By James E. Gentle

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**Example text**

At the end of this period several freight cars left the base loaded with material that the model said was not needed; several arrived with spares that the new Base Stockage Model (BSM) recommended. Then the test was run for another six months and the performance was compared. The field test was reported on by the Air Force Logistics Command (1967). Introduction 11 The Air Force could have used the model to obtain either better system performance at the same inventory investment, the same system performance at less cost, or some intermediate combination of better performance and less cost as at Hamilton AFB.

For example, suppose a base finds that there is no spare on the shelf at its usual supporting depot; if it is able to go to other depots in search of that spare, it is violating the arborescence assumption. Or if the base can go to other bases to effect a “lateral” shipment, it is violating the assumption. Some model assumptions are bound to be violated at least occasionally in the real world. The modeler’s art is to incorporate in the theory as much of the “physics” of the problem as possible.

5 there are k backorders. The expected number of backorders, EBO(s), is thus: The expected number of backorders is a non-negative quantity. 1 for the mean of a distribution. Thus, EBO(0) = E[X]. 1 The number of backorders is defined as: B(X|s) = (X - s) if X > s = 0 otherwise where X is the random variable for the number of units due in and s is the stock level. 7. Since this is no longer a function of X, we use EBO(s) to simplify the notation in the text. We used a similar simplification for expected fill rate, EFR(s) and later for the variance in backorders, VBO(s).