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Lecture 5: Economic Lot Scheduling Example
Consider the economic lot sizing problem with
n
items, setup times
s
i
, demand rate
λ
i
, holding
cost rate
h
i
, production rate
μ
i
and ﬁxed costs
K
i
for all
i
= 1
,...,n
. The goal is to determine
the cycle times,
T
i
for each item. In other words if
T
i
is the cycle period for item
i
, item
i
should
be produced for
ρ
i
T
i
amount of time every
T
i
units of time. Note that in this problem we have a
constraint that the machine can only process a single item at a time.
We discussed that the following capacity constraint is necessary for a feasible solution to exist.
n
X
i
=1
±
s
i
T
i
+
ρ
i
²
≤
1
.
The left hand side of the above constraint is the average utilization of the machine per unit time
or the fraction of time the machine must be busy to satisfy all the demand. However, we can
show that
T
i
satisfying the above constraint may not produce a feasible schedule.
Example
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This note was uploaded on 10/25/2010 for the course IEOR E4000 taught by Professor Vineet during the Fall '10 term at Columbia.
 Fall '10
 vineet

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