Chapter 6

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Questions and Answers

What is the purpose of the Solver Parameters window in Excel?

To input the problem data

To select the starting solution procedure

To solve the problem (correct)

To display the solution

What is the purpose of the transportation module in QM for Windows?

To solve linear programming problems

To solve transportation problems (correct)

To solve assignment problems

To solve integer programming problems

What are the three starting solution procedures used in QM for Windows?

Hungarian method, Vogel's approximation method, and Russell's approximation method

Simplex method, dual simplex method, and graphical method

Graphical method, simplex method, and dual simplex method

Northwest corner, minimum cell cost, and VAM (correct)

Why does it make no difference which starting procedure is used in QM for Windows?

Because these techniques are not included in the text Signup and view all the answers

What is the main principle followed when developing constraints for the grain elevators?

Inflow equals outflow Signup and view all the answers

What type of linear programming model is formulated for a class of problems with the characteristics of transporting a product from sources to destinations at the minimum possible cost?

Transportation Model Signup and view all the answers

What are the two main characteristics of the transportation model?

Transporting a product from sources to destinations at minimum cost and meeting fixed demand Signup and view all the answers

What type of model is referred to when supply exactly equals demand?

Balanced transportation model Signup and view all the answers

In the transportation model, what is the fixed quantity at each source?

Supply of the product Signup and view all the answers

What is the name of the solution approach used to solve transportation problems?

Transportation Method Signup and view all the answers

What is the main goal of the transportation model?

Minimizing cost Signup and view all the answers

What is the result of not having enough total supply to meet total demand?

One of the demand constraints will not be met Signup and view all the answers

What happens when supply exceeds demand in a transportation model?

The supply constraints become ≤ Signup and view all the answers

How can a prohibited route in a transportation model be handled?

By assigning a very large relative cost as the coefficient of this prohibited variable in the objective function Signup and view all the answers

What software packages can be used to solve a transportation problem?

Excel and QM for Windows Signup and view all the answers

What is a transportation problem formulated as?

A linear programming model Signup and view all the answers

What is the purpose of using QM for Windows in the transportation problem?

To find the optimal solution to the transportation problem Signup and view all the answers

Study Notes

Transportation, Transshipment, and Assignment Problems

Special types of linear programming model formulations that are part of a larger class of network flow problems
Have special mathematical characteristics that enable efficient solution approaches

Learning Outcomes

Differentiate between transportation, transshipment, and assignment models
Apply computer solutions for these types of linear programming models

The Transportation Model

Formulated for problems with unique characteristics:
- Product transported from sources to destinations at minimum cost
- Each source has a fixed supply, and each destination has a fixed demand
Can be applied to various problems, but most familiar application is the transportation of goods
Example: Wheat harvested in the Midwest and stored in grain elevators in three cities
Characteristics:
- Supply equals demand in a balanced transportation model
- Unbalanced problems can occur when supply exceeds demand or vice versa

Computer Solution of a Transportation Problem

Can be solved using Excel or QM for Windows
Excel solution:
- Set up the problem with necessary formulas
- Use the Solver feature to find the solution
QM for Windows solution:
- Access the transportation module
- Input the problem data
- Select an initial solution method (e.g., northwest corner, minimum cell cost, or VAM)

Transshipment Model

Items can be transported from sources through transshipment points to destinations
Expansion of the wheat-shipping example to demonstrate the formulation of a transshipment model
Shipping costs from farms to grain elevators and from grain elevators to mills
Graphical network in Figure 6.3 shows the basic structure of the model
Supply-and-demand constraints are developed for farms, grain elevators, and mills
Constraints for grain elevators ensure that the amount of grain shipped in is also shipped out

Assignment Problem

Example: Assigning ACC officials to games
Solution using QM for Windows
Exhibits 6.17 and 6.18 show the data input and solution

Business Problem and Activities/Assessments

Concrete company transports concrete from three plants to three construction sites
Determine the decision variables, objective function, and constraints of the problem
Use Excel Solver to find the solution

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