  A widely used heuristic for solving stochastic optimization problems is to
use a deterministic rolling horizon procedure, which has been modified to
handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been
criticized for its use of a deterministic approximation of a stochastic
problem, which is the major motivation for stochastic programming. We recast
this debate by identifying both deterministic and stochastic approaches as
policies for solving a stochastic base model, which may be a simulator or the
real world. Stochastic lookahead models (stochastic programming) require a
range of approximations to keep the problem tractable. By contrast, so-called
deterministic models are actually parametrically modified cost function
approximations which use parametric adjustments to the objective function
and/or the constraints. These parameters are then optimized in a stochastic
base model which does not require making any of the types of simplifications
required by stochastic programming. We formalize this strategy and describe a
gradient-based stochastic search strategy to optimize the parameters.
