Dynamic Programming: A Computational Tool

Prof. Lew Art, Dr. Holger Mauch (auth.)9783540370130, 3-540-37013-7, 3540370137

This book provides a practical introduction to computationally solving discrete optimization problems using dynamic programming. From the unusually numerous and varied examples presented, readers should more easily be able to formulate dynamic programming solutions to their own problems of interest.

We also provide and describe the design, implementation, and use of a software tool, named DP2PN2Solver, that has been used to numerically solve all of the problems presented earlier in the book. This computational tool can be used by students to solve academic problems if this book is used in coursework, and by practitioners to solve many real-world problems if the state space is not too large.

Finally, this book is also a research monograph that describes a novel application of Petri net theory. DP2PN2Solver takes user input in the form of the DP functional equation for a problem, automatically constructs a Petri net model, called a Bellman net, as an internal computer representation for the DP problem, and then generates from the Bellman net the numerical solution for the DP problem. This solution can be obtained using Java, a spreadsheet, a Petri net tool, and other systems.

Table of contents :
Front Matter….Pages i-xviii
Front Matter….Pages 1-1
Introduction to Dynamic Programming….Pages 3-43
Applications of Dynamic Programming….Pages 45-100
Front Matter….Pages 101-101
The DP Specification Language gDPS….Pages 103-123
DP Problem Specifications in gDPS….Pages 125-203
Bellman Nets: A Class of Petri Nets….Pages 205-220
Bellman Net Representations of DP Problems….Pages 221-244
Front Matter….Pages 245-245
DP2PN2Solver Tool….Pages 247-257
DP2PN Parser and Builder….Pages 259-269
The PN2Solver Modules….Pages 271-289
Front Matter….Pages 292-292
Java Solver Results of DP Problems….Pages 293-320
Other Solver Results….Pages 321-327
Conclusions….Pages 329-337
Back Matter….Pages 339-379