Combinatorial optimization problems spans through several applications such as task scheduling and resources allocation, where an optimal element is to be determined from the analysis of computational complexity; which characterized the optimality as best solution from feasible regions by objective functions. Some decision making problems can be solved by surface scanning as it is in dynamic programming technique, where optimal solutions comes by simple segmentation operations. Many algorithms on decision tree C4.5 and logical clustering to search solution space use dynamic programming. In this paper, optimization techniques and mathematical modeling for solving hard combinatorial problems were explored and juxtaposed with computer programming as computational aid. Technical computing and program module shows the algorithm efficacy for implementation and correctness of combinatorial structure to obtain optimal solution.