The allocation problem in health care can be characterised as a mathematical programming problem but attempts to incorporate uncertainty in costs and effect have suffered from important limitations. A two-stage stochastic mathematical programming formulation is developed and applied to a numerical example to explore and demonstrate the implications of this more general and comprehensive approach. The solution to the allocation problem for different budgets, budgetary policies, and available actions are then demonstrated. This analysis is used to evaluate different budgetary policies and examine the adequacy of standard decision rules in cost-effectiveness analysis. The research decision is then considered alongside the allocation problem. This more general formulation demonstrates that the value of further research depends on: (i) the budgetary policy in place; (ii) the realisations revealed during the budget period; (iii) remedial actions that may be available; and (iv) variability in parameters values.