Setup cost reduction a multi-stage order quantity model

In this paper, a single item, multi-stage serial order quantity (MSOQ) model with constant demand is discussed. The objective of the model is to minimize the total cost which includes the setup cost and the inventory holding cost. This paper examines and analyses the investment in a one-time cost to reduce the (current) setup level and adds a per unit item amortization of this cost to the other costs associated with the MSOQ model. We consider the setup cost to be decreased on each stage with the same rate and the cost of the joint setup cost reduction is a logarithmic cost function.