Collaborative Research:
Modeling the Efficacy of Inventory for
Extreme Event Preparedness Decision Making
in Interdependent Systems
• This work extends the Dynamic Inoperability Input-Output Model (DIIM) for
assessing productivity degradations due to disasters.
• Inventory policies are formulated and incorporated within the DIIM to evaluate
the impact of inventories on the resilience of disrupted interdependent
systems.
Joost R. Santos, Ph.D.
Industrial Engineering
Engineering Management and
Systems Engineering
The George Washington University
NSF CMMI 0963718
Kevin B. Wright, Ph.D.
Communication
University of Oklahoma
NSF CMMI 0927299
Model Background
Basic Leontief economic input-output
model was extended to describe how
inoperability, or a proportion of
“dysfunctionality,” propagates through a
set of interconnected infrastructure and
industry sectors with the Inoperability
Input-Output Model (IIM) [Santos 2006]:

q  A*q  c*  q  I  A

* 1 *
c
• q: inoperability
• A*: interdependency matrix
• c*: sector perturbation
Interdependency parameters are derived
from Bureau of Economic Analysis accounts.
Inventory-Based Interdependency Model
Extended to address dynamic onset of and
recovery from disruptive event with
Dynamic Inoperability Input-Output Model
(DIIM) [Lian and Haimes 2006]:
qt  1  qt   K[ A*qt   c* t   qt ]
•
•
•
•
• Allows decision makers to model the efficacy of risk management strategies
which involve the implementation of inventory policies, the efficacy of which
can be evaluated by quantifying how inventory delays inoperability, how
operability in interdependent sectors is then sustained, and how economic
losses are reduced.



q t   k c t   q t   a q t 
if X t  1  p t  1x t  1
q(t): inoperability at time t
K: resilience coefficient
A*: interdependency matrix
c*(t): sector perturbation at time t
0.2
0.16
0.12
0.08
0.04
0
At time t for sector i
• qi(t): inoperability
• pi(t): production inoperability
• xi(t): total anticipated output
• Xi(t): inventory level
• li: repair coefficient
Sector 1
Sector 2
0
5
10
15
20
25
30
Time after Disruption (days)
n
 i


i
i
ij j
i
i
i
j 1





X i t  1




p
t

1

 i

xi t  1
if 0  X i t  1  p i t  1xi t  1

max 
n



q i t   k i ci t   q i t    a ij q j t 


j 1


q i t  1  


 p i t  1
if X i t  1  0, X i t   0


n


max
q t   k c  t   q t   a  q t 



i i
i
ij j
 i

j

1





n

if X i t  1  X i t   0
 

q i t   k i ci t   q i t    a ij q j t 

j 1



i
Inoperability
Abstract
Kash Barker, Ph.D.

Application 1: BEA Inventory Data
Application 2: Workforce Disruption
Summary and Conclusions
• BEA national income and product account (NIPA) tables provide inventories in
manufacturing and trade sectors in dollars and as a ratio of inventory-to-sales.
The inventory-to-sales ratio can be used to describe the likelihood that
inventory will change due to some change in demand.
• Inventory DIIM was used to evaluate the key sectors affected by and affecting
other sectors in a workforce-centered production inoperability scenario. Total
output and workforce compensation data for 15 sectors from BEA below.
• After a disruptive event, two broad categories of economic effects can be
observed: (i) inability of some
Code
Sector
xi
wi
workforce sectors to commute
S1 Agriculture, forestry
368,230
42,095
to work, and (ii) delay in
S2 Mining
478,703
63,128
S3 Utilities
436,036
43,450
shipments of commodities.
S4 Construction
1,370,568
478,267
• We consider a workforceS5 Manufacturing
5,013,074
924,098
S6 Wholesale trade
1,206,890
453,152
debilitating scenario that affects
S7 Retail trade
1,271,569
482,286
the entire nation, such as a
S8 Transport. and warehousing
782,347
248,461
S9 Information
1,340,850
238,903
pandemic, lasting potentially
S10 Finance, ins., real estate
4,488,080
727,069
from weeks to months.
S11 Prof. and business services
2,791,250 1,218,463
S12 Educ. services, health care
1,732,105
849,620
• Assume nationwide pandemic
S13 Arts, entertainment
954,631
319,672
scenario with workforce “attack
S14 Other services, except gov.
746,742
262,473
rate” of 30%: qi 0  wi xi 0.30
S15 Government
2,887,447 1,468,234
And assume recovery period for
The total economic benefit
extended to all sectors given a
all sectors to match a 30-day
t0 = 2 day delay in inoperability in
pandemic duration.
each sector (in 106 dollars)
• Key sectors identified according
to: (i) the impact of a sector’s
inventory on other sectors
(benefit extended), and (ii) the
Average sector economic benefit
impact of other sectors’
received by a t0 = 2 day delay in
inventory on a particular sector
inoperability in each sector
(benefit received).
(in 106 dollars)
• Such a ranking provides best
candidates for implementing
inventory policies.
• Results from these application areas provide insights on disaster policy
formulation. Through exhaustive assessment and sensitivity analysis of scenariospecific parameter values associated with the Inventory DIIM, results of this
model can provide systemic resource allocation strategies that address
budgetary constraints, scope of preparedness investments, and post-disaster
recovery enhancement in a multiobjective framework, e.g., below.
• Due to the data limitations in inventory-to-sales ratios, only three sectors were
assumed to maintain inventories, namely Manufacturing (S5), Wholesale trade
(S6), and Retail trade (S7).
• Illustration assumptions: 20% initial production inoperability uniformly applied
to all the 15 sectors, sectors recover within a simulated 30-day horizon.
• Due to sector interdependencies, results show the cascade of benefits to other
sectors that are assumed to
have no inventories in place,
including Agriculture (S1),
Mining (S2), Utilities (S3),
and Transportation and
warehousing (S8).
Code
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
Name
Agriculture, forestry
Mining
Utilities
Construction
Manufacturing
Wholesale trade
Retail trade
Transport. and warehousing
Information
Finance, insurance, real estate
Prof. and business services
Educ. services, health care
Arts, entertainment
Other services, except gov.
Government
Details of these findings can be found in the following papers:
• Barker, K. and J.R. Santos. 2010. A Risk-based Approach for Identifying Key Economic and Infrastructure Sectors. Risk Analysis, 30(6): 962-974.
• Barker, K. and J.R. Santos. 2010. Measuring the Efficacy of Inventory with a Dynamic Input-Output Model. International Journal of Production
Economics, 126(1): 130-143.
Weighing
inventory costs
with potential
losses in all
sectors
Multiobjective
ranking of
sectors that (i)
provide benefit
and (ii) receive
benefit
Current and Future Work
• Inventory surveys will be launched in coming weeks. Surveys will gather
inventory data from local industries for comparison to regionalized BEA data
while collecting risk perception towards inventory policies. Focus is given to
Oklahoma industries preparing for winter ice storms.
• A tool for hurricane-driven workforce productivity losses has been developed for
low- and high-intensity hurricanes, including a graphical user interface which
combines data, scenario generation, computation, and visualization modules.
• A multi-regional interdependency model extension is being integrated with
decision models of supplier dependability to better model inventory/supplier
decision making behavior and the larger scale impacts of those decisions.
• Uncertainty in BEA and other data sources is being modeled using interval
arithmetic, and methods for making decisions will be developed.
This research is supported in part by the National Science Foundation, Division of Civil, Mechanical, and
Manufacturing Innovation (CMMI) under award 0927299/0963718, “Collaborative Research: Modeling the Efficacy
of Inventory for Extreme Event Preparedness Decision Making in Interdependent Systems.” Points of view in this
poster are those of the authors and do not necessarily represent the official positions of the National Science
Foundation, the University of Oklahoma, and The George Washington University.