In a realistic register-transfer-level component library, there usually exist several different hardware implementations for one generic function. This gives rise to a large design space of component selection which is interleaved with the scheduling of operations. Previous methods ignored the presence of multicomponent selection in the process of lower/upper bound estimation of scheduling, and produced the local lower/upper bounds which would cause the suboptimum designs. Opposite to the previous methods, we compute, in this paper, the lower/upper bounds which consider scheduling and component selection simultaneously. A new problem of multicomponent selection integrated with interval scheduling is studied.We present a very interesting and important result that both the lower bound and upper bound of multicomponent selection are obtained on the most cost-effective components which have the minimum area-delay products. This property leads to that the lower bound and upper bound of multicomponent selection can be calculated efficiently. An integer linear programming model and a surrogate relaxation technique are proposed to derive an optimum surrogate lower bound which has the asymptotic performance ratio less than two for a single type of function. An upper bound with the same asymptotic performance ratio is also obtained which turns out to be the optimum solution value of the traditional unicomponent selection with the most cost-effective components. Both the theoretical analysis and the experimental results show that the performance of our bounds are very promising.