A lost-sales production/inventory model with two discrete production modes

A discrete production/inventory model is considered in which batch orders for a single item arrive at a production facility according to a Poisson process. The items can be produced according to two production modes, regular mode or high speed mode. Changing production mode requires a setup time during which production is disabled. Demand that cannot be satisfied from stock is lost. To control this model with respect to a suitable cost criterion, two-level hysteretic switching strategies are considered. Using generally applicable methods, tractable expressions are obtained for the fraction of lost demand and the average inventory level, amongst others. In these methods an essential role is played by the discrete Fast Fourier Transform