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1
1
Inventory Decision Making
Chapter 6
(Part 4)
2
Estimation of Discrete Distribution
The frequency counts of past demand during lead time can be used
to determine a probability distribution as follows:
1.
add the frequencies to obtain the number of observations (i.e.,
sample size)
2.
divide each frequency by the sample size
frequency
800
= 0.06
800
= 0.01
Demand
Number of Cycles
Probability
100
8
110
48
120
192
.24
130
304
.38
140
192
.24
150
48
.06
160
8
.01
800
1.00
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3
Expected Value
The expected value, or
mean
, of a random variable X with
probability distribution p(X) is expressed as:
E(X) = ∑ x
i
p(x
i
)
Determine the expected value for the following demand distribution.
Demand
Probability
100
0.01
110
0.06
120
0.24
130
0.38
140
0.24
150
0.06
160
0.01
x
i
p(x
i
)
100 (0.01)
=
1.0
110 (0.06)
=
6.6
120 (0.24)
=
28.8
49.4
33.6
9.0
1.6
130.0
4
The second of two perspectives involving uncertainty when
determining the reorder point (ROP) for the basic EOQ model
will be considered now.
1. Reorder point based on customer service level
2. Reorder point based on minimizing costs
EOQ Reorder Point Under Uncertainty
3
5
Assumptions
The EOQ model assumptions hold, except that demand is
uncertain with a discrete probability distribution which can
be estimated.
Two expected costs need to be calculated based on the
discrete demand distribution:
expected
carrying cost
per year
E[CC] =
W V e
expected
stockout cost
per year
E[SC] =
G R / Q
ROP is based on minimizing expected total cost expressed as:
Expected Total Cost = E[CC] + E[SC]
ROP Based on Minimizing Costs
6
Excess Inventory or Shortage?
Consider each of the combinations of demand and reorder points shown
below.
When is there excess inventory and when is there a shortage (which
may result in lost sales or backorders)?
Insert these quantities in the table.
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This note was uploaded on 04/11/2011 for the course WCOB 2023 taught by Professor Billthompson during the Spring '07 term at Arkansas.
 Spring '07
 billthompson

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