Optimum Aggregate Inventory in the Lot Scheduling Problem with Non-Zero Setup Time

In this paper, the minimization of the maximum aggregate inventory of all products for the common cycle time approach to the scheduling problem of a multi-products single machine system is considered. In the case of non-zero set up time and limited resources, a simply and easy to apply rule has been obtained for this optimization problem. Using this rule, one can obtain the optimal production sequence among n! possible schedules, just by comparison of values of the maximum aggregate inventory of only n possible schedules.