Transportation, Transshipment and Assignment Problems
3 important questions on Transportation, Transshipment and Assignment Problems
How do you formulate a transportation problem? [Electricity]
Powerplant:
xi,j = amount of electricity sent from plant i to city j
Constraints
- Each plant is a supply point. A supply constraint ensures that the total quantity sent from a plant does not exceed the plants capacity
- Each city is a demand point. A demand constraint ensures that each city receives its demand.
- Since a negative amount of electricity can not be shipped all xi,j's must be nonnegative
xi,j = amount of electricity sent from plant i to city j
Constraints
- Each plant is a supply point. A supply constraint ensures that the total quantity sent from a plant does not exceed the plants capacity
- Each city is a demand point. A demand constraint ensures that each city receives its demand.
- Since a negative amount of electricity can not be shipped all xi,j's must be nonnegative
What are transshipment problems
- A transportation problem allows shipments that go directly from supply points to demand points
- In many situations, shipments are allowed between supply points or between demand points
- Sometimes there may also be points (called transshipment points) through which goods can be transshipped on their journey from a supply point to a demand point
- In many situations, shipments are allowed between supply points or between demand points
- Sometimes there may also be points (called transshipment points) through which goods can be transshipped on their journey from a supply point to a demand point
What is an assignment problem?
- Is an integer programming problem since it asks the decision variable to take values 0 or 1
- But it is a very special integer programming problem
- Its matrix has a proerty called total unmodularity
- When the constraint matrix is totally unimodular and the right hand side of the constraints is integral, all extreme points of the linear program are integral. This happens because the inverse of each basis B is integral
- Then the integer program is equivalent to the linear program and is easy to solve
- This does not happen in general
- But it is a very special integer programming problem
- Its matrix has a proerty called total unmodularity
- When the constraint matrix is totally unimodular and the right hand side of the constraints is integral, all extreme points of the linear program are integral. This happens because the inverse of each basis B is integral
- Then the integer program is equivalent to the linear program and is easy to solve
- This does not happen in general
The question on the page originate from the summary of the following study material:
- A unique study and practice tool
- Never study anything twice again
- Get the grades you hope for
- 100% sure, 100% understanding
Remember faster, study better. Scientifically proven.
