Stochastic Inventory Management With General Replenishment Cost Under Lost-Sale Setting

We study a stochastic periodic-review inventory management system for a general ordering cost function under lost-sale setting.Assume the replenishment cost function is piecewise linear and increasing,we provide two different conditions on cost parameters.By introducing a new concept,we manage to fully characterize the optimal ordering policy,which shares a common structure,i.e.what we call modified generalized(s,S)policy.Under the framework of general replenishment cost,we further study several specific but representative ordering cost structures.We study a quantity dependent fixed cost,a general concave ordering cost function,a general convex variable cost as well as a concave-convex variable cost.We fully characterize the optimal ordering policy therein.At the same time,we study two special ordering cost functions,that with minimum ordering quantity or all-units discount.The former's feasible set is unconnected and the latter's ordering cost function is not increasing,which make them not belong to the general ordering cost function.However,by applying the main results in this paper,we fully characterize the optimal ordering policy for the two special ordering cost structures and provide guidelines for further research on such problems.