This preview shows pages 1–3. Sign up to view the full content.
Inventory, Production & Supply Chain Mgt.
Chapter 17
493
17
Inventory, Production, and
Supply Chain Management
17.1 Introduction
One carries inventory for a variety of reasons:
a)
protect against uncertainty in demand,
b)
avoid high overhead costs associated with ordering or producing small quantities
frequently,
c)
supply does not occur when demand occurs, even though both are predictable
(e.g., seasonal products such as agricultural products, or antifreeze)
d)
protect against uncertainty in supply,
e)
unavoidable “pipeline” inventories resulting from long transportation times (e.g.,
shipment of oil by pipeline, or grain by barge)
f)
for speculative reasons because of an expected price rise.
We will illustrate models useful for choosing appropriate inventory levels for situations (a), (b),
(c) and (d).
17.2 One Period News Vendor Problem
For highly seasonal products, such as ski parkas, the catalog merchant, L. L. Bean makes an estimate
for the upcoming season, of the mean and standard deviation of the demand for each type of parka.
Because of the short length of the season, L.L. Bean has to make the decision of how much to produce
of each parka type before it sees any of the demand. There are many other products for which
essentially the same decision process applies, for example, newspapers, Christmas trees, antifreeze,
and road salt. This kind of problem is sometimes known as the oneperiod newsvendor problem.
To analyze the problem, we need the following data:
c
= purchase cost/unit.
v
= revenue per unit sold.
h
= holding cost/unit purchased, but not sold. It may be negative if leftovers have a positive
salvage value.
p
= explicit penalty per unit of unsatisfied demand, beyond the lost revenue.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 494
Chapter 17
Inventory, Production & Supply Chain Mgt.
In addition, we need some information about the demand distribution (e.g., its mean and standard
deviation). For the general case, we will presume for any value
x
:
F
(
x
) = probability demand (
D
) is lessthanorequalto
x
.
17.2.1 Analysis of the Decision
We want to choose:
S
= the stockupto level (i.e., the amount to stock in anticipation of demand).
We can determine the best value for
S
by marginal analysis as follows. Suppose we are about to
produce
S
units, but we ask, “What is the expected marginal value of producing one more unit?” It is:

c
+ (
v
+
p
) * Prob{ demand >
S
} –
h
* Prob{ demand
d
S
}
= 
c
+ (
v
+
p
) * ( 1 –
F
(
S
)) –
h
*
F
(
S
)
= 
c
+
v
+
p
– (
v
+
p
+
h
) *
F
(
S
).
If this expression is positive, then it is worthwhile to increase
S
by at least one unit. In general, if
this expression is zero, then the current value of
S
is optimal. Thus, we are interested in the value of
S
for which:
c + v + p –
(
v + p + h
)
* F
(
S
)
=
0
or rearranging:
F
(
S
)
=
(
v + p – c
) / (
v + p + h
)
=
(
v + p – c
) / [(
v + p – c
) + (
c + h
)].
Rephrasing the last line in words:
Probability of not stocking out should = (opportunity shortage cost)/[(opportunity shortage
cost) + ( opportunity holding cost)].
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 05/12/2010 for the course ESI 6323 taught by Professor Guan during the Summer '09 term at University of Florida.
 Summer '09
 Guan

Click to edit the document details