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Optimization I
ob
eachman
Rob Leachman
E10, Spring, 2010
February 1, 2010
Feb. 1, 2010
E10 Optimization I
Prof. Leachman
1
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View Full Document hat is Optimization
What is Optimization
• Calculation of how best to operate or configure a
ystem
system
– Decision variables (
A
for what we can
adjust
)
– Objective function (
B
for what’s
best
)
– Constraints on variables (
C
for how are we
constrained
)
• Mathematical methods of optimization
– Calculus: Functional characterization of possible
decisions and economic consequences
– Search: Enumeration and evaluation of alternative
decisions
• Directed search (always move to a better alternative)
•S
topping rule: Proof of optimality without evaluating every
Feb. 1, 2010
E10 Optimization I
Prof. Leachman
2
pp g
p
y
g
y
alternative
ventory Replenishment Problem
Inventory Replenishment Problem
• Demand for a good occurs at a steady rate
D
per unit time and must be met from onhand
inventory.
•
e replenish inventory by ordering in batches It
We replenish inventory by ordering in batches. It
takes
L
units of time from the time we place a
replenishment order until the order arrives.
• When we order, we buy the good at a cost of
c
per unit. In addition, there is a fixed
replenishment cost
A
per order (regardless of
how small or large the order is).
• We have to finance and store onhand inventory.
his costs
er unit per unit time
Feb. 1, 2010
E10 Optimization I
Prof. Leachman
3
This costs
h
per unit per unit time.
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View Full Document et up the Optimization Model
Set up the Optimization Model
• Understand the problem.
• What do we have to decide (A)?
– When to order, how much to order
Q
• What’s best (B)?
– We have to worry about the ordering cost and the
inventory holding cost. We want to minimize costs.
• How are we constrained (C)?
– We have to meet the demand, i.e., we have to keep
the inventory from running out.
yg
– We must place an order when the inventory falls to
level
L*D
(and there is no reason to place an order
before then).
Feb. 1, 2010
E10 Optimization I
Prof. Leachman
4
odel set p (cont )
Model set up (cont.)
Figure 1. Inventory Level vs. Time 
=200, D=1,000
Q 200, D 1,000
250
150
200
ry Level
50
100
Invent
o
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ime
Feb. 1, 2010
E10 Optimization I
Prof. Leachman
5
Time
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View Full Document odel set p (cont )
Model set up (cont.)
• If we order a very large batch, we delay
spending
A
again, but we have to pay
h
on a
large inventory (which gets worked off at rate
D
)
we order a small batch we pay
nasma
l
l
• If we order a small batch, we pay
h
on a small
inventory, but we will have to pay
A
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This note was uploaded on 02/19/2010 for the course ENGINEERIN 72826 taught by Professor Sengupta/leachman/johnson during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Sengupta/Leachman/Johnson
 Optimization

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