A Branching Process for Convergent Product Optimization

Abstract

We consider a discrete time branching process where the population consists of k types of convergent products, an action is chosen for that which affects the lifetime, the number and types of its functions, and the profit received. The problem of maximizing the expected profit is shown to be equivalent to a generalized Markov decision problem of maximizing the expected profit is shown to be equivalent to a generalized Markov decision problem where the  transition matrices are non-negative but not necessarily sub stochastic.