Setup cost reduction in (Q, r) policy with lot size, setup time and lead-time interactions

It is often assumed in most deterministic and stochastic inventory models that lead-time is a given parameter and the optimal operating policy is determined on the basis of this unrealistic assumption. However, the manufacturing lead-time is made up of several components (moving time, waiting time, setup time, lot size, and rework time) most of which should be treated as controllable variables. In this paper the effect of setup cost reduction is addressed in a stochastic continuous review inventory system with lead-time depending on lot size and setup time. An efficient iterative procedure is developed to determine the near optimal lot size, reorder point and setup time. Furthermore, a sensitivity analysis is carried out to assess the cost savings that can be realised by investing in setup.