1. Transportation and Assignment Problems
Chapter 6
Transportation and Assignment Problems

2. The Transportation Problem
Given:
Capacity of each source;
Demand of each destination;
Transportation cost to ship one unit from a source to a destination.
To find the most economical way of satisfying the demands of the destinations by using the resources.

4. Solving Transportation Problem
The solution method (algorithm) is elegant. But, as business people, we do not need to know the details since computers can help us solve it.
Use the ‘transportation module’ in QM.

5. Total Supply and Total Demand
Total supply is not necessary equal to total demand.
A dummy source or a dummy destination appears in the QM result if total supply is not equal to total demand.

6. Dummy Source or Destination
A dummy source in the result of QM indicates an overall shortage, and at which destinations shortages will occur.
A dummy destination in the result of QM indicates an overall surplus, and which sources will have surpluses.

7. Prohibited Route
If a route is prohibited to use, just set the unit transportation cost of that route to a very large number.

8. The Assignment Problem
Given
The cost (or efficiency index) for a person to a job.
To assign Y persons to Y jobs so that the total cost is minimized or total efficiency is maximized.

10. Solving Assignment Problem
It is a special transportation problem (why?), so it can be solved by using ‘Transportation Module’ in QM.
More conveniently, we use the ‘Assignment Module’ in QM.

11. Assignment Problem vs. Transportation Problem
The assignment problem is a special case of the transportation problem in which demands of all destinations are 1, and capacities of all sources are 1.