  This paper studies chance-constrained stochastic optimization problems with
finite support. It presents an iterative method that solves reduced-size
chance-constrained models obtained by partitioning the scenario set. Each
reduced problem is constructed to yield a bound on the optimal value of the
original problem. We show how to adapt the partitioning of the scenario set so
that our adaptive method returns the optimal solution of the original
chance-constrained problem in a finite number of iterations. At the heart of
the method lie two fundamental operations: refinement and merging. A refinement
operation divides a subset of the partition, whereas a merging operation
combines a group of subsets into one. We describe how to use these operations
to enhance the bound obtained in each step of the method while preserving the
small size of the reduced model. Under mild conditions, we prove that, for
specific refinement and merge operations, the bound obtained after solving each
reduced model strictly improves throughout the iterative process. Our general
method allows the seamless integration of various computational enhancements,
significantly reducing the computational time required to solve the reduced
chance-constrained problems. The method's efficiency is assessed through
numerical experiments on chance-constrained multidimensional knapsack problems.
We study the impact of our method's components and compare its performance
against other methods from the recent literature.
