1. Collaborative Research: Modeling the Efficacy of Inventory for Extreme Event Preparedness Decision Making in Interdependent Systems Joost R. Santos, Ph.D. Engineering Management and Systems Engineering The George Washington University NSF CMMI 0963718 Kash Barker, Ph.D. Industrial Engineering Kevin B. Wright, Ph.D. Communication University of Oklahoma NSF CMMI 0927299 Abstract Model Background Inventory-Based Interdependency Model • 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. • 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. 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]: Extended to address dynamic onset of and recovery from disruptive event with Dynamic Inoperability Input-Output Model (DIIM) [Lian and Haimes 2006]: • q(t): inoperability at time t • K: resilience coefficient • A*: interdependency matrix • c*(t): sector perturbation at time t • 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 • q: inoperability • A*: interdependency matrix • c*: sector perturbation Interdependency parameters are derived from Bureau of Economic Analysis accounts. 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. • 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 • 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 • Results from these application areas provide insights on disaster policy formulation. Through exhaustive assessment and sensitivity analysis of scenario-specific 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. • observed: (i) inability of some workforce sectors to commute to work, and (ii) delay in shipments of commodities. • We consider a workforce-debilitating scenario that affects the entire nation, such as a pandemic, lasting potentially from weeks to months. • Assume nationwide pandemic scenario with workforce “attack rate” of 30%: • And assume recovery period for all sectors to match a 30-day pandemic duration. • Key sectors identified according to: (i) the impact of a sector’s inventory on other sectors (benefit extended), and (ii) the impact of other sectors’ inventory on a particular sector (benefit received). • Such a ranking provides best candidates for implementing inventory policies. Weighing inventory costs with potential losses in all sectors Multiobjective ranking of sectors that (i) provide benefit and (ii) receive benefit sectors that are assumed to have no inventories in place, including Agriculture (S1), Mining (S2), Utilities (S3), and Transportation and warehousing (S8). 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 dependabilityto 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. The total economic benefit extended to all sectors given a t0 = 2 day delay in inoperability in each sector (in 106 dollars) Average sector economic benefit received by a t0 = 2 day delay in inoperability in each sector (in 106 dollars) • 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. 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.