Optimal strategies for an inventory system with cost functions of general form (Q1570273)

The inventory process with state space \([0,Q]\), \(Q>0\) is of the form \(X_{n+1}= \max(X_n+ \eta_nD_n- \xi_n,0)\), \(n\in\mathbb{N}\) where \(\{\xi_n\}\) is a sequence of independent, identically distributed random demands, \(D_n\in [0,Q-X_n]\) is an order decision and \(\{\eta_n\}\) is a sequence of random Bernoulli distributed variables. The cost functions associated with storekeeping, order decisions, goods replenishment, and deficiency are considered. The optimality criterion is an average expected cost per unit of time on an infinite time interval. The existence of the optimal order policy for a large class of cost functions is proved. An algorithm for determination of the optimal policy based on stochastic approximation is presented.