Instability of Total Production Inventory and Its Stabilization

This paper shows the instability of the total production inventory in a multi-commodity and varying quantity production, and proposes a schedule control for gaining its stability.

The production demand of each commodity is a random variable of a non-stationary process, since a new product is immediately old-fashioned. However, the total production demand is a random variable of a stationary process, since the maker develops new products constantly to keep the working ratio of the production facilities at a high level.

The minimization of the sum of the inventory loss and the changeover loss must be realized by the control of the total inventory, not by each commodity inventory. If the total inventory increases (decreases), the changeover loss decreases (increases) and the effective production capability increases (decreases). The production factory usually tries to maximize its working ratio of the production facilities. Therefore, once the total inventory quantity increases (decreases), it increases (decreases) moreover. This is the instability of the total inventory.

The feedback control for stabilizing the total inventory is a regulation of the working time, not a re-scheduling. The feed forward control is realized by a production schedule..