An inventory system under periodic review is considered. If at the time of review the stock has fallen below a given level, L, a fixed quantity, Q, is ordered; otherwise no action is taken. It is assumed that delivery time is negligible. Two costs are considered to be of importance: one...

The statistical model of a chance constrained variable which is the sum of stochastically independent random variables is considered, using the machine loading problem as an expository case. The resulting chance constrained statement, Pr {\sum ⁿ_i₌₁\sum ^x_i_k₌₀a_ik H} < \beta, is shown to be different in substance from the classical case, Pr{\sum ⁿ_i₌₁ a'_ix_i < H} > \beta, where x_i...</h}></\beta,>