Setup cost reduction in a dynamic lot size model with multiple finite production rates

This paper analyzes the subject of reducing setup cost in a dynamic lot size model where production in a period is restricted to a value taken in the set {0,P,...,mP} with a given constant P and a positive integer m. The model assumes that the setup cost is charged only for changing the state of production from zero to any positive production rate and that the inventory holding cost is linearly increasing. The analysis is made to investigate the effect of setup cost reduction on total inventory cost and total inventory level. A parametric algorithm is suggested and its illustration is made with a numerical example. An experimental study is also made to investigate the variations of the associated block decision and block forecast horizons.