The Stockout versus Holding Problem
The last section was concerned with the question "How much to order". This section
will be concerned with "When to order". For a given size of order will only satisfy
the demand for stock for a certain period and if a subsequent order is delayed the
chance of running out of stock will be higher than if the order were placed at an
earlier moment in time. More specifically the probability of a stockout occurring will
depend on the variability of demand during lead time and the variability of lead time
itself. If both were constant, say a lead time of 10 days and a demand of 20 items per
day, then there would be no point in ordering when, for example, 250 items were in
stock. If this were done a new delivery would always be made when the stock level was
50 items. On the other hand if either or both lead time and demand were variable with
an average of 10 days and 20 items per day respectively then a stockout would occur
whenever demand during lead time exceeded 200 items. The problem is therefore to
decide what the re-order level should be in order to minimise the sum of the cost of
holding stock which, on average, is "dead" (and which is referred to as buffer or
safety stock) and the cost of being out of stock. As was mentioned earlier however the
placing of a reliable cost on a stockout is difficult to achieve and this has led to an
alternative view being widely adopted; namely service level. In this, shortage cost is
not made explicit and re-order level is determined by the requirement to offer a
particular level of service. Approaches using both shortage cost and service level
will be considered. As the latter is more usually used in practice it will be examined
first.