A note on the economic management of inventory or resource under stochastic prices

The Markovian optimal policies are studied for the problem of economic inventory control or resource management in a finite time horizon. Under some conditions, in particular, when the prices are stochastic and there is a positive fixed setup cost K, the existence of {S,s}-type Markovian optimal management policies is proved. When K=0, the optimal policies are of {S}-type, in which case a comparison is made between the optimal policies under stochastic and deterministic prices. It turns out that under stochastic prices the optimal policies should be more conservative in order to maximize the present value of expected revenue.