150 + 200 + 250) and the total demand is also 600 units (125 + 175 + 200 + 100), making the problem balanced.
What is the least cost cell method as explained in the video?
-The least cost cell method is a technique used to solve Transportation Problems by selecting the cell with the lowest cost in the cost matrix and allocating the minimum of the corresponding supply and demand to that cell.
What is the procedure when a tie occurs in the least cost cell method, as described in the video?
-When a tie occurs, meaning the same lowest cost is found in multiple cells, the procedure is to select the cell that allows for the maximum allocation based on the remaining supply and demand.
How does the video demonstrate the allocation of the least cost cell?
-The video demonstrates the allocation by comparing the demand and supply for the selected cell, allocating the minimum of the two, and then updating the matrix by cancelling the row or column if the supply or demand is met.
What is the total transportation cost calculated at the end of the video?
-The total transportation cost calculated at the end of the video is 900 rupees.
What is the next topic the video series will cover according to the video?
-The next topic the video series will cover is how to solve unbalanced Transportation Problems using the least cost cell method.
How can viewers find more videos on this topic as mentioned in the video?
-Viewers can find more videos on this topic by looking in the description box of the video for links to additional related content.

Outlines

00:00

📚 Introduction to Solving Transportation Problems with Least Cost Cell Method

This paragraph introduces the video's focus on solving transportation problems using the least cost cell method. The presenter explains that this video is a continuation of a series on transportation problems and provides links to previous videos in the description box. The video aims to find an initial basic feasible solution to a given transportation problem with a cost matrix that includes three sources and four destinations, along with their respective demands and supplies. The presenter checks if the problem is balanced by comparing the total supply with the total demand, confirming that it is a balanced problem. The solution process involves selecting the least cost cell and allocating the minimum of the demand and supply to that cell, then repeating the process until all cells are allocated or canceled. The paragraph concludes with the allocation of 150 units to the least cost cell, leaving a balance of 25 in the supply.

05:04

🔍 Allocating Maximum Values in Case of Ties Using Least Cost Cell Method

This paragraph continues the explanation of the least cost cell method by addressing ties in the cost matrix. When two cells have the same least cost, the presenter advises selecting the cell that allows for the maximum allocation. The process involves comparing the remaining demand and supply for each cell and choosing the one that maximizes allocation. The presenter demonstrates this by allocating 125 units to one cell and then canceling the column. The process is repeated, and another tie occurs with two cells having the same cost. The presenter again selects the cell that allows for the maximum allocation, which is 150 units, and cancels the row. The video concludes with the final allocation of 25 units to the last undeleted cell, resulting in all cells being canceled and the total transportation cost being calculated as 900 rupees. The presenter thanks the viewers and encourages them to like, comment, subscribe, and share the video, promising to cover unbalanced transportation problems in the next video.

Mindmap

Keywords

💡Transportation Problem

A transportation problem is a classic linear programming issue that deals with the most cost-effective way to transport goods from multiple sources to multiple destinations, given the supply at each source and the demand at each destination. In the video, the theme revolves around solving such problems using a specific method known as the least cost cell method.

💡Least Cost Cell Method

The least cost cell method is a technique used to find an initial basic feasible solution for a transportation problem. It involves selecting the cell with the lowest cost in the cost matrix and allocating the minimum of the supply and demand to that cell. The method is central to the video's demonstration of solving a balanced transportation problem.

💡Cost Matrix

A cost matrix is a table that lists the costs associated with transporting goods from each source to each destination. In the video, the cost matrix is used to identify the least cost cell, which is the starting point for the allocation process in the least cost cell method.

💡Initial Basic Feasible Solution

An initial basic feasible solution is a starting point for solving linear programming problems that satisfies all constraints. In the context of the video, finding an initial basic feasible solution is the first step in solving the transportation problem using the least cost cell method.

💡Balanced Transportation Problem

A balanced transportation problem is one where the total supply equals the total demand. In the video, it is mentioned that the problem at hand is balanced, as the total supply (600) matches the total demand (600), which allows for a straightforward application of the least cost cell method.

💡Supply and Demand

Supply refers to the amount of goods available at each source, while demand is the amount required at each destination. In the video, the supply and demand figures are crucial for determining allocations and ensuring that the transportation plan meets all requirements without surplus or shortage.

💡Dummy Column/Row

A dummy column or row is a concept mentioned in the video for dealing with unbalanced transportation problems. If the total supply does not equal the total demand, a dummy column or row is added to balance the problem, allowing the application of the least cost cell method.

💡Allocation

Allocation in the context of the video refers to the process of assigning quantities to cells in the cost matrix based on the least cost cell method. It is a step-by-step process that involves comparing supply and demand to determine how much of a good should be transported from a source to a destination.

💡Tie

A tie occurs when two or more cells have the same least cost value, as mentioned in the video. In such cases, the decision on which cell to allocate involves considering which allocation would result in the maximum quantity being transported, as illustrated by the choice between allocating 125 or 100 in the video.

💡Total Transportation Cost

The total transportation cost is the sum of the costs associated with all the allocations made in the cost matrix. In the video, the presenter calculates this by multiplying the allocated quantities by the corresponding costs and summing them up, resulting in a total cost of 900 rupees.

💡Unbalanced Transportation Problem

An unbalanced transportation problem is one where the total supply does not equal the total demand. The video briefly mentions that this type of problem would require a different approach, such as adding a dummy column or row, which will be covered in a separate video.

Highlights

Introduction to solving Transportation problems using the least cost cell method.

Providing a list of videos on the topic of Transportation problems.

Explaining the importance of checking whether a Transportation problem is balanced or unbalanced.

Demonstrating how to find the total supply and demand to determine if the problem is balanced.

Discussing the necessity of adding dummy columns or rows for unbalanced problems.

Guiding viewers on how to select the least cost in the cost Matrix.

Allocating the minimum value between demand and supply to the selected cell.

Deleting the row or column once all cells in it have been allocated.

Handling ties in the cost Matrix by selecting the cell that allows for maximum allocation.

Comparing demand and supply to decide on allocation amounts in case of ties.

Allocating the maximum possible amount to the selected cell in case of a tie.

Continuing the allocation process until all cells are canceled.

Calculating the total transportation cost using the allocated values.

Providing the final transportation cost as 900 rupees.

Announcing the next video's focus on solving unbalanced Transportation problems using the least cost cell method.

Encouraging viewers to like, comment, subscribe, and share the video.