debris management operations - isye home · 2009-10-03 · debris management operations waste...
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Debris Management Operations
José Antonio Carbajal, Monica VillarrealOzlem Ergun, Pinar Keskinocak
1
Georgia Tech Supply Chain & Logistics InstituteCenter for Humanitarian Logistics
Debris Management Operations
� Waste generated after a disaster:� Vegetation� Construction waste� Household hazardous waste� White goods� Dead animals, etc.
Short term impact:
2
� Short term impact:� Transportation of relief resources� Access to critical facilities
� Long term impact:� Threat to human health� Environmental impact
Pictures taken from FEMA (Federal Emergency Management Agency)
Motivation
� Amount equivalent to years of normal solid waste.� Hurricane Ike (2008): 19 million CY 1
� Hurricane Katrina (2005): More than 100 million CY 2
� Costly, long and complicated process: � About 27% of the disaster recovery cost 3
� Three months after Hurricane Ike hit: 4
� 30 mile debris pile in Smith Point, TX.$40 million and 8 months to dispose it
3
� $40 million and 8 months to dispose it
� Federal and local guidelines3
� Focus on ‘what’, rather than ‘how’� Need of model/tools for planning and execution
[1] Myers, R. (2008). “FEMA extends registration deadline, sticks to debris removal deadline”. Beaumont Enterprise. [2] “Disaster Debris Removal After Hurricane Katrina: Status and Associated Issues”. CRS Report for Congress.[3] “Public Assistance Debris Management Guide”. Federal Emergency Management Agency (FEMA). [4] “Texas Residents Watch Hurricane Ike Debris Mount”. National Public Radio..
Debris Management Operations Components
Design Event andDebris Forecasts
Debris Collection Procurement
Strategy
Pre-Disaster Post-DisasterResponse
Disaster Timeline
Debris Collection
Response Operations Recovery OperationsResponse Operations
4
Strategy
Debris Management Sites
Planning
Debris Management SitesOperation
Debris Reduce/ Recycling
Debris Final Disposal
Response Operations Recovery OperationsResponse Operations
Debris Management Operations Components
Design Event andDebris Forecasts
Debris Collection Procurement
Strategy
Pre-Disaster Post-DisasterResponse
Disaster Timeline
Debris Collection
Response Operations Recovery OperationsResponse Operations
5
Strategy
Debris Management Sites
Planning
Debris Management SitesOperation
Debris Reduce/ Recycling
Debris Final Disposal
Response Operations Recovery OperationsResponse Operations
Debris Management Operations Components
Design Event andDebris Forecasts
Debris Collection Procurement
Strategy
Pre-Disaster Post-DisasterResponse
Disaster Timeline
Debris Collection
Response Operations Recovery OperationsResponse Operations
6
Strategy
Debris Management Sites
Planning
Debris Management SitesOperation
Debris Reduce/ Recycling
Debris Final Disposal
Response Operations Recovery OperationsResponse Operations
Similar Problems in the Literature� Vehicle routing for urban snow plowing operations1
� Determine route to serve all segments� Objective function related to time� “Clean” segments have higher speed
� Multiple Hierarchical Chinese Postman Problem� Road hierarchy is a model input
� Emergency repair of road systems2
� Determine teams’ schedule to repair a road system
7
� Determine teams’ schedule to repair a road system� Minimize time to tasks completion� “Blocked” roads have no through traffic
� Time-space Network Model� There is no road priority
� Use of heuristics to solve real size problems
[1] Perrier, N., Langevin, A. 2008. Vehicle routing for urban snow plowing operations. Transportation Science. 42, 44-56[2] Yan, S., Shi, Y. 2007. A time-space network model for work team scheduling after a major disaster. Journal of the Chinese Institute of Engineers 30, 63-75
Debris Collection: Response Model
SSSS
2222
DDDD
1111
SSSS
1111
S#
S#
D#
D#
Relief Supply
Relief Demand
Debris-blocked arc
Clear arc
SSSS
2222
8
� Input: Road network condition, clearance capacity, effort required, relief supply/demand locations
� Output: which/when road segments to open
� Main idea: penalties for unconnected demand locations
DDDD
1111
DDDD
1111
DDDD
1111
DDDD
1111
Model Formulation (1/2)
Total Penalty
9
Balance Equations(per period, location and
relief type)
Model Formulation (2/2)
Effort / budget(per period)
Blocked arc restrictions
(per period and arc)
10
Integrality & Nonnegativity
(per period)
Bidirectional clearance
(per period and arc)
Experimental Setting: Grid Network
� Network sizes
� Condition of the network (all/some blocked)
� Effort to unblock an arc
Size
Configuration
Small
16 nodes
(2 supply , 14 demand)
Medium
144 nodes
(4 supply , 140 demand)
Large
576 nodes
(16 supply , 560 demand)
11
48 arcs 528 arcs 2208 arcs
All blocked,
Effort: all same� “Grid” networks
� 1 relief type
� 10 replications per scenario
� Penalty ~ U(100,200)
All blocked,
Effort: 50% low, 50% high
50% blocked,
Effort: all same
50% blocked
Effort: 50% low, 50% high
MIP Model Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort: all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
01:40 hrs
00:44 hrs
40.7%
12:00 hrs
11:20 hrs
43.4%
12:00 hrs
11:32 hrs
All blocked,
Effort: 50% low, 50%
Optimality GAP:
Run Time:
0.0%
05:44 hrs
51.9%
12:00 hrs
55.7%
12:00 hrs
12
CPLEX 11.110 ran for (at most) 12 hrs
Optimality GAP = (Upper Bound – Lower Bound)/Upper Bound = (Best IP Soln – LP Relaxation Soln) / Best IP Soln
Effort: 50% low, 50% high
Run Time:
Time to Best :
05:44 hrs
02:02 hrs
12:00 hrs
11:13 hrs
12:00 hrs
10:51 hrs
50% blocked,
Effort: all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
21.4%
12:00 hrs
03:22 hrs
25.3%
12:00 hrs
9:57 hrs
50% blocked
Effort: 50% low, 50% high
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
28.2%
12:00 hrs
07:05 hrs
39.2%
12:00 hrs
11:25 hrs
MIP Model Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
01:40 hrs
00:44 hrs
40.7%
12:00 hrs
11:20 hrs
43.4%
12:00 hrs
11:32 hrs
All blocked,
Effort= 50% low, 50%
Optimality GAP:
Run Time:
0.0%
05:44 hrs
51.9%
12:00 hrs
55.7%
12:00 hrs
13
Effort= 50% low, 50% high
Run Time:
Time to Best :
05:44 hrs
02:02 hrs
12:00 hrs
11:13 hrs
12:00 hrs
10:51 hrs
50% blocked,
Effort= all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
21.4%
12:00 hrs
03:22 hrs
25.3%
12:00 hrs
9:57 hrs
50% blocked
Effort= 50% low, 50% high
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
28.2%
12:00 hrs
07:05 hrs
39.2%
12:00 hrs
11:25 hrs
CPLEX 11.110 ran for (at most) 12 hrs
Optimality GAP = (Upper Bound – Lower Bound)/Upper Bound = (Best IP Soln – LP Relaxation Soln) / Best IP Soln
MIP Model Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
01:40 hrs
00:44 hrs
40.7%
12:00 hrs
11:20 hrs
43.4%
12:00 hrs
11:32 hrs
All blocked,
Effort= 50% low, 50%
Optimality GAP:
Run Time:
0.0%
05:44 hrs
51.9%
12:00 hrs
55.7%
12:00 hrs
14
Effort= 50% low, 50% high
Run Time:
Time to Best :
05:44 hrs
02:02 hrs
12:00 hrs
11:13 hrs
12:00 hrs
10:51 hrs
50% blocked,
Effort= all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
21.4%
12:00 hrs
03:22 hrs
25.3%
12:00 hrs
9:57 hrs
50% blocked
Effort= 50% low, 50% high
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
28.2%
12:00 hrs
07:05 hrs
39.2%
12:00 hrs
11:25 hrs
CPLEX 11.110 ran for (at most) 12 hrs
Optimality GAP = (Upper Bound – Lower Bound)/Upper Bound = (Best IP Soln – LP Relaxation Soln) / Best IP Soln
1.8
2
2.2
2.4
2.6
2.8 All Blocked, Same Effort
All Blocked, 50% Low & 50% High Effort
50% Blocked, Same Effort
50% Blocked, 50% Low & 50% High Effort
MIP Model Results vs. Run Rime
Medium Network M
IP S
olu
tio
n/ L
ow
er B
ou
nd
15
1
1.2
1.4
1.6
1.8
0 1 2 3 4 5 6 7 8 9 10 11 12
Run Time (Hrs)
MIP
So
luti
on
/ Lo
wer
Bo
un
d
MIP Model Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
01:40 hrs
00:44 hrs
40.7%
12:00 hrs
11:20 hrs
43.4%
12:00 hrs
11:32 hrs
All blocked,
Effort= 50% low, 50%
Optimality GAP:
Run Time:
0.0%
05:44 hrs
51.9%
12:00 hrs
55.7%
12:00 hrs
16
Effort= 50% low, 50% high
Run Time:
Time to Best :
05:44 hrs
02:02 hrs
12:00 hrs
11:13 hrs
12:00 hrs
10:51 hrs
50% blocked,
Effort= all same
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
21.4%
12:00 hrs
03:22 hrs
25.3%
12:00 hrs
9:57 hrs
50% blocked
Effort= 50% low, 50% high
Optimality GAP:
Run Time:
Time to Best :
0.0%
< 1 min
< 1 min
28.2%
12:00 hrs
07:05 hrs
39.2%
12:00 hrs
11:25 hrs
CPLEX 11.110 ran for (at most) 12 hrs
Optimality GAP = (Upper Bound – Lower Bound)/Upper Bound = (Best IP Soln – LP Relaxation Soln) / Best IP Soln
5
6
7
8 All Blocked, Same Effort
All Blocked, 50% Low & 50% High Effort
50% Blocked, Same Effort
50% Blocked, 50% Low & 50% High Effort
MIP Model Results vs. Run Rime
MIP
So
luti
on
/ Lo
wer
Bo
un
dLarge Network
17
1
2
3
4
0 1 2 3 4 5 6 7 8 9 10 11 12
MIP
So
luti
on
/ Lo
wer
Bo
un
d
Run Time (Hrs)
Experimental Setting: Ring Network
Size
Configuration
Small
17 nodes
(2 supply , 15 demand)
Medium
145 nodes
(4 supply , 141 demand)
Large
577 nodes
(16 supply , 561 demand)
18
64 arcs 576 arcs 2304 arcs
All blocked,
Effort: all same� “Ring” networks
� 1 relief type
� 10 replications per scenario
� Penalty ~ U(100,200)
All blocked,
Effort: 50% low, 50% high
50% blocked,
Effort: all same
50% blocked
Effort: 50% low, 50% high
MIP Model Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort: all same
Optimality GAP:
Run Time:
Time to Best :
6.06%
12:00 hrs
0:51 hrs
39.3%
12:00 hrs
11:07 hrs
41. 6%
12:00 hrs
11:37 hrs
All blocked,
Effort: 50% low, 50%
Optimality GAP:
Run Time:
1.72%
10:54 hrs
43.8%
12:00 hrs
49.1%
12:00 hrs
19
CPLEX 11.110 ran for (at most) 12 hrs
Optimality GAP = (Upper Bound – Lower Bound)/Upper Bound = (Best IP Soln – LP Relaxation Soln) / Best IP Soln
Effort: 50% low, 50% high
Run Time:
Time to Best :
10:54 hrs
0:43 hrs
12:00 hrs
11:06 hrs
12:00 hrs
11:36 hrs
50% blocked,
Effort: all same
Optimality GAP:
Run Time:
Time to Best :
0%
<1 min
<1 min
19.8%
12:00 hrs
3:36 hrs
23.2%
12:00 hrs
11:07 hrs
50% blocked
Effort: 50% low, 50% high
Optimality GAP:
Run Time:
Time to Best :
0%
<1 min
<1 min
25.83%
12:00 hrs
6:58 hrs
35.93%
12:00 hrs
11:32 hrs
Experimental Setting: Incomplete Grid Network
Size
Configuration
Small
16 nodes
(2 supply , 14 demand)
36 arcs avg.
Medium
144 nodes
(4 supply , 140 demand)
306 arcs avg.
Large
576 nodes
(16 supply , 560 demand)
1196 arcs avg.
20
36 arcs avg. 306 arcs avg. 1196 arcs avg.
All blocked,
Effort: all same� “Incomplete Grid” networks
� Arcs removed randomly: 25% avg. small, and ~40% avg. medium & large
� 1 relief type
� 10 replications per scenario
� Penalty ~ U(100,200)
All blocked,
Effort: 50% low, 50% high
50% blocked,
Effort: all same
50% blocked
Effort: 50% low, 50% high
MIP Model Results
Size
Configuration
Small
16 nodes
36 arcs avg.
Medium
144 nodes
306 arcs avg.
Large
576 nodes
1196 arcs avg.
All blocked,
Effort: all same
Optimality GAP:
Run Time:
Time to Best :
0%
0:35 hrs
0:11 hrs
46.1%
12:00 hrs
7:37 hrs
48.8%
12:00 hrs
11:07 hrs
All blocked,
Effort: 50% low, 50%
Optimality GAP:
Run Time:
0%
0:04 hrs
49.5%
12:00 hrs
49.9%
12:00 hrs
21
CPLEX 11.110 ran for (at most) 12 hrs
Optimality GAP = (Upper Bound – Lower Bound)/Upper Bound = (Best IP Soln – LP Relaxation Soln) / Best IP Soln
Effort: 50% low, 50% high
Run Time:
Time to Best :
0:04 hrs
0:00 hrs
12:00 hrs
9:39 hrs
12:00 hrs
11:06 hrs
50% blocked,
Effort: all same
Optimality GAP:
Run Time:
Time to Best :
0%
<1 min
<1 min
20.8%
12:00 hrs
0:53 hrs
28.3%
12:00 hrs
7:38 hrs
50% blocked
Effort: 50% low, 50% high
Optimality GAP:
Run Time:
Time to Best :
0%
<1 min
<1 min
24.4%
12:00 hrs
5:59 hrs
34.4%
12:00 hrs
10:39 hrs
Heuristics
� Periodic LP Heuristic
� Periodic MIP Heuristic
� Hybrid Heuristic
22
� Hybrid Heuristic
Periodic LP Heuristic
� Main Idea
� Modify the input and solve the LP relaxation
� Fix the variables per period according to some ranking (largest LP value)
� Main steps :
� Update available resources
Use LP value to create a ranked list of road segments
23
� Use LP value to create a ranked list of road segments
� From the ones feasible to open (given resources available), choose the largest and fix to ‘open’
� If no road segment is feasible, move to next period
� Solve the resulting LP and repeat the steps
Why to adjust the demand input?
� Main Idea
� Demand input = connectivity demand
� =1 � demand of connecting a demand node with a supply node
� =0, otherwise
� LP value reflects ‘usage’ of road segment to connect supply nodes with demand nodes, but not the importance of such connection
� Approach
� Adjust demand input with penalty
24
S
D
D
D
P=1
P=1
P=10
2
1
1
1
S
D
D
D
P=1
P=1
P=10
2
1
1
10
Which arc is more important?
Adjusted Demand InputOriginal Demand Input
Periodic MIP Heuristic
� Main Idea
� Do the best possible at current period
� Fix optimally the variables on each period
� … Only efficient with short instances � limit runtime
� Main steps :
� Solve for period t, up to allowed runtime
=minimize penalty at period t
25
� =minimize penalty at period t
� Fix best found integer solution for period t
� Use as initial road conditions for next periods
� Repeat
Hybrid Heuristic� Main Idea
� Use Periodic LP Heuristic to find an initial solution to the Periodic MIP
� Hybrid vs Periodic MIP
� Start at a potentially better initial solution for each period t
� Solution is improved (up to limit runtime)
� Main steps :
Run the Periodic LP Heuristic
26
� Run the Periodic LP Heuristic
� Use solutions for period t as initial solutions for the Periodic MIP heuristic, period t
� Run Periodic MIP heuristic for the period t, up to allowed runtime
� Fix best found integer solution for period t
� Repeat
Heuristics Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.1%
< 1 min
Hybrid
-7.4%
8 min
Periodic LP
-12.24%
3 min
All blocked,
Effort= 50% low,
Heuristic:
Solution Vs. MIP:
Periodic MIP
0.1%
Hybrid
-16.6%
Periodic LP
-12.66%
27
Effort= 50% low, 50% high
Solution Vs. MIP:
Run Time:
0.1%
< 1 min
-16.6%
9 min
-12.66%
4 min
50% blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
1.4%
2 min
Periodic LP
0.2%
2 min
50% blocked
Effort= 50% low, 50% high
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
-1.43%
4 min
Periodic LP
-4.3%
2 min
Heuristics Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.1%
< 1 min
Hybrid
-7.4%
8 min
Periodic LP
-12.24%
3 min
All blocked,
Effort= 50% low,
Heuristic:
Solution Vs. MIP:
Periodic MIP
0.1%
Hybrid
-16.6%
Periodic LP
-12.66%
28
Effort= 50% low, 50% high
Solution Vs. MIP:
Run Time:
0.1%
< 1 min
-16.6%
9 min
-12.66%
4 min
50% blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
1.4%
2 min
Periodic LP
0.2%
2 min
50% blocked
Effort= 50% low, 50% high
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
-1.43%
4 min
Periodic LP
-4.3%
2 min
Heuristics Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.1%
< 1 min
Hybrid
-7.4%
8 min
Periodic LP
-12.24%
3 min
All blocked,
Effort= 50% low,
Heuristic:
Solution Vs. MIP:
Periodic MIP
0.1%
Hybrid
-16.6%
Periodic LP
-12.66%
29
Effort= 50% low, 50% high
Solution Vs. MIP:
Run Time:
0.1%
< 1 min
-16.6%
9 min
-12.66%
4 min
50% blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
1.4%
2 min
Periodic LP
0.2%
2 min
50% blocked
Effort= 50% low, 50% high
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
-1.43%
4 min
Periodic LP
-4.3%
2 min
Heuristics Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.1%
< 1 min
Hybrid
-7.4%
8 min
Periodic LP
-12.24%
3 min
All blocked,
Effort= 50% low,
Heuristic:
Solution Vs. MIP:
Periodic MIP
0.1%
Hybrid
-16.6%
Periodic LP
-12.66%
30
Effort= 50% low, 50% high
Solution Vs. MIP:
Run Time:
0.1%
< 1 min
-16.6%
9 min
-12.66%
4 min
50% blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
1.4%
2 min
Periodic LP
0.2%
2 min
50% blocked
Effort= 50% low, 50% high
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
< 1 min
Hybrid
-1.43%
4 min
Periodic LP
-4.3%
2 min
-10.00%
-5.00%
0.00%
5.00%
0 2 10 20 30
All Blocked, Same EffortAll Blocked, 50% Low & 50% High Effort50% Blocked, Same Effort50% Blocked, 50% Low & 50% High EffortAll Large
Hybrid Heuristic: Time Tradeoff(Large Instances)
So
luti
on
Vs.
MIP
31
-25.00%
-20.00%
-15.00%
-10.00%
Max. Time per MIP (min)
So
luti
on
Vs.
MIP
Max. Time per MIP (min)
To
tal R
un
Tim
e
0:00
0:14
0:28
0:43
0:57
1:12
1:26
1:40
1:55
2:09
2:24
0 2 10 20 30
Heuristics Results
Size
Configuration
Small
16 nodes
48 arcs
Medium
144 nodes
528 arcs
Large
576 nodes
2208 arcs
All blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
<1 min
Hybrid
-6.8%
4 min
Periodic LP
-10.27%
2 min
All blocked,
Effort= 50% low,
Heuristic:
Solution Vs. MIP:
Periodic MIP
0.0%
Hybrid
-10.41%
Periodic LP
-10.22%
32
Effort= 50% low, 50% high
Solution Vs. MIP:
Run Time:
0.0%
<1 min
-10.41%
6 min
-10.22%
3 min
50% blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.0%
<1 min
Hybrid
1.5%
2 min
Periodic LP
0.8%
2 min
50% blocked
Effort= 50% low, 50% high
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.9%
<1 min
Hybrid
1.6%
4 min
Periodic LP
-0.14%
2 min
Heuristics Results
Size
Configuration
Small
16 nodes
36 arcs avg.
Medium
144 nodes
306 arcs avg.
Large
576 nodes
1196 arcs avg.
All blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.9%
<1 min
Hybrid
-8.0%
8 min
Hybrid
-9.3%
16 min
All blocked,
Effort= 50% low,
Heuristic:
Solution Vs. MIP:
Periodic MIP
6.9%
Hybrid
-10.1%
Hybrid
-6.3%
33
Effort= 50% low, 50% high
Solution Vs. MIP:
Run Time:
6.9%
<1 min
-10.1%
11min
-6.3%
18 min
50% blocked,
Effort= all same
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
0.15%
<1 min
Hybrid
-1.01%
4 min
Hybrid
-3.2%
6 min
50% blocked
Effort= 50% low, 50% high
Heuristic:
Solution Vs. MIP:
Run Time:
Periodic MIP
2.9%
<1 min
Hybrid
-4.4%
4 min
Hybrid
-9.4%
10 min
Operational Insights
� How do different priorities for different sectors affect the outcome?
� Higher priority for the downtown area
� Higher priority of lower income population, etc.
What is the impact of increasing debris clearance
34
� What is the impact of increasing debris clearance capacity?
� FEMA’s Gap Analysis between requirements and capabilities
Miami-Dade setting
� Node: road intersection (545 nodes)
� Arc: road segment joining two nodes (1968 arcs)
� Homogenous network
� 13 supply locations� Points of Distribution, PODs
(Hurricane Wilma)
35
(Hurricane Wilma)
� Penalty based on each node’s estimated population� Per period, while node is
unconnected to POD
� Results using Periodic LP Heuristic POD
Debris-blocked arc
Impact of different priorities
� Nodes classified as high, medium or low income
� Municipality income level
� Two scenarios
� All nodes have the same priority
Lower income node are more urgent to connect
36
� Lower income node are more urgent to connect
� Medium income: double penalty factor
� Low income: quadruple penalty factor
Impact of different priorities
Same priority Lower income ���� higher priority
37
Low IncomeMedium IncomeHigh Income
POD
Low Income, connectedMedium Income, connectedHigh Income, connected
Impact of different priorities
Same priority Lower income ���� higher priority
38
Low IncomeMedium IncomeHigh Income
POD
Low Income, connectedMedium Income, connectedHigh Income, connected
Impact of different priorities
Same priority Lower income ���� higher priority
39
Low IncomeMedium IncomeHigh Income
POD
Low Income, connectedMedium Income, connectedHigh Income, connected
Impact of different priorities
Same priority Lower income ���� higher priority
40
Low IncomeMedium IncomeHigh Income
POD
Low Income, connectedMedium Income, connectedHigh Income, connected
Impact of different priorities
Same priority Lower income ���� higher priority
41
Low IncomeMedium IncomeHigh Income
POD
Low Income, connectedMedium Income, connectedHigh Income, connected
Impact of different priorities
Same priority Lower income ���� higher priority
1,500
2,000
2,500
1,500
2,000
2,500
42
0
500
1,000
Period #2 Period #3 Period #4 Period #5
0
500
1,000
Period #2 Period #3 Period #4 Period #5
Low Income, connectedMedium Income, connectedHigh Income, connected
Impact of additional resources
% C
han
ge
in T
ota
l Pen
alty
wrt
Bas
e C
ase
10%
20%
30%
40%
50%
60%
70%
43
% C
han
ge
in T
ota
l Pen
alty
wrt
Bas
e C
ase
% Change in Resources wrt Base Case
-40%
-30%
-20%
-10%
0%
10%
-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Impact of additional resources
% C
han
ge
in T
ota
l Pen
alty
wrt
Bas
e C
ase
10%
20%
30%
40%
50%
60%
70%
44
% C
han
ge
in T
ota
l Pen
alty
wrt
Bas
e C
ase
% Change in Resources wrt Base Case
-40%
-30%
-20%
-10%
0%
10%
-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Next Steps
� Computational
� Further Instances
� Different network structures (clustered, hub, etc.)
� Non-homogeneous networks
� Additional Heuristics
� Randomized rounding heuristics
45
� Randomized rounding heuristics
� Theoretical
� Strong valid inequalities to strengthen the Lower Bounds