Multi-item Inventory

Suppose there are n different parts. Each part has a demand that follows the Normal distribution with mean q and standard deviations. Therefore the Cycle Stock = mean demand = q. Suppose that to achieve the desired service level the Safety Stock carried is twice the standard deviation (this implies that the chance of not having a stock-out is around 95%). Thus the Safety Stock for each item = 2s and

• Target Stock Level for each item = q + 2s,
• Total Target Stock for all the items = n(q + 2s), (sum of the individual stocks)
• Total Safety Stock = 2ns.

If we replace the individual parts by a single generic part, the total Cycle Stock becomes the sum of the individual items, since the expected value of the sum of the demand is the sum of the expected value, and so the Cycle Stock for the generic item = nq.  The variance of the demand for the generic items is the sum of the variance of the demand for the individual items, that is, the pooled variance = ns2.. Therefore, the standard deviation of the generic items becomes . To achieve the same service level, we again use a safety stock of twice the standard deviation.  Hence,

• Pooled Target Stock = ,
• Pooled Safety Stock  = 

Thus, by using a generic item we get a reduction in the amount of safety stock we require. The ratio of the Pooled to Individual Safety Stock  = .

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