A dynamic programming problem is called invariant if its transition mechanism depends only on the action taken and does not depend on the current state of the systm. Replacement and maintenance problems are two typical types of problems which arise in applications and are often invariant. The...

We consider the best-choice secretary problem, with a known number, n, of applicants, and a random, independent "freeze" variable M, with known distribution. No hiring is possible after time M. The goal is to choose the best among the n applicants, where the decisions must be made depending only...