Multiobjective Prioritization Methodology and Decision Support System for Evaluating Inventory Enhancement Strategies for Disrupted Interdependent Sectors

Disruptions in the production of commodities and services resulting from disasters influence the vital functions of infrastructure and economic sectors within a region. The interdependencies inherent among these sectors trigger the faster propagation of disaster consequences that are often associated with a wider range of inoperability and amplified losses. This article evaluates the impact of inventory‐enhanced policies for disrupted interdependent sectors to improve the disaster preparedness capability of dynamic inoperability input‐output models (DIIM). In this article, we develop the dynamic cross‐prioritization plot (DCPP)—a prioritization methodology capable of identifying and dynamically updating the critical sectors based on preference assignments to different objectives. The DCPP integrates the risk assessment metrics (e.g., economic loss and inoperability), which are independently analyzed in the DIIM. We develop a computer‐based DCPP tool to determine the priority for inventory enhancement with user preference and resource availability as new dimensions. A baseline inventory case for the state of Virginia revealed a high concentration of (i) manufacturing sectors under the inoperability objective and (ii) service sectors under the economic loss objective. Simulation of enhanced inventory policies for selected critical manufacturing sectors has reduced the recovery period by approximately four days and the expected total economic loss by $33 million. Although the article focuses on enhancing inventory levels in manufacturing sectors, complementary analysis is recommended to manage the resilience of the service sectors. The flexibility of the proposed DCPP as a decision support tool can also be extended to accommodate analysis in other regions and disaster scenarios.     

Modeling Uncertainties in Workforce Disruptions from Influenza Pandemics Using Dynamic Input‐Output Analysis

Influenza pandemic is a serious disaster that can pose significant disruptions to the workforce and associated economic sectors. This article examines the impact of influenza pandemic on workforce availability within an interdependent set of economic sectors. We introduce a simulation model based on the dynamic input‐output model to capture the propagation of pandemic consequences through the National Capital Region (NCR). The analysis conducted in this article is based on the 2009 H1N1 pandemic data. Two metrics were used to assess the impacts of the influenza pandemic on the economic sectors: (i) inoperability, which measures the percentage gap between the as‐planned output and the actual output of a sector, and (ii) economic loss, which quantifies the associated monetary value of the degraded output. The inoperability and economic loss metrics generate two different rankings of the critical economic sectors. Results show that most of the critical sectors in terms of inoperability are sectors that are related to hospitals and health‐care providers. On the other hand, most of the sectors that are critically ranked in terms of economic loss are sectors with significant total production outputs in the NCR such as federal government agencies. Therefore, policy recommendations relating to potential mitigation and recovery strategies should take into account the balance between the inoperability and economic loss metrics.     

Risk‐Based Input‐Output Analysis of Influenza Epidemic Consequences on Interdependent Workforce Sectors

Outbreaks of contagious diseases underscore the ever‐looming threat of new epidemics. Compared to other disasters that inflict physical damage to infrastructure systems, epidemics can have more devastating and prolonged impacts on the population. This article investigates the interdependent economic and productivity risks resulting from epidemic‐induced workforce absenteeism. In particular, we develop a dynamic input‐output model capable of generating sector‐disaggregated economic losses based on different magnitudes of workforce disruptions. An ex post analysis of the 2009 H1N1 pandemic in the national capital region (NCR) reveals the distribution of consequences across different economic sectors. Consequences are categorized into two metrics: (i) economic loss, which measures the magnitude of monetary losses incurred in each sector, and (ii) inoperability, which measures the normalized monetary losses incurred in each sector relative to the total economic output of that sector. For a simulated mild pandemic scenario in NCR, two distinct rankings are generated using the economic loss and inoperability metrics. Results indicate that the majority of the critical sectors ranked according to the economic loss metric comprise of sectors that contribute the most to the NCR's gross domestic product (e.g., federal government enterprises). In contrast, the majority of the critical sectors generated by the inoperability metric include sectors that are involved with epidemic management (e.g., hospitals). Hence, prioritizing sectors for recovery necessitates consideration of the balance between economic loss, inoperability, and other objectives. Although applied specifically to the NCR, the proposed methodology can be customized for other regions.     

Comparing the Economic Impact of Natural Disasters Generated by Different Input–Output Models: An Application to the 2007 Chehalis River Flood (WA)

Due to the concentration of assets in disaster‐prone zones, changes in risk landscape and in the intensity of natural events, property losses have increased considerably in recent decades. While measuring these stock damages is common practice in the literature, the assessment of economic ripple effects due to business interruption is still limited and available estimates tend to vary significantly across models. This article focuses on the most popular single‐region input–output models for disaster impact evaluation. It starts with the traditional Leontief model and then compares its assumptions and results with more complex methodologies (rebalancing algorithms, the sequential interindustry model, the dynamic inoperability input–output model, and its inventory counterpart). While the estimated losses vary across models, all the figures are based on the same event, the 2007 Chehalis River flood that impacted three rural counties in Washington State. Given that the large majority of floods take place in rural areas, this article gives the practitioner a thorough review of how future events can be assessed and guidance on model selection.     

On the Local Sensitivity Analysis of the Inoperability Input‐Output Model

Natural and man‐made disasters are currently a source of major concern for contemporary societies. In order to understand their economic impacts, the inoperability input‐output model has recently gained recognition among scholars. In a recent paper, Percoco (2006) has proposed an extension of the model to map the technologically most important sectors through so‐called fields of influence. In the present note we aim to show that this importance measure also has a clear connection with local sensitivity analysis theory.     

International Trade Inoperability Input-Output Model (IT-IIM): Theory and Application

The inoperability input-output model (IIM) has been used for analyzing disruptions due to man-made or natural disasters that can adversely affect the operation of economic systems or critical infrastructures. Taking economic perturbation for each sector as inputs, the IIM provides the degree of economic production impacts on all industry sectors as the outputs for the model. The current version of the IIM does not provide a separate analysis for the international trade component of the inoperability. If an important port of entry (e.g., Port of Los Angeles) is disrupted, then international trade inoperability becomes a highly relevant subject for analysis. To complement the current IIM, this article develops the International Trade-IIM (IT-IIM). The IT-IIM investigates the resulting international trade inoperability for all industry sectors resulting from disruptions to a major port of entry. Similar to traditional IIM analysis, the inoperability metrics that the IT-IIM provides can be used to prioritize economic sectors based on the losses they could potentially incur. The IT-IIM is used to analyze two types of direct perturbations: (1) the reduced capacity of ports of entry, including harbors and airports (e.g., a shutdown of any port of entry); and (2) restrictions on commercial goods that foreign countries trade with the base nation (e.g., embargo).     

Robust Stochastic Lot‐Sizing by Means of Histograms

Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control using the estimated distributions. These approaches often lead to fragile solutions whenever the preselected family of distributions was inadequate. In this article, we propose a minimax robust model that integrates data fitting and inventory optimization for the single‐item multi‐period periodic review stochastic lot‐sizing problem. In contrast with the standard assumption of given distributions, we assume that histograms are part of the input. The robust model generalizes the Bayesian model, and it can be interpreted as minimizing history‐dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular, we analyze the robust model based on the chi‐square goodness‐of‐fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under generous conditions. Its effectiveness is also validated by numerical experiments.     

A Framework for Linking Cybersecurity Metrics to the Modeling of Macroeconomic Interdependencies

Hierarchical decision making is a multidimensional process involving management of multiple objectives (with associated metrics and tradeoffs in terms of costs, benefits, and risks), which span various levels of a large-scale system. The nation is a hierarchical system as it consists multiple classes of decisionmakers and stakeholders ranging from national policymakers to operators of specific critical infrastructure subsystems. Critical infrastructures (e.g., transportation, telecommunications, power, banking, etc.) are highly complex and interconnected. These interconnections take the form of flows of information, shared security, and physical flows of commodities, among others. In recent years, economic and infrastructure sectors have become increasingly dependent on networked information systems for efficient operations and timely delivery of products and services. In order to ensure the stability, sustainability, and operability of our critical economic and infrastructure sectors, it is imperative to understand their inherent physical and economic linkages, in addition to their cyber interdependencies. An interdependency model based on a transformation of the Leontief input-output (I-O) model can be used for modeling: (1) the steady-state economic effects triggered by a consumption shift in a given sector (or set of sectors); and (2) the resulting ripple effects to other sectors. The inoperability metric is calculated for each sector; this is achieved by converting the economic impact (typically in monetary units) into a percentage value relative to the size of the sector. Disruptive events such as terrorist attacks, natural disasters, and large-scale accidents have historically shown cascading effects on both consumption and production. Hence, a dynamic model extension is necessary to demonstrate the interplay between combined demand and supply effects. The result is a foundational framework for modeling cybersecurity scenarios for the oil and gas sector. A hypothetical case study examines a cyber attack that causes a 5-week shortfall in the crude oil supply in the Gulf Coast area.     

Pandemic Recovery Analysis Using the Dynamic Inoperability Input-Output Model

Economists have long conceptualized and modeled the inherent interdependent relationships among different sectors of the economy. This concept paved the way for input-output modeling, a methodology that accounts for sector interdependencies governing the magnitude and extent of ripple effects due to changes in the economic structure of a region or nation. Recent extensions to input-output modeling have enhanced the model's capabilities to account for the impact of an economic perturbation; two such examples are the inoperability input-output model^{( 1 , 2 )} and the dynamic inoperability input-output model (DIIM).^{( 3 )} These models introduced sector inoperability, or the inability to satisfy as-planned production levels, into input-output modeling. While these models provide insights for understanding the impacts of inoperability, there are several aspects of the current formulation that do not account for complexities associated with certain disasters, such as a pandemic. This article proposes further enhancements to the DIIM to account for economic productivity losses resulting primarily from workforce disruptions. A pandemic is a unique disaster because the majority of its direct impacts are workforce related. The article develops a modeling framework to account for workforce inoperability and recovery factors. The proposed workforce-explicit enhancements to the DIIM are demonstrated in a case study to simulate a pandemic scenario in the Commonwealth of Virginia.     

On the Sensitivity Analysis of the IIM: A Rejoinder

In this note I reply to the comments by Haimes et al. on my paper on the sensitivity analysis of the inoperability input‐output model. I make the case for a moment‐independent sensitivity analysis.     

Hold Safety Inventory Before,At, or After the Fan‐Out Point?

We consider a product sold in multiple variants, each with uncertain demand, produced in a multi‐stage process from a standard (i.e., generic) sub‐assembly. The fan‐out point is defined as the last process stage at which outputs are generic (outputs at every subsequent stage are variant‐specific). Insights gained from an analytical study of the system are used to develop heuristics that determine the stage(s) at which safety inventory should be held. We offer a relatively‐simple heuristic that approaches globally‐optimal results even though it uses only two relatively‐local parameters. We call this the VAPT, or value‐added/processing time heuristic, because it determines whether a (local) stage should hold inventory based only on the value added at that local stage relative to its downstream stage, along with the processing time at that local stage relative to its downstream stage. Another key insight is that, contrary to possible intuition, safety inventory should not always be held at the fan‐out point, although a fan‐out point does hold inventory under a wider range of conditions. We also explore when postponement is most valuable and illustrate that postponement may often be less beneficial than suggested by Lee and Tang (1997).     

A classification approach based on the outranking model for multiple criteria ABC analysis

The multiple criteria ABC analysis is widely used in inventory management, and it can help organizations to assign inventory items into different classes with respect to several evaluation criteria. Many approaches have been proposed in the literature for addressing such a problem. However, most of these approaches are fully compensatory in multiple criteria aggregation. This means that an item scoring badly on one or more key criteria could be placed in good classes because these bad performances could be compensated by other criteria. Thus, it is necessary to consider the non-compensation in the multiple criteria ABC analysis. To the best of our knowledge, the ABC classification problem with non-compensation among criteria has not been studied sufficiently. We thus propose a new classification approach based on the outranking model to cope with such a problem in this paper. However, the relational nature of the outranking model makes the search for the optimal classification solution a complex combinatorial optimization problem. It is very time-consuming to solve such a problem using mathematical programming techniques when the inventory size is large. Therefore, we combine the clustering analysis and the simulated annealing algorithm to search for the optimal classification. The clustering analysis groups similar inventory items together and builds up the hierarchy of clusters of items. The simulated annealing algorithm searches for the optimal classification on different levels of the hierarchy. The proposed approach is illustrated by a practical example from a Chinese manufacturer. Furthermore, we validate the performance of the approach through experimental investigation on a large set of artificially generated data at the end of the paper.     

A Note on the Inoperability Input-Output Model

In this note, we propose some comments and some extensions of the inoperability input-output model (IIOM), as recently proposed by Santos and Haimes (2004). In particular, we propose the use of some analytic tools capable of providing information on the reaction of sectors subsequent to a terrorist attack on infrastructure service sectors. These tools, namely, the field of influence and the multiplier product matrix, provide information on the way sectors react to a shock on the aggregate demand and/or to a (temporary or permanent) change of production function coefficients. Finally, using the 2003 65 sectors input-output matrix for the U.S. economy, a simple empirical example is presented.     

Economic Manufacturing Quantity and Its Integrating Implications

Several contradictions are noted among the Economic Order Quantity (EOQ), Just‐In‐Time (JIT), and Optimized Production Technology (OPT) approaches and the economic framework for profit maximization. A fundamental model referred to as the Economic Manufacturing Quantity (EMO) is developed and examined for its integrating implications for the three approaches. An implication for the classic EOQ approach is that the balance between setup and inventory carrying costs is valid when a production facility is operating at or below a certain critical level but not when operating above that level. An implication for the JIT approach is that one must reduce setup cost at non‐bottlenecks and setup time at bottlenecks to reduce inventory. An implication for the OPT approach is that trade‐offs between setup and inventory carrying costs may indeed be ignored while determining process batch sizes, provided each facility in a production system is operating at or above Its critical level. Economic theoretic analysis of the EMO model provides a basis for unification of JIT which advocates stability in operating level as a key to improved productivity and quality, and OPT that advocates maximizing operating level with resultant emphasis on bottlenecks as a key to increased profits. This unifying basis states that a profit‐maximizing production facility or system will operate at the full and stable level as long as market demand remains relatively sensitive to price and operating at the full (maximum) level provides positive unit contribution.     

The Bayesian Microbial Subtyping Attribution Model: Robustness to Prior Information and a Proposition

Attributing foodborne illnesses to food sources is essential to conceive, prioritize, and assess the impact of public health policy measures. The Bayesian microbial subtyping attribution model by Hald et al. is one of the most advanced approaches to attribute sporadic cases; it namely allows taking into account the level of exposure to the sources and the differences between bacterial types and between sources. This step forward requires introducing type and source‐dependent parameters, and generates overparameterization, which was addressed in Hald's paper by setting some parameters to constant values. We question the impact of the choices made for the parameterization (parameters set and values used) on model robustness and propose an alternative parameterization for the Hald model. We illustrate this analysis with the 2005 French data set of non‐typhi Salmonella. Mullner's modified Hald model and a simple deterministic model were used to compare the results and assess the accuracy of the estimates. Setting the parameters for bacterial types specific to a unique source instead of the most frequent one and using data‐based values instead of arbitrary values enhanced the convergence and adequacy of the estimates and led to attribution estimates consistent with the other models’ results. The type and source parameters estimates were also coherent with Mullner's model estimates. The model appeared to be highly sensitive to parameterization. The proposed solution based on specific types and data‐based values improved the robustness of estimates and enabled the use of this highly valuable tool successfully with the French data set.     

Integrality in Stochastic Inventory Models

We study several finite‐horizon, discrete‐time, dynamic, stochastic inventory control models with integer demands: the newsvendor model, its multi‐period extension, and a single‐product, multi‐echelon assembly model. Equivalent linear programs are formulated for the corresponding stochastic dynamic programs, and integrality results are derived based on the total unimodularity of the constraint matrices. Specifically, for all these models, starting with integer inventory levels, we show that there exist optimal policies that are integral. For the most general single‐product, multi‐echelon assembly system model, integrality results are also derived for a practical alternative to stochastic dynamic programming, namely, rolling‐horizon optimization by a similar argument. We also present a different approach to prove integrality results for stochastic inventory models. This new approach is based on a generalization we propose for the one‐dimensional notion of piecewise linearity with integer breakpoints to higher dimensions. The usefulness of this new approach is illustrated by establishing the integrality of both the dynamic programming and rolling‐horizon optimization models of a two‐product capacitated stochastic inventory control system.     

Risk Management for Leontief-Based Interdependent Systems

When stricken by a terrorist attack, a war, or a natural disaster, an economic unit or a critical infrastructure may suffer significant loss of productivity. More importantly, due to interdependency or interconnectedness, this initial loss may propagate into other systems and eventually lead to much greater derivative loss. This belongs to what is known as a cascading effect. It is demonstrated in this article that the cascading effect and the derivative loss can be significantly reduced by effective risk management. This is accomplished by deliberately distributing the initial inoperability to other systems so that the total loss (or inoperability) is minimized. The optimal distribution strategy is found by a linear programming technique. The same risk management can also be applied to situations where objectives need to be prioritized. A case study featuring 12 economic sectors illustrates the theory. The result suggests that using the same amount of resources, minimizing risk (inoperability) of infrastructures will generally give rise to highest payoff, whereas overlooking it may result in greatest total loss. The framework developed in this work uses a steady-state approach that applies primarily to managing situations where the attack is catastrophic resulting in very long recovery time.     

供需不确定条件下基于CVaR的零售商库存鲁棒优化模型

在经典报童模型下考虑供应和需求不确定性,研究了具有风险厌恶的零售商库存优化问题。采用条件风险值（CVaR）对库存绩效进行度量,构建了基于CVaR的零售商库存运作模型;在此基础上,考虑上游供应商供货能力和下游市场需求不确定性,并采用一系列未知概率的离散情景进行描述,给出了供需不确定条件下基于CVaR的零售商库存鲁棒优化模型。进一步,采用区间不确定集对未知情景概率进行建模,给出了基于最大最小准则的鲁棒对应模型。针对同时考虑供需不确定性导致的模型非凸性,采用标准对偶理论将其转化为易于求解的数学规划问题。最后,通过数值计算分析了不同风险厌恶程度和不确定性程度对零售商库存决策以及库存绩效的影响。结果表明,供需不确定性的存在虽然会导致零售商库存绩效损失,但损失值较小。特别地,依据文中模型得到的鲁棒库存策略在多数情况下能够保证零售商获得更优的库存绩效。此外,不确定性和风险厌恶程度的增加虽然会影响零售商库存决策和运作绩效,但在同等风险厌恶态度下,随着不确定性程度的增加,基于文中方法得到的鲁棒库存策略仍能确保零售商获得理想的库存绩效,表明文中所建模型在应对供需不确定性方面具有良好的鲁棒性。     

How Inventory Cost Influences Introduction Timing of Product Line Extensions

In the industry with radical technology push or rapidly changing customer preference, it is firms' common wisdom to introduce high‐end product first, and follow by low‐end product‐line extensions. A key decision in this “down‐market stretch” strategy is the introduction time. High inventory cost is pervasive in such industries, but its impact has long been ignored during the presale planning stage. This study takes a first step toward filling this gap. We propose an integrated inventory (supply) and diffusion (demand) framework and analyze how inventory cost influences the introduction timing of product‐line extensions, considering substitution effect among successive generations. We show that under low inventory cost or frequent replenishment ordering policy, the optimal introduction time indeed follows the well‐known “now or never” rule. However, sequential introduction becomes optimal as the inventory holding gets more substantial or the product life cycle gets shorter. The optimal introduction timing can increase or decrease with the inventory cost depending on the marketplace setting, requiring a careful analysis.