Dynamic programming (DP) has quite a different model form than the other types of mathematical programming. Instead of an objective function and constraints, dynamic programming models consist of a collection of equations that describe a sequential decision process.
The process begins in some initial state, the first decision moves it to a second state, and then continues through alternating decisions and states until a final state is reached
Example Problem:
http://www.me.utexas.edu/~jensen/ORMM/models/unit/dynamic/subunits/investment/index.html
Also
http://www.csc.liv.ac.uk/~ped/teachadmin/algor/dyprog.html