Separable markovian decision problems

The special structure of a class of Markovian decision problems is exploited to simplify the determination of optimum policies. For certain pairs consisting of a state i and decision k, the cost cik separates (cik = ai + bh), while the transition probabilities pkij and transition time distributions Fkij are independent of i. Equivalence of a second Markovian decision problem which exploits this structure is demonstrated for the discounted and averaging cases. In addition, streamlined approaches are presented for dealing directly with the original problem, and a particular inventory model is further simplified.