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Debris Management Operations José Antonio Carbajal, Monica Villarreal Ozlem Ergun, Pinar Keskinocak 1 Georgia Tech Supply Chain & Logistics Institute Center for Humanitarian Logistics

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Page 1: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Debris Management Operations

José Antonio Carbajal, Monica VillarrealOzlem Ergun, Pinar Keskinocak

1

Georgia Tech Supply Chain & Logistics InstituteCenter for Humanitarian Logistics

Page 2: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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)

Page 3: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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..

Page 4: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 5: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 6: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 7: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 8: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 9: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Model Formulation (1/2)

Total Penalty

9

Balance Equations(per period, location and

relief type)

Page 10: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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)

Page 11: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 12: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 13: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 14: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 15: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 16: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 17: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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)

Page 18: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 19: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 20: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 21: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 22: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Heuristics

� Periodic LP Heuristic

� Periodic MIP Heuristic

� Hybrid Heuristic

22

� Hybrid Heuristic

Page 23: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 24: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 25: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 26: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 27: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 28: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 29: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 30: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 31: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

-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

Page 32: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 33: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 34: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 35: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 36: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 37: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Impact of different priorities

Same priority Lower income ���� higher priority

37

Low IncomeMedium IncomeHigh Income

POD

Low Income, connectedMedium Income, connectedHigh Income, connected

Page 38: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Impact of different priorities

Same priority Lower income ���� higher priority

38

Low IncomeMedium IncomeHigh Income

POD

Low Income, connectedMedium Income, connectedHigh Income, connected

Page 39: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Impact of different priorities

Same priority Lower income ���� higher priority

39

Low IncomeMedium IncomeHigh Income

POD

Low Income, connectedMedium Income, connectedHigh Income, connected

Page 40: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Impact of different priorities

Same priority Lower income ���� higher priority

40

Low IncomeMedium IncomeHigh Income

POD

Low Income, connectedMedium Income, connectedHigh Income, connected

Page 41: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

Impact of different priorities

Same priority Lower income ���� higher priority

41

Low IncomeMedium IncomeHigh Income

POD

Low Income, connectedMedium Income, connectedHigh Income, connected

Page 42: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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

Page 43: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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%

Page 44: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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%

Page 45: Debris Management Operations - ISyE Home · 2009-10-03 · Debris Management Operations Waste generated after a disaster: Vegetation Construction waste Household hazardous waste White

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