The paper deals with the stochastic programming problem \[ \underset{K\subset X}{\text{maximize}} \int_\Xi f(x, \xi) P(d\xi), \] where \(X\) and \(\Xi\) are complete separable metric spaces (\(\Xi\) equipped with a Borel structure), \(P\) is a probability measure on \(\Xi\), \(f(x, \xi): X\times \Xi\to [-\infty, +\infty]\), \(f(\cdot, \cdot)\) is admitted to be discontinuous.
The aim of the paper is to investigate the stability of the problem with respect to variations of the integrand \(f(\cdot, \cdot)\), or the probability measure \(P\). The problem is demonstrated on the case of the newsboy problem. The achieved results are applied to the stability of sensors.