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Service and manufacturing firms often attempt to mitigate demand-supply mismatch risks by deploying flexible resources that can be adapted to serve multiple demand classes. It is critical to evaluate the trade-off between the cost of investing in such resources and the resulting benefits. In this paper, we show that the heavily advocated “chaining” heuristic can sometimes perform unsatisfactorily when resources are not perfectly flexible. Alternatively, we propose an integer stochastic programming formulation as an attempt to optimize the flexibility structure. Although it is intractable to compute the optimal solution exactly, we propose a Lagrangian-relaxation heuristic that generates high-quality solutions efficiently. Using computational experiments, we identify conditions under which our approach can outperform the popular chaining solution.