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Questions and Answers
What is the initial total shipping cost before any adjustments?
What is the initial total shipping cost before any adjustments?
What procedure is formalized in this example as 'the transportation algorithm'?
What procedure is formalized in this example as 'the transportation algorithm'?
Minimize z = ∑(c_ij * x_ij) subject to supply and demand constraints.
The cost is always reduced when units are sent along route (1,3).
The cost is always reduced when units are sent along route (1,3).
True
When sending 20 units along route (1,3), the cost is reduced by ___.
When sending 20 units along route (1,3), the cost is reduced by ___.
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Match the following terms with their descriptions:
Match the following terms with their descriptions:
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What does the equation $ ext{Minimize } z = rac{ ext{sum of costs}}{ ext{total shipment}}$ represent in the transportation problem?
What does the equation $ ext{Minimize } z = rac{ ext{sum of costs}}{ ext{total shipment}}$ represent in the transportation problem?
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An optimal solution is reached when all entering variables are negative.
An optimal solution is reached when all entering variables are negative.
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What happens to the variable $x_{14}$ when $x_{13}=20$?
What happens to the variable $x_{14}$ when $x_{13}=20$?
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What is the primary goal of formulating the transportation problem?
What is the primary goal of formulating the transportation problem?
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What is the objective of the transportation problem formulated in the document?
What is the objective of the transportation problem formulated in the document?
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The transportation problem can only be solved using the simplex method.
The transportation problem can only be solved using the simplex method.
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How many tons per week can the San Antonio plant supply?
How many tons per week can the San Antonio plant supply?
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The transportation problem is always feasible if the total supply equals the total demand.
The transportation problem is always feasible if the total supply equals the total demand.
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The San Antonio warehouse needs __________ tons per week.
The San Antonio warehouse needs __________ tons per week.
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What do the variables $x_{ij}$ represent in the transportation problem?
What do the variables $x_{ij}$ represent in the transportation problem?
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Which shipping route has the lowest cost per ton from Salt Lake City?
Which shipping route has the lowest cost per ton from Salt Lake City?
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The total supply and total demand for the transportation model include _______ which must be equal for feasibility.
The total supply and total demand for the transportation model include _______ which must be equal for feasibility.
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Match the shipping routes with their costs.
Match the shipping routes with their costs.
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Which of the following constraints represents the supply from the first plant in the given model?
Which of the following constraints represents the supply from the first plant in the given model?
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The total supply of the plants matches the total demand of the warehouses in this transportation problem.
The total supply of the plants matches the total demand of the warehouses in this transportation problem.
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Match the following terms with their correct descriptions:
Match the following terms with their correct descriptions:
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What type of system does the transportation problem apply to?
What type of system does the transportation problem apply to?
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In the given model, all variables must be non-negative integers.
In the given model, all variables must be non-negative integers.
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Study Notes
Transportation Problem
- The transportation problem involves finding the optimal way to transport goods from multiple origins (e.g., plants) to multiple destinations (e.g., warehouses).
- The objective is to minimize the total transportation cost.
- The problem is defined by constraints that ensure supply is equal to demand.
Example: Plastic Manufacturing Company
- A plastic manufacturing company has three plants (Salt Lake City, Denver, San Antonio) and four warehouses (Los Angeles, Chicago, New York City, San Antonio).
- The company wants to minimize the cost of shipping polyethylene from plants to warehouses.
- The supply of each plant and the demand of each warehouse is known.
Model
- Shipping costs are represented by a cost matrix (C).
- Each cell in the matrix represents the cost of shipping one unit from the origin to the destination.
- The model seeks to minimize total shipping cost by choosing the optimal shipping routes and amounts.
- The model ensures that supply meets demand at each warehouse, and that no more than the plant's supply is shipped.
Transportation Algorithm
- The transportation algorithm is used to solve the transportation problem.
- The algorithm involves finding an initial basic feasible solution (using the minimum cost rule) and then iteratively improving it.
- The improvement process involves identifying entering and departing variables, modifying the tableau, and re-evaluating the cost function.
- The algorithm stops when no entering variable can be chosen, indicating an optimal solution has been found.
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Description
Explore the transportation problem which focuses on minimizing shipping costs while ensuring supply equals demand. This quiz will cover definitions, constraints, and application through a case study of a plastic manufacturing company. Test your understanding of optimal transportation methods and cost-effective solutions.
