TABLE OF CONTENTS In case a single order of spares must last a fixed time period, or a fixed number of spares undergo repairs and be returned to the spares kit, to last a certain period of time, the understock versus overstock model can be used. A typical example would be a Navy ship whose maintenance facilities must be supplied with enough spares before a cruise, and the spares are expected to be used for some fixed time period. The model [10] balances the cost of having excess parts that are never used versus the cost of being short of parts when needed.
If the variable x denotes the number of spares in stock supplied for a certain period of time, then the expected number of spares in stock for the case when the actual demand is less than the stock level x, is given by
where
| p i = P[ N( t) = i] = | probability of demand of i units. |
Similarly, a shortage of spares occurs when the actual demand of spares is higher than the stock level. Then, the expected number of shortages is given by
The total inventory cost is the sum of the expected overstocking plus expected cost of understocking, or
where
| C h = | holding cost per one unit, |
| C sh = | shortage cost per one unit. |
The optimum stock level which minimizes the total...
