The classic transportation problem concerns minimizing the cost of transporting a single product from sources to destinations. It is a network-flow problem that arises in industrial logistics and is considered as a special case of linear programming. The total number of units produced at each source, the total number of units required at each destination and the cost to transport one unit from each source to each destination are the basic inputs. The objective is to minimize the total cost of transporting the units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and 3) improving the current solution through iteration. Modeling and solving the classic transportation problem rely strongly on network models, least-cost path algorithms, and location-allocation analysis in the field of geographic information science (GIScience). Thus, it represents a key component in the network analytics and modeling area of GIS&T

Topic Description:

1. Definitions

2. Modeling the Classic Transportation Problem

3. Solving the Classic Transportation Problem

4. The Classic Transportation Problem and GIS&T

Learning Objectives:

Describe the classic transportation problem

Demonstrate how the classic transportation problem can be structured as a linear program

Implement the transportation simplex method to determine the optimal solution

Explain why, if supply equals demand, there will always be a feasible solution to the classic transportation problem

The classic transportation problem concerns minimizing the cost of transporting a single product from sources to destinations. It is a network-flow problem that arises in industrial logistics and is considered as a special case of linear programming. The total number of units produced at each source, the total number of units required at each destination and the cost to transport one unit from each source to each destination are the basic inputs. The objective is to minimize the total cost of transporting the units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and 3) improving the current solution through iteration. Modeling and solving the classic transportation problem rely strongly on network models, least-cost path algorithms, and location-allocation analysis in the field of geographic information science (GIScience). Thus, it represents a key component in the network analytics and modeling area of GIS&T

1. Definitions

2. Modeling the Classic Transportation Problem

3. Solving the Classic Transportation Problem

4. The Classic Transportation Problem and GIS&T