Transcript ISE 195 Lecture 1 - Berkeley Industrial Engineering and

Introduction to Industrial Engineering
(II)
Z. Max Shen
Dept. of Industrial Engineering and Operations
Research
University of California
1
IE and Systems
Industrial engineering really takes a
system-level perspective
The tools and techniques of the IE allow
the IE to examine the system, the
interactions among the components of
the system, all while keeping in mind the
objective or purpose of the system
An IE seeks to optimize systems
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Supply Chain Structure
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Example: Military Supply Chain
Army Lt. Gen. Ricardo Sanchez, the senior U.S. military
commander in Iraq from June 2003 until the summer of 2004,
complained last winter to the Pentagon that a poor supply
situation was threatening the Army's ability to fight.
“The lack of key spare parts for tanks, helicopters and other
systems was such a severe problem that I cannot continue to
support sustained combat operations with rates this low”.
It is reported that U.S. Army combat units fighting in Iraq last
year had to resort to capturing key supplies such as lubricants
and explosives from enemy stockpiles. In addition, food
supplies barely met demand, and stocks of ammunition and
spare parts were nearly depleted during combat.
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Example: TSP
Given a set of n nodes and distances for each
pair of nodes, find a roundtrip of minimal total
length visiting each node exactly once.
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6
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Facilities Concerns
How many?
Where to locate?
How to assign customers to facilities?
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Example
Ambulance location
 A number of facilities for ambulances should be
located in various places of a city.
 Driving time/distance is a critical factor in
rescues, and should be minimized.
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Absolute 1-Center problem on a tree
F
A
8
9
7
B
10
C
E
5
11
13
D
H
G
10
15
F
A
8
19
9
0
7
B
7
10
C
E
10
5
11
13
D
5
e1
20
H
21
G
Step 1: Pick any point on the tree and find the vertex that is farthest away
from the point that was picked. Call this vertex e1.
11
36
F
A
8
20
9
21
7
B
28
10
C
E
11
5
11
13
D
41
H
e2
26
e1
0
G
Step 2: Find the vertex that is farthest from e1 and call this vertex e2.
12
F
A
8
9
9.5
7
B
C
10
5
E
11
13
D
e2 H
e1
G
Step 3: The absolute 1-center is at the midpoint of the path from e1 to e2.
The vertex 1-center is at the vertex of the tree that is closest to the
absolute 1-center.
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Absolute 2-Centers
F
A
8
9
9.5
7
B
C
10
5
E
11
13
D
e2 H
e1
G
Step 1: Using the algorithm for the absolute 1-center, find the absolute 1center.
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F
A
8
9
7
B
C
E
5
11
13
D
e2 H
e1
G
Step 2: Delete from the tree the arc containing the absolute 1-center.(If
the absolute 1-center is on a node, delete one of the arcs incident on the
center which is on the path from e1 to e2.) This divides the tree into two
disconnected subtrees.
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F
A
8
B
9
7
X2*
C
E
5
X1*
11
13
D
12.5
10.0
H
e1
G
Step 3: Use the absolute 1-center algorithm to find the absolute 1-center
of each of the subtrees. These locations constitute a solution to the
absolute 2-center problem.
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Median Problem
Find the location of P facilities on a
network so that the total cost of serving
demands is minimized.
Inputs:
hi: demand at node i
dij: distance between demand node i and
candidate site j
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1-median problem on a tree
If half or more of the total demand
is at any node then one optimal
solution consists of locating the
facility at that node.
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Example (P=1): 1-median problem on a tree
hA=10
A
8
hC=7
B
C
hE=14
10
7
hB=5
E
5
D
hD=12
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Example (cont’d)
We start with node A
Fold the demand onto the node that is
incident to node A (B)
Figure 2
Delete node A
hB=15
hC=7
B
C
hE=14
E
10
7
5
Effect of folding tip
node A onto B
D
hD=12
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Example (cont’d)
In Figure 2 none of the nodes has more than half
of the total demand.
Select a tip node
Fold it onto the node which is incident.
hB=15
hC=19
B
C
7
hE=14
10
E
Figure 3
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Example (cont’d)
In Figure 3 none of the nodes has more than
half of the total demand.
Select a tip node
Fold it onto the node which is incident.
Figure 4
hB=15
B
C
7
hC=33
•Now the demand at node C is over half of the total demand.
•Optimal location for the 1-median on the tree is node C
dAC*hA+dBC*hB+dEC*hE+dDC*hD= 15*10+7*5+10*14+5*12 = 385
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A Typical Network Design Model
Several products are produced at several
plants.
Each plant has a known production capacity.
There is a known demand for each product at
each customer zone.
The demand is satisfied by shipping the
products via regional distribution centers.
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A Typical Network Design Model
There may be an upper bound on the
distance between a distribution center and
a market area served by it
A set of potential location sites for the new
facilities was identified
Costs:
 Set-up costs
 Transportation cost is proportional to the
distance
 Storage and handling costs
 Production/supply costs
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Complexity of Network Design Problems
Location problems are, in general, very
difficult problems.
The complexity increases with
 the number of customers,
 the number of products,
 the number of potential locations for
warehouses, and
 the number of warehouses located.
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Solution Techniques
Mathematical optimization techniques:
 Exact algorithms: find optimal solutions
 Heuristics: find “good” solutions, not
necessarily optimal
Simulation models: provide a
mechanism to evaluate specified
design alternatives created by the
designer.
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Heuristics and
the Need for Exact Algorithms
Single product
Two plants p1 and p2
 Plant p1 has an annual capacity of 200,000 units.
 Plant p2 has an annual capacity of 60,000 units.
The two plants have the same production costs.
There are two warehouses w1 and w2 with
identical warehouse handling costs.
There are three markets areas c1,c2 and c3 with
demands of 50,000, 100,000 and 50,000,
respectively.
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Heuristics and
the Need for Exact Algorithms
Table 1
Distribution costs per unit
Facility
Warehouse
W1
W2
P1
P2
C1
C2
C3
0
5
4
2
3
2
4
1
5
2
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Why Optimization Matters?
$0
Cap = 200,000
$4
$5
$5
D = 100,000
$2
$4
Cap = 60,000
D = 50,000
$3
$2
$1
$2
D = 50,000
Production costs are the same, warehousing costs are the same
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