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Integer programming Problem is concerned with the optimization problems in which some or all of the variables are required to take on discrete values. Solution methods of Integer programming can be classified as an 'optimal' and a 'heuristic'. An 'optimal' tactic is one which mathematically guarantees to find the optimal solution. A 'Heuristic' approach is a tactic that should optimistically find a feasible solution. In fact, it is often the case that a well-designed heuristic approaches can give good quality (near-optimal) results. This book consists of five chapters, starting with an introductory chapter and deals with the study of Integer programming problem. The present book provides the some heuristic approaches for finding the integer solutions. It also provides insight on the 'A-T' cut and some special cuts. The cuts are developed to reduce the feasible region under which an optimum solution is achieved in a minimum number of steps. The computational details of the procedure are illustrated through the numerical examples. This book can also develop awareness among the researcher regarding establishing the new ideas to form the cuts and the heuristic approaches.