In this paper, we propose a general and formal framework to treat the dual-mode batch-to-batch optimization (DMBBO) problem based on Markov decision processes and information states. This framework adopts a Bayesian view of the parameter estimation and provides the general equations describing the solution of the DMBBO problem. This framework does not require the concept of optimality loss function used in previous works. We use this framework to explain a classic heuristic for tackling the DMBBO problem as a two-batch approximation of the proposed equations, and we propose extensions of these heuristics to the N-batch DMBBO problem. For the sake of brevity, these approximations will focus on the unconstrained DMBBO case.