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428 CHAPTER 10 INVENTORY MODELS

This inventory model is In situations in which the demand rate is not deterministic, other models treat
the first in the chapter demand as probabilistic and best described by a probability distribution. In this
that explicitly treats
probabilistic demand. section we consider a single-period inventory model with probabilistic demand.
Unlike the EOQ model, it The single-period inventory model refers to inventory situations in which one
is for a single period with order is placed for the product; at the end of the period, the product has either
unused inventory not
carried over to future sold out, or a surplus of unsold items will be sold for a salvage value. The single-
periods. period inventory model is applicable in situations involving seasonal or perishable
items that cannot be carried in inventory and sold in future periods. Seasonal
clothing (such as bathing suits and winter coats) are typically handled in a single-
period manner. In these situations, a buyer places one pre-season order for each
item and then experiences a stock-out or holds a clearance sale on the surplus
stock at the end of the season. No items are carried in inventory and sold the
following year. Newspapers are another example of a product that is ordered one
time and is either sold or not sold during the single period. Although newspapers
are ordered daily, they cannot be carried in inventory and sold in later periods.
So, newspaper orders may be treated as a sequence of single-period models; that
is, each day or period is separate, and a single-period inventory decision must be
made each period (day). Because we order only once for the period, the only
inventory decision we must make is how much of the product to order at the start
of the period.
Obviously, if the demand were known for a single-period inventory situation,
the solution would be easy; we would simply order the amount we knew would be
demanded. However, in most single-period models, the exact demand is not
known. In fact, forecasts may show that demand can have a wide variety of values.
If we are going to analyze this type of inventory problem in a quantitative manner,
we need information about the probabilities associated with the various demand
values. So, the single-period model presented in this section is based on proba-
bilistic demand.

Juliano Shoe Company
Let us consider a single-period inventory model that could be used to make a how-
much-to-order decision for the Juliano Shoe Company. The buyer for the Juliano
Shoe Company decided to order a men’s shoe shown at a buyers’ meeting in Milan,
Italy. The shoe will be part of the company’s spring-summer promotion and will be
sold through nine retail stores in the UK. Because the shoe is designed for spring
and summer months, it cannot be expected to sell in the autumn. Juliano plans to
hold a special August clearance sale in an attempt to sell all shoes not sold by
July 31. The shoes cost E40 a pair and retail for E60 apair. At thesale price of E30
a pair, all surplus shoes can be expected to sell during the August sale. If you were
the buyer for the Juliano Shoe Company, how many pairs of the shoes would you
order?
An obvious question at this time is: What are the possible values of demand for
the shoe? We need this information to answer the question of how much to order.
Let us suppose that the uniform probability distribution shown in Figure 10.8 can be
used to describe the demand for a given shoe size. In particular, note that the range
of demand is from 350 to 650 pairs of shoes, with an average, or expected, demand
of 500 pairs of shoes.
Incremental analysis is a method that can be used to determine the optimal order
quantity for a single-period inventory model. Incremental analysis addresses the
how-much-to-order question by comparing the cost or loss of ordering one additional
unit with the cost or loss of not ordering one additional unit. The costs involved are
defined as follows:

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