Optimum Aggregate Inventory for Scheduling Multi-product Single Machine System with Zero Setup Time

In this paper we adopt the common cycle approach to economic lot scheduling problem and minimize the maximum aggregate inventory. We allow the occurrence of the idle times between any two consecutive products and consider limited capital for investment in inventory. We assume the setup times are negligible. To achieve the optimal investment in inventory we first find the idle times which minimize the maximum aggregate inventory for a given sequence of production runs and for any arbitrary cycle time T. Then, we show that these values of idle times, for the given sequence, are also optimal idle times for any other sequence. The result is an easy-to-apply rule that greatly simplifies the task of scheduling to achieve minimum required investment in inventory.