Question

Fomula to calculate lost sales cost in backlogging inventory model

Answer 1

EXAMPLE 1 Wholesale Distribution of Bicycles
A wholesale distributor of bicycles is having trouble with shortages of a popular model
(a small, one-speed girl’s bicycle) and is currently reviewing the inventory policy for this
model. The distributor purchases this model bicycle from the manufacturer monthly and
then supplies it to various bicycle shops in the western United States in response to pur-
chase orders. What the total demand from bicycle shops will be in any given month is
quite uncertain. Therefore, the question is, How many bicycles should be ordered from
the manufacturer for any given month, given the stock level leading into that month?
The distributor has analyzed her costs and has determined that the following are
important:
1. The ordering cost, i.e., the cost of placing an order plus the cost of the bicycles be-
ing purchased, has two components: The administrative cost involved in placing an or-
der is estimated as $200, and the actual cost of each bicycle is $35 for this wholesaler.
2. The holding cost, i.e., the cost of maintaining an inventory, is $1 per bicycle remain-
ing at the end of the month. This cost represents the costs of capital tied up, warehouse
space, insurance, taxes, and so on.
3. The shortage cost is the cost of not having a bicycle on hand when needed. This par-
ticular model is easily reordered from the manufacturer, and stores usually accept a

delay in delivery. Still, although shortages are permissible, the distributor feels that she
incurs a loss, which she estimates to be $15 per bicycle per month of shortage. This
estimated cost takes into account the possible loss of future sales because of the loss
of customer goodwill. Other components of this cost include lost interest on delayed
sales revenue, and additional administrative costs associated with shortages. If some
stores were to cancel orders because of delays, the lost revenues from these lost sales
would need to be included in the shortage cost. Fortunately, such cancellations nor-
mally do not occur for this model.
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