اندازه گیری اثر بخشی موجودی با یک مدل داده ستانده پویا

This paper extends the recently developed 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. The Inventory DIIM can provide practical insights to preparedness decision making through explicit tradeoff analysis of multiple objectives, including inventory costs and economic loss reductions. The model is demonstrated in several illustrative examples to depict various nuances of inventory policies. The paper then culminates in a case study that utilizes input–output and inventory accounts from the Bureau of Economic Analysis.

The focus of infrastructure risk management and decision making has recently shifted from prevention and protection of infrastructure systems from disruptive events to recovery and response. For example, the US Department of Homeland Security (DHS) through its national infrastructure protection plan (Department of Homeland Security, 2006) has highlighted that the US must prepare for the inevitable occasion when a disruptive event occurs, stressing risk management strategies that “strengthen national preparedness, timely response, and rapid recovery in the event” of an attack or disaster. Furthermore, Department of Homeland Security (2006) underscores the need for instituting preparedness and resilience plans for critical infrastructure and key resources (CI/KR) of the nation. Discussions of preparedness and resilience appear in Haimes (2006) and Haimes et al. (2008), where the connection is made between preparedness activities prior to a disruptive event to the resilience achieved following the disruptive event. Resilience is defined as the “ability to cushion or mute potential losses” (Rose, 2004) from a disruptive event. In general, economic resilience is defined as the ability or capability of a system to absorb or cushion against damage or loss (Holling, 1973; Perrings, 2001). Increasing the resilience of a sector reduces its recovery time as well as the associated economic losses. Of particular interest to the discussion of preparedness and resilience are interdependencies among critical infrastructure and economic systems. The operation of such critical systems, or essential services, without interruption is of incredible importance, and failing to prepare can result in “widespread uncertainty about restoration of services, lack of viable economic and social networks, serious loss of public confidence, and even social collapse” (La Porte, 2006). The interdependence of such essential services and the private infrastructure components of supply chains is well documented (e.g., Rinaldi et al., 2001; Little, 2002; Kormos and Bowe, 2006). Due to the interdependencies among production activities in various sectors of the economy, a disruption in production can have far-reaching effects. One significant means of preparedness and resilience in a production environment comes from the availability of inventory. The above motivates this work to strengthen our ability to model the impact of inventory policies on interdependent infrastructure systems. Several risk-based interdependency modeling schemes have been developed recently, including the inoperability input–output model (IIM) (Haimes and Jiang, 2001; Jiang and Haimes, 2004; Santos and Haimes, 2004). A derivative of the IIM which models the dynamic recovery of interdependent sectors and evaluates the effect of risk management strategies on that recovery is the dynamic IIM (DIIM) (Lian and Haimes, 2006). While the IIM and its derivatives successfully measure the effects of certain risk management strategies, they are unable to account for strategies that add resilience through inventory. This paper integrates the DIIM with an inventory model to quantify the efficacy of inventory strategies employed in interdependent infrastructure sectors and other members of a supply chain. Ultimately, the model provides a metric quantifying how different risk management strategies involving inventory will affect recovery following a disruption, as depicted in Fig. 1. From left to right, the first component in Fig. 1 depicts various preparedness strategies used to reduce the effects of a disruptive event and the DIIM parameters that vary with each strategy. They serve as inputs to the Inventory DIIM, which quantifies inoperability experienced by different sectors of the economy over time and quantifies the economic losses resulting from a disruptive event. Such inoperability trajectories and economic losses are calculated for each strategy, and the strategies are compared with a multiobjective framework where tradeoffs between costs and benefits are calculated. Full-size image (27 K) Fig. 1. Depiction of modeling preparedness strategies which involve inventory policies. Figure options 2. Methodological background Discussed in this section are several models of inventory, including previous input–output-based representations of inventory, and the risk-based interdependency model used in this paper, the dynamic inoperability input–output model.

Due to the interdependencies among production activities in various economic and infrastructure sectors, an adverse impact to production brought about by any number of disruptive events can have far-reaching effects. Recent emphasis has been placed on improving resilience in these sectors, namely in their ability to respond and recover to such disruptive events. Previous risk-based interdependency models, including the IIM and DIIM, were developed to measure the efficacy of several different preparedness options designed to improve sector resilience. This paper describes an important extension to this modeling paradigm, the Inventory DIIM, which models the efficacy of inventory policies in making economic and infrastructure sectors more resilient to disruptive events. Thus, the Inventory DIIM provides a metric with which one can compare a number of preparedness strategies in a multiobjective framework. Its usefulness is illustrated with three pedagogical examples and also a case study using actual inventory ratio data provided by the Bureau of Economic Analysis. Although a proof of concept in the case study demonstrates the execution of the Inventory DIIM using actual data, further refinements have been identified. Many economic and infrastructure sectors, particularly those providing “essential services” for which preparedness planning is of major interest, are not of the nature where finished goods inventory is appropriate or perhaps possible, e.g., electric power, and future work includes adapting the model to such sectors. As BEA inventory data are available only for national-level economic sectors, an opportunity exists to collect regional inventory surveys from local private and public organizations to understand how national-level data can be interpolated to local inventory decision making. The relationship between firm-level inventory and disruptions and regional- and national-level inventory and disruptions should be modeled. Further, the significant assumption of time-invariant total outputs, as described in Eq. (3), and their derivation from annual input–output data should be addressed to improve the efficacy of the model. Finally, the spatial aspects of inventory location and firm- and sector-level interdependencies will be addressed in future refinements of the model.