This book presented solutions to some combinatorial programming problems using Lexi search approach and Heuristic Approach. In each model we find shortest path based on the given constraints. This book classified into five chapters and an exact algorithm is proposed for each problem. The algorithm solves the problem on identifying the key patterns which optimize the objective of the cost and requirement of respective nodes. The algorithm calculates the solution incrementally for different patterns and the best combination is taken as the solution. We tested the algorithms using C language. The proposed algorithms shows encouraging results and compared with existing algorithms. This book is very useful to young researchers and students.