Lot scheduling problem for continuous demand

This paper deals with a lot scheduling problem for multi-item continuous demand utilizing a single machine with setup times. The problem involves dynamic determination of lot-sizes to minimize the inventory level. In such systems, the lowest inventory level is realized by maximizing the number of setups under the condition of no stockout. Based on the above fact, first, an analytical solution of lot-sizes for a cyclic schedule is given based on a constant-demand model. Secondly, a stochastic-demand model is developed, and some heuristic setup rules are studied using the concept of time inventory, defined from the solution based on a constant-demand model. These rules realize a stable system with a lower average stockout level and a lower inventory level. Effects of the setup rules on the system are revealed by Monte Carlo simulations.