If you observe that a very long time passes before the branch & cut algorithm begins processing nodes, it may be that the root relaxation problem itself is taking a long time. The standard screen display will print a line telling "Root relaxation solution time =" once this root solve is complete, and a large solution time would be an indicator of an opportunity for tuning. If you set the MIPDisplay parameter to 4, you may get a further indication of the difficulties this root solve has run into. Tuning techniques found in Chapter 5, Solving Linear Programming Problems or Chapter 7, Solving Quadratic Programming Problems, would be applicable to tuning the root solve of a MIP model too. In particular, it is worth considering setting the RootAlg parameter to a nondefault setting, such as the Barrier optimizer, to see if a simple change in algorithm will speed up this step sufficiently.

For some problems, ILOG CPLEX will spend a significant amount of time performing computation at node 0, apart from solving the LP or QP relaxation. While this investment of time normally saves in the overall branch & cut, it does not always do so. Time spent at node 0 can be reduced by two parameters.

First, you can try turning off the node heuristic by setting the parameter HeurFreq to -1. Second, try a less expensive variable selection strategy by setting the parameter VarSel to 4, pseudo reduced costs.

It is worth noting that setting the MIPEmphasis parameter to 1, resulting in an emphasis on feasibility instead of optimality, often also speeds up the processing of the root node. If your purposes are compatible with this emphasis, consider using it.