This paper deals with the application of dynamic programming to systems whose duration is uncertain, and which duration may or may not be a function of the decisionmaker's policy. It extends some of Bellman's work in that the transformed states at successive stages may not have the properties...

In this technical note we examine a method of extending a problem over a finite set of actions, to a problem of maximising a function over a bi-product set. The solution set is characterised in terms of fixed point solutions and partial solutions, and two improvement algorithms are given.