The Transportation Model
SUPPLEMENT TO CHAPTER EIGHT
THE TRANSPORTATION MODEL
LEARNING OBJECTIVES
After completing this supplement you should be able to:
1. Describe the nature of a transportation problem.
2. Solve transportation problems manually and interpret the results.
SUPPLEMENT OUTLINE
Introduction
Obtaining an Initial Solution
The Intuitive Lowest-Cost Approach
Testing for Optimality
Evaluating Empty Cells: The Stepping-Stone Method
Evaluating Empty Cells: The MODI Method
Obtaining an Improved Solution
Special Problems
Unequal Supply and Demand
Degeneracy
Summary of Procedure
Key Terms
Solved Problems
Discussion and Review Questions
Problems
The Transportation problem involves finding the lowest-cost plan for distributing stocks of goods or supplies from multiple origins to multiple destinations that demand the goods. For instance, a firm might have three factories, all of which are capable of producing identical units of the same product, and four warehouses that stock or demand those products, as depicted in Figure 1. The transportation model can be used to determine how to allocate the supplies available from the various factories to the warehouses that stock or demand those goods, in such a way that total shipping cost is minimized. Usually, analysis of the problem will produce a shipping plan that pertains to a certain period of time (day, week), although once the plan is established, it will generally not change unless one or more of the parameters of the problem (supply, demand, unit shipping cost) changes.
The transportation model starts with the development of a feasible solution, which is then sequentially tested and improved until an optimal solution is obtained. The description of the technique on the following pages focuses on each of the major steps in the process in this order:
1. Obtaining an initial solution.
2. Testing the solution for optimality.
3. Improving sub optimal solutions.
THE TRANSPORTATION MODEL
LEARNING OBJECTIVES
After completing this supplement you should be able to:
1. Describe the nature of a transportation problem.
2. Solve transportation problems manually and interpret the results.
SUPPLEMENT OUTLINE
Introduction
Obtaining an Initial Solution
The Intuitive Lowest-Cost Approach
Testing for Optimality
Evaluating Empty Cells: The Stepping-Stone Method
Evaluating Empty Cells: The MODI Method
Obtaining an Improved Solution
Special Problems
Unequal Supply and Demand
Degeneracy
Summary of Procedure
Key Terms
Solved Problems
Discussion and Review Questions
Problems
The Transportation problem involves finding the lowest-cost plan for distributing stocks of goods or supplies from multiple origins to multiple destinations that demand the goods. For instance, a firm might have three factories, all of which are capable of producing identical units of the same product, and four warehouses that stock or demand those products, as depicted in Figure 1. The transportation model can be used to determine how to allocate the supplies available from the various factories to the warehouses that stock or demand those goods, in such a way that total shipping cost is minimized. Usually, analysis of the problem will produce a shipping plan that pertains to a certain period of time (day, week), although once the plan is established, it will generally not change unless one or more of the parameters of the problem (supply, demand, unit shipping cost) changes.
The transportation model starts with the development of a feasible solution, which is then sequentially tested and improved until an optimal solution is obtained. The description of the technique on the following pages focuses on each of the major steps in the process in this order:
1. Obtaining an initial solution.
2. Testing the solution for optimality.
3. Improving sub optimal solutions.