  This paper examines a Markovian model for the optimal irreversible investment
problem of a firm aiming at minimizing total expected costs of production. We
model market uncertainty and the cost of investment per unit of production
capacity as two independent one-dimensional regular diffusions, and we consider
a general convex running cost function. The optimization problem is set as a
three-dimensional degenerate singular stochastic control problem.
  We provide the optimal control as the solution of a Skorohod reflection
problem at a suitable boundary surface. Such boundary arises from the analysis
of a family of two-dimensional parameter-dependent optimal stopping problems
and it is characterized in terms of the family of unique continuous solutions
to parameter-dependent nonlinear integral equations of Fredholm type.
