debris management operations - isye home · 2009-10-03 · debris management operations waste...

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