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Optimal Resource Allocation for Preparedness and Recovery of - - PowerPoint PPT Presentation

Oct 08, 2022 158 likes β€’314 views

Optimal Resource Allocation for Preparedness and Recovery of Interdependent Systems Cameron MacKenzie, Defense Resources Management Institute, Naval Postgraduate School Kash Barker, School of Industrial and Systems Engineering, University of

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Optimal Resource Allocation for Preparedness and Recovery of Interdependent Systems

Cameron MacKenzie, Defense Resources

Management Institute, Naval Postgraduate School

Kash Barker, School of Industrial and Systems

Engineering, University of Oklahoma

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Deepwater Horizon oil spill

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Research questions

  • What is the optimal division between

allocating to prepare for a disruption and allocating to respond to a disruption?

  • What is the level of resources that should be

allocated to individual industries to minimize impact of disruption?

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Key assumptions

  • Objective function minimizes expected

economic impact of a disruption

  • Preparedness resources reduce chances of

disruption

  • Response resources reduce economic impact
  • f disruption

– Allocation to individual industries – Allocation to all industries

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Impacted area

Texas, Louisiana, Mississippi, Alabama, and Florida

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Directly impacted industries

Fishing Real estate Accommodations Amusements Oil and gas

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Resource allocation model

min π‘žπ²βŠΊπ‚π βˆ’ 1 βˆ’ π‘ž 𝑕 π‘Ž βˆ’ π‘¨π‘ž 𝑑𝑗 = 𝑑 𝑗exp βˆ’π‘™π‘—π‘¨π‘— βˆ’ π‘™π»π‘“π‘œπ‘“π‘ π‘π‘š π‘¨π»π‘“π‘œπ‘“π‘ π‘π‘š 2 π‘¨π‘ž + π‘¨πΊπ‘—π‘‘β„Ž + π‘¨π‘†π‘“π‘π‘šπΉπ‘‘π‘’π‘π‘’π‘“ + 𝑨𝐡𝑛𝑣𝑑𝑓 + 𝑨𝐡𝑑𝑑𝑝𝑛 + π‘¨π‘π‘—π‘š + π‘¨π»π‘“π‘œπ‘“π‘ π‘π‘š ≀ π‘Ž π‘¨π‘ž β‰₯ 0, 𝑨𝑗 β‰₯ 0, π‘¨π»π‘“π‘œπ‘“π‘ π‘π‘š β‰₯ 0 i = {Fish, Real Estate, Amusements, Accommodations, Oil}

Normal production Direct impacts with no resources Allocation to industry Allocation to benefit all industries Effectiveness of recovery allocation Overall budget Interdependent matrix

subject to π‘ž = π‘ž exp βˆ’π‘™π‘žπ‘¨π‘ž

Vector of direct impacts (proportional) Probability of disruption Probability with no resources Allocation to prepare Effectiveness of preparedness allocation Increased production if no disruption

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Input parameters for oil spill

Industry 𝒍𝒋 (per $1 mil) 𝒅 𝒋 Fishing 0.074 0.0084 Real estate 0.047 Amusements 0.0038 0.21 Accommodations 0.0027 0.16 Oil and gas 0.0057 0.079 Preparedness π‘™π‘ž = 0.0031 π‘ž = 0.045 All industries π‘™π»π‘“π‘œπ‘“π‘ π‘π‘š = 7.4*10-9

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Parameter estimation for fishing

$62 million lost sales from Gulf Coast fishing οƒ  0.84% of region’s fishing and forestry production Studies on food safety and impact of positive media stories οƒ  $792,000 to reduce losses by $40 million

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Optimal allocation (preparedness)

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Optimal allocation (response)

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Sensitivity analysis

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Probability of oil spill π‘ž Effectiveness of allocating for preparedness π‘™π‘ž Proportion of $10M budget allocated for preparedness

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Insights

  • Aligns with other studies that economic consequences of

Deepwater Horizon oil spill range from $10 to $20 billion

  • Integrates interdependent economic impacts into

decision making

  • Provides guidelines for allocating resources to prepare

for and respond to a disruption

– Relatively small proportion of total budget for reducing probability – Importance of response actions to benefit all industries

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Future research

  • Include multiple scenarios
  • Incorporate risk aversion
  • Analyze conditions for optimality

Email: camacken@nps.edu

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