Migrate concurrent root LP to OMP

cpp/src/mip_heuristics/mip_constants.hpp

@@ -21,3 +21,8 @@
 #define CUOPT_MIP_RINS_REQUIRED_THREAD_COUNT        4
 #define CUOPT_MIP_BATCH_PDLP_REQUIRED_THREAD_COUNT  3
 #define CUOPT_MIP_CLIQUE_CUTS_REQUIRED_THREAD_COUNT 3
+// Concurrent LP root solve from inside MIP: barrier runs as a third OMP task alongside PDLP
+// and dual simplex. Disabled below this thread count so the barrier work doesn't overshoot
+// the MIP solver's num_cpu_threads budget (need 1 PDLP + 1 dual simplex + 1 barrier).
+// Stand-alone LP always runs all three concurrently regardless of this gate.
+#define CUOPT_CONCURRENT_LP_BARRIER_REQUIRED_THREAD_COUNT 3