Academic journal article Review - Federal Reserve Bank of St. Louis

Inventory Models

Academic journal article Review - Federal Reserve Bank of St. Louis

Inventory Models

Article excerpt

Production Smoothing

The accompanying figure on page 21 illustrates the production smoothing motivation when increasing marginal costs exist. If Q1 and Q 2 represent the demand in periods 1 and 2, respectively, then point A represents the average cost if Q1 is produced in period 1 and Q2 is produced in period 2. Point B represents the average cost if (Q1+Q2)/2 is produced in both periods, with the excess produced in period 1 carried over to period 2. The trade-off is between the cost of storage for one period versus the savings from smoothing.(1) The difference between A and B must be greater than the cost of holding inventory to justify smoothing. Note also that if mean demand is expected to decrease below current production for an extended period (that is, Q2 is current demand and Q1 is next period's expected demand), then it becomes optimal to reduce production and serve part of current demand from inventory. Thus, production smoothing motivation can lead to level changes if forecast sales change direction.

(S,s) Rule

If costs are linear, as in the case when marginal costs are constant, and there is a significant fixed cost of purchasing in each period, then it can be shown that "lumpy" adjustment is preferred to smoothing. An economic batch run, or a purchase which minimizes the total expected cost including the cost of storage of excess inventory, and the cost of lost sales can be determined. The inventory management technique used under these circumstances is referred to as (S,s) and entails determining maximum (S) and minimum (s) levels of inventory. …

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