An inventory model with stochastic lead-time and stochastic demand

In this paper, the periodic review stochastic inventory control problem is investigated where the logistics cost consists of holding costs, shortage costs and ordering costs. The goal is to coordinate a sequence of orders of a single commodity, aiming to supply stochastic demands over a discrete finite horizon with minimum expected costs. Under some assumptions, the convexity of the cost function is proved and the global optimal solution can be given by explicit form. Finally, the numerical examples are presented to illustrate the validity for solving this model using Simulated Annealing algorithm.