The first step in a branch and bound approach to solving integer programming problems is to

The first step in a branch and bound approach to solving integer programming problems is to relax the integer constraints of the problem. This means that instead of requiring the decision variables to take on integer values, you allow them to be continuous (real numbers). The goal of this initial step is to solve the relaxed linear programming problem using methods such as the Simplex method.

Once you have solved the relaxed problem, you will obtain an optimal solution for the relaxed version, along with the optimal value of the objective function. If the solution obtained is integer feasible (all integer values for decision variables), then this solution is also optimal for the original integer programming problem.

If the solution is not integer feasible, the next step is to identify which variables are fractional and create subproblems by branching on these variables—i.e., creating new constraints to force the variables to take on integer values. This forms the basis for exploring different branches of solutions systematically while pruning non-promising branches based on the bound of the objective function.

Overall, the branch and bound method is an effective strategy for navigating the solution space of integer programming problems by systematically dividing and conquering the problem with informed bounding decisions.