Optimal Control of (Q, r) Inventory System with Service Level Constraint

After putting forward a lead-time reduction cost function with characteristics of subsection linear, which bases on the fact that additional investment is not necessary to reduce lead-time, this paper studied a two-stage (Q, r) policy coordination problem with service level constraint. By applying some means of optimization theory, the problem was decomposed into two problems: one problem without constraint and the other with equation constraint. Theoretic analysis and numerical study show that, service level can be improved prominently and the total cost can be minimized. The order quantity, reorder point and lead-time expediting factor were obtained at the same time.