# Single order inventory control model

Single inventory control models are inventory or production models which apply to single event circumstances that are different from other events the business or process may handle. They are one off sale or production events which must be handled efficiently by the supply chain. Yield management applications are considered single order cases.

So the issue in these cases is the amount of inventory needed to satisfy demand with minimal stock-out costs and over production/ over stock costs, because after the event or sale period has passed the inventory will be obsolete.Below is a simple procedure for this type of inventory decision.

A simple way to approach this type of inventory decision is to use either historical average of similar items/sales together with the cumulative normal probability distribution. This is assuming that the sale of this item in question is normally distributed.

Use the following steps in order to get the optimal amount of items to order in excess of the historical sales average:

1- Determine the historical sales/demand average and its standard deviation.
Where Avg: Historical average of item sales
Where s: Standard deviation of sales

2-Find the probability of items not being sold by solving for P:

P = x / (x+y)

Where x : Cost of overestimating the demand for the item (individual cost of unsold items written off)
Where y : Cost of underestimating the demand for the item (usually individual stock out costs)

3-Once you have finished solving for P, use the NORMSINV() probability function in Microsoft excel to solve for the number of standard deviation to be ordered (also called the Z value). For this step the Normal cumulative distribution tables from a statistics book can also be used.

4-Once the Z value is obtained, number of standard deviations, we just multiply the standard deviation for historical sales we obtained in step 1 (s), times the Z value obtained in step 4 and this will give the number of items to produce/purchase in excess (positive number) or less (negative number) from the Average sales figure obtained in step 1 (Avg).

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