Optimality conditions for the two-period inventory management problem in case of the stochastic demand

The multi-period inventory management problems in case of the stochastic demand in order to maximize the total expected profit in the case of loss and in the case of a pending unsatisfied demand are described. The relationship between these problems is shown and the existence of the solutions of these problems is proved. The necessary and sufficient optimality conditions for the two-period problem of expected profit maximization in the case of a pending unsatisfied demand are obtained.