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Questions and Answers
What is the purpose of Phase I in the solution of a transportation problem?
What method is NOT used for obtaining the Initial Basic Feasible Solution in transportation problems?
What characterizes a loop in the context of a transportation problem?
According to the provided text, which method is used for obtaining the Optimum Basic Solution in a transportation problem?
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In a balanced transportation problem with 3 supply points and 4 demand points, how many variables should contain no loop to yield a basic solution?
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Why do the cells represented by a loop in a transportation problem indicate an issue?
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What is the primary objective of applying the transportation problem?
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What type of transportation problem is relatively easy to solve due to binding constraints?
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How is a transportation problem balanced when the total supply exceeds the total demand?
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What happens if the total supply is less than the total demand in a transportation problem?
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What is a transportation tableau used for in a transportation problem?
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How are shipments to a dummy demand point in a transportation problem assigned?
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What is the primary objective in a transportation problem?
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Why is the simplex method not suitable for solving transportation problems?
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What is the relationship between the cost of shipping and the number of units shipped?
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What is the representation of the supply at source i?
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What is the goal of finding the minimum-cost distribution of a given commodity?
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What are the two groups involved in the transportation problem?
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Study Notes
Transportation Problem
- A transportation problem is a special type of Linear Programming Problem (LPP) that aims to minimize the cost of distributing a product from multiple sources to multiple destinations.
- The problem has a special structure, making the usual simplex method unsuitable for its solution.
Phases of Solution
- Phase I: Obtains the initial basic feasible solution using methods such as:
- North West Corner Rule (NWCR)
- Least Cost Method (LCM)
- Vogel Approximation Method (VAM)
- Phase II: Obtains the optimal basic solution using methods such as:
- Stepping Stone Method
- Modified Distribution Method (MODI Method)
Initial Basic Feasible Solution
- NWCR: starts with the top-left cell and moves to the right or down, allocating as much as possible to each cell.
- LCM: selects the cell with the lowest cost and allocates as much as possible to that cell.
- VAM: calculates the penalty and selects the cell with the highest penalty.
Loop and Path
- An ordered sequence of at least 4 different cells is called a loop if:
- Any 2 consecutive cells lie in either the same row or same column.
- No 3 consecutive cells lie in the same row or column.
- The last cell in the sequence has a row or column in common with the first cell.
Theorem
- In a balanced transportation problem, the cells corresponding to a set of (m + n – 1) variables contain no loop if and only if the (m + n – 1) variables yield a basic solution.
Application of Transportation Problem
- Minimize shipping costs
- Determine low-cost location
- Find minimum cost production schedule
- Military distribution system
Types of Transportation Problem
- Balanced Transportation Problem: total supply equals total demand
- Unbalanced Transportation Problem: total supply is not equal to total demand
Balancing a Transportation Problem
- If total supply exceeds total demand: create a dummy demand point with demand equal to the excess supply
- If total supply is less than total demand: add a dummy supply point to balance the problem
Transportation Tableau
- A table that summarizes the relevant data, including supply, demand, and shipping costs.
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Description
Learn about transportation problems in the context of Linear Programming. Explore how to minimize costs when distributing products from sources to destinations. Discover the special structure and solutions required for transportation problems.
