Optimal selection of stochastic intervals under a sum constraint.

We model a selection process arising in certain storage problems. A sequence (X(1),...,X(n) of non-negative, independent and identically distributed random variables is given. F(x) denotes the common distribution of the X(i)'s. With F(x) given we seek a decision rule for selecting a maximum number of the X(i)'s subject to the following constraints: (1) the sum of the elements selected must not exceed a given constant c > 0, and (2) the X(i)'s must be inspected in strict sequence with the decision to accept or reject an element being final at the time it is inspected.