SLIDE 1
2 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Interdependent Systems Cameron MacKenzie Hiba Baroud Kash Barker - - PowerPoint PPT Presentation
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
SLIDE 2
SLIDE 3
3 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
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?
SLIDE 4
4 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Impacted area
Texas, Louisiana, Mississippi, Alabama, and Florida
SLIDE 5
5 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Directly impacted industries
Fishing Real estate Accommodations Amusements Oil and gas
SLIDE 6
6 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Static model: no interdependencies
minimize 𝐸 = 𝐲⊺𝐝∗ subject to 𝑑𝑗
∗ = 𝑑 𝑗 ∗exp −𝑙𝑗𝑨𝑗 − 𝑙𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 2
𝑨𝐺𝑗𝑡ℎ + 𝑨𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 + 𝑨𝐵𝑛𝑣𝑡𝑓 + 𝑨𝐵𝑑𝑑𝑝𝑛 + 𝑨𝑝𝑗𝑚 + 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≤ 𝑎 𝑨𝑗 ≥ 0, 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≥ 0 i = {Fish, Real Estate, Amusements, Accommodations, Oil}
Total direct losses Vector of direct impacts (proportional) Normal production Direct impacts with no resources Allocation to industry General allocation Effectiveness of allocation Overall budget
SLIDE 7
7 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Input parameters
Industry 𝒍𝒋 𝒅 𝒋
∗
Fishing 0.074 0.0084 Real estate 0.047 Amusements 0.0038 0.21 Accommodations 0.0027 0.16 Oil 0.0057 0.079 General 7.4*10-9
SLIDE 8
8 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
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
SLIDE 9
9 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Allocation with no interdependencies
SLIDE 10
10 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Static model: with interdependencies
minimize 𝑅 = 𝐲⊺𝐂𝐝∗ subject to 𝑑𝑗
∗ = 𝑑 𝑗 ∗exp −𝑙𝑗𝑨𝑗 − 𝑙𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 2
𝑨𝐺𝑗𝑡ℎ + 𝑨𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 + 𝑨𝐵𝑛𝑣𝑡𝑓 + 𝑨𝐵𝑑𝑑𝑝𝑛 + 𝑨𝑝𝑗𝑚 + 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≤ 𝑎 𝑨𝑗 ≥ 0, 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 ≥ 0 i = {Fish, Real Estate, Amusements, Accommodations, Oil}
Total production losses Vector of direct impacts (proportional) Normal production Direct impacts with no resources Allocation to industry General allocation Effectiveness of allocation Overall budget Interdependent matrix
SLIDE 11
11 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Allocation with interdependencies
SLIDE 12
12 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Sensitivity analysis on effectiveness
Proportion of budget to be allocated to help all industries as a function of allocation effectiveness parameter
SLIDE 13
13 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Discrete-time dynamic model
minimize 𝐾 = 𝐲⊺𝐂𝐝∗ 𝑢
𝑢𝑔 𝑢=1
subject to 𝑑𝑗
∗ 𝑢 + 1 = 𝑑𝑗 ∗ 𝑢 exp −𝑙𝑗 𝑢 𝑨𝑗 𝑢 − 𝑙𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 2
i = {Fish, Real Estate, Amusements, Accommodations , Oil}
Allocation to industry at time t General allocation at time t Effectiveness of allocation
𝑨𝐺𝑗𝑡ℎ 𝑢 + 𝑨𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 𝑢 + 𝑨𝐵𝑛𝑣𝑡𝑓 𝑢
𝑢𝑔−1 𝑢=0
+ 𝑨𝐵𝑑𝑑𝑝𝑛 𝑢 + 𝑨𝑝𝑗𝑚 𝑢 + 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 ≤ 𝑎
Direct impact at time t Total production losses Vector of direct impacts (proportional) Normal production Interdependent matrix
𝐝∗ 0 = 𝐝 ∗
Overall budget
SLIDE 14
14 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Dynamic models and effect of time
SLIDE 15
15 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Dynamic models and effect of time
SLIDE 16
16 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Dynamic models and effect of time
SLIDE 17
17 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Discrete-time dynamic model
minimize 𝐾 = 𝐲⊺𝐂𝐝∗ 𝑢
𝑢𝑔 𝑢=1
subject to 𝑑𝑗
∗ 𝑢 + 1 = 𝑑𝑗 ∗ 𝑢 exp −𝑢 ∗ 𝑙𝑗𝑨𝑗 𝑢 − 𝑙𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 2
i = {Fish, Real Estate, Amusements, Accommodations , Oil}
Allocation to industry at time t General allocation at time t Effectiveness of allocation
𝑨𝐺𝑗𝑡ℎ 𝑢 + 𝑨𝑆𝑓𝑏𝑚𝐹𝑡𝑢𝑏𝑢𝑓 𝑢 + 𝑨𝐵𝑛𝑣𝑡𝑓 𝑢
𝑢𝑔 𝑢=1
+ 𝑨𝐵𝑑𝑑𝑝𝑛 𝑢 + 𝑨𝑝𝑗𝑚 𝑢 + 𝑨𝐻𝑓𝑜𝑓𝑠𝑏𝑚 𝑢 ≤ 𝑎
Direct impact at time t Total production losses Vector of direct impacts (proportional) Normal production Interdependent matrix
𝐝∗ 0 = 𝐝 ∗
Overall budget
SLIDE 18
18 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
Dynamic allocation
SLIDE 19
19 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
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
SLIDE 20
20 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”
- 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
SLIDE 21
21 MacKenzie, Baroud, and Barker, “Optimal resource allocation for interdependent systems”