Interdependent Systems Cameron MacKenzie Hiba Baroud Kash Barker - PowerPoint PPT Presentation

Optimal Resource Allocation for Interdependent Systems Cameron MacKenzie Hiba Baroud Kash Barker Industrial and Systems Engineering Research Conference May 21, 2012

Deepwater Horizon oil spill MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 2

Research questions • What is the level of resources that should be allocated to individual industries to minimize impact of disruption? • Should the allocation change if both direct and indirect impacts of disruption are considered? • In a dynamic model, how does the optimal allocation change over time? MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 3

Impacted area Texas, Louisiana, Mississippi, Alabama, and Florida MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 4

Directly impacted industries Real estate Fishing Accommodations Oil and gas Amusements MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 5

Static model: no interdependencies Normal production Total direct losses Vector of direct impacts minimize 𝐸 = 𝐲 ⊺ 𝐝 ∗ (proportional) Direct impacts with no resources Allocation to industry ∗ = 𝑑 𝑗 ∗ exp −𝑙 𝑗 𝑨 𝑗 − 𝑙 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 2 subject to 𝑑 𝑗 Effectiveness of allocation General allocation i = { Fish , Real Estate , Amusements , Accommodations , Oil } 𝑨 𝐺𝑗𝑡ℎ + 𝑨 𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 + 𝑨 𝐵𝑛𝑣𝑡𝑓 + 𝑨 𝐵𝑑𝑑𝑝𝑛 + 𝑨 𝑝𝑗𝑚 + 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≤ 𝑎 Overall budget 𝑨 𝑗 ≥ 0 , 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≥ 0 MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 6

Input parameters ∗ 𝒋 𝒍 𝒋 𝒅 Industry Fishing 0.074 0.0084 Real estate 0 0.047 Amusements 0.0038 0.21 Accommodations 0.0027 0.16 Oil 0.0057 0.079 7.4*10 -9 General MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 7

Parameter estimation for fishing $62 million lost sales from Gulf Coast fishing  0.84% of region’s fishing and forestry production Studies on food safety and impact of positive media stories  $792,000 to reduce losses by $40 million MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 8

Allocation with no interdependencies MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 9

Static model: with interdependencies Normal production Total production losses Interdependent matrix Vector of direct impacts minimize 𝑅 = 𝐲 ⊺ 𝐂𝐝 ∗ (proportional) Direct impacts with no resources Allocation to industry ∗ = 𝑑 𝑗 ∗ exp −𝑙 𝑗 𝑨 𝑗 − 𝑙 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 2 subject to 𝑑 𝑗 Effectiveness of allocation General allocation i = { Fish , Real Estate , Amusements , Accommodations , Oil } 𝑨 𝐺𝑗𝑡ℎ + 𝑨 𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 + 𝑨 𝐵𝑛𝑣𝑡𝑓 + 𝑨 𝐵𝑑𝑑𝑝𝑛 + 𝑨 𝑝𝑗𝑚 + 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≤ 𝑎 Overall budget 𝑨 𝑗 ≥ 0 , 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≥ 0 MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 10

Allocation with interdependencies MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 11

Sensitivity analysis on effectiveness Proportion of budget to be allocated to help all industries as a function of allocation effectiveness parameter MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 12

Discrete-time dynamic model Normal production Interdependent matrix Total production losses 𝑢 𝑔 Vector of direct minimize 𝐾 = 𝐲 ⊺ 𝐂𝐝 ∗ 𝑢 impacts (proportional) Direct impact at time t 𝑢=1 Allocation to industry at time t ∗ 𝑢 + 1 = 𝑑 𝑗 ∗ 𝑢 exp −𝑙 𝑗 𝑢 𝑨 𝑗 𝑢 − 𝑙 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 2 subject to 𝑑 𝑗 Effectiveness of allocation General allocation at time t i = { Fish , Real Estate , Amusements , Accommodations , Oil } 𝑢 𝑔 −1 𝑨 𝐺𝑗𝑡ℎ 𝑢 + 𝑨 𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 𝑢 + 𝑨 𝐵𝑛𝑣𝑡𝑓 𝑢 𝑢=0 + 𝑨 𝐵𝑑𝑑𝑝𝑛 𝑢 + 𝑨 𝑝𝑗𝑚 𝑢 + 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 ≤ 𝑎 𝐝 ∗ 0 = 𝐝 ∗ Overall budget MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 13

Dynamic models and effect of time MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 14

Dynamic models and effect of time MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 15

Dynamic models and effect of time MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 16

Discrete-time dynamic model Normal production Interdependent matrix Total production losses 𝑢 𝑔 Vector of direct minimize 𝐾 = 𝐲 ⊺ 𝐂𝐝 ∗ 𝑢 impacts (proportional) Direct impact at time t 𝑢=1 Allocation to industry at time t ∗ 𝑢 + 1 = 𝑑 𝑗 ∗ 𝑢 exp −𝑢 ∗ 𝑙 𝑗 𝑨 𝑗 𝑢 − 𝑙 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 2 subject to 𝑑 𝑗 Effectiveness of allocation General allocation at time t i = { Fish , Real Estate , Amusements , Accommodations , Oil } 𝑢 𝑔 𝑨 𝐺𝑗𝑡ℎ 𝑢 + 𝑨 𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 𝑢 + 𝑨 𝐵𝑛𝑣𝑡𝑓 𝑢 𝑢=1 + 𝑨 𝐵𝑑𝑑𝑝𝑛 𝑢 + 𝑨 𝑝𝑗𝑚 𝑢 + 𝑨 𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 ≤ 𝑎 𝐝 ∗ 0 = 𝐝 ∗ Overall budget MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 17

Dynamic allocation MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 18

Conclusions • Static model – Including interdependencies only slightly changes optimal allocation – As budget increases, allocate greater proportion to help all industries recover simultaneously – Model results sensitive to allocation effectiveness to all industries • Dynamic model – If effectiveness of resources is constant or decreases with time, optimal to spend entire budget early – Allocate large amount of budget to help all industries recover immediately MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 19

• This work was supported by the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation, under award 0927299 • MacKenzie, C. A., H. Baroud, and K. Barker, 2012. Optimal resource allocation for recovery of interdependent systems: Case study of the Deepwater Horizon oil spill. Proceedings of the 2012 Industrial and Systems Engineering Research Conference Email: cmackenzie@ou.edu MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 20

End of Presentation contact: cmackenzie@ou.edu MacKenzie, Baroud , and Barker, “Optimal resource allocation for interdependent systems” 21