The inventory has an important function which controls time and quantity between productions and sales. It is, however, liable for financial cost and also a prolonged stock tends to be the dead stock. It is, therefore, made an effort to minimize. But, if the stock is too small quantity, an opportunity loss will be suffered because of the shortage of it. It is always an important subject, from this point of view, to establish an.economic inventory which minimizes the total amount of inventory-earring cost and shortage loss. As a usual equation for the inventory control of purchasing, there is the ordering point K as follows : K= x + K_a σ_x, where.x is the average demand, and K_a and σ_x are the safety coefficient and the standard deviation of the monthly demand respectively. For convenience' sake, σ_x was simply applied from the standard devision of demand in the past. But in the actual production and sales management system, σ_x in the production planning of the next month should be necessarily equivalent to the forecasted demand D. However, the related function between.x and σ_x, has never been known. This paper intends to clarify the relation between.x and σ_x, and to improve the accuracy of safety allowance K_a· σ_x and the standard inventory K.These parameters are then applied to an actual production and inventory control system. As the following regression formula has been found to come into existence between x and σ_x, it may be made possible to estimateσ_x with accuracy.
σ_x=ax+b√x
where, a and b are the regression coefficients depending on the products. By putting the forecasted demand D of a unit period in x in order to obtain the σ_D the standard inventory K_T may be then obtained as follows :
K_T=TD+K_a√Tσ_D.
As a result, the K_T may be applicable to any production planning and inventory cotrol systems. This relation is found in any product group. It maybe, therefore, applied to any production and inventory control when the similar regression formula has been obtained.