Optimal Resource Allocation for Interdependent Systems Cameron MacKenzie Hiba Baroud Kash Barker

Transcription

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

2 Deepwater Horizon oil spill 2

3 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? 3

4 Impacted area Texas, Louisiana, Mississippi, Alabama, and Florida 4

5 Directly impacted industries Fishing Real estate Amusements Accommodations Oil and gas 5

6 Static model: no interdependencies Total direct losses Normal production minimize D = x c Vector of direct impacts (proportional) Direct impacts with no resources Allocation to industry subject to c i = ci exp k i z i k General z General 2 Effectiveness of allocation General allocation i = {Fish, Real Estate, Amusements, Accommodations, Oil} z Fish + z RealEstate + z Amuse + z Accom + z oil + z General Z z i 0, z General 0 Overall budget 6

7 Input parameters Industry k i c i Fishing Real estate Amusements Accommodations Oil General 7.4*10-9 7

8 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 8

9 Allocation with no interdependencies 9

10 Static model: with interdependencies Total production losses Normal production minimize Q = x Bc Interdependent matrix Vector of direct impacts (proportional) Direct impacts with no resources Allocation to industry subject to c i = ci exp k i z i k General z General 2 Effectiveness of allocation General allocation i = {Fish, Real Estate, Amusements, Accommodations, Oil} z Fish + z RealEstate + z Amuse + z Accom + z oil + z General Z z i 0, z General 0 Overall budget 10

11 Allocation with interdependencies 11

12 Sensitivity analysis on effectiveness Proportion of budget to be allocated to help all industries as a function of allocation effectiveness parameter 12

13 Discrete-time dynamic model Total production losses Direct impact at time t Normal production minimize J = t f t=1 x Bc t Interdependent matrix Vector of direct impacts (proportional) Allocation to industry at time t subject to c i t + 1 = c i t exp k i t z i t k General t z General t 2 Effectiveness of allocation General allocation at time t t f 1 t=0 i = {Fish, Real Estate, Amusements, Accommodations, Oil} z Fish t + z RealEstate t + z Amuse t + z Accom t + z oil t + z General t Z c 0 = c Overall budget 13

14 Dynamic models and effect of time 14

15 Dynamic models and effect of time 15

16 Dynamic models and effect of time 16

17 Discrete-time dynamic model Total production losses Direct impact at time t Normal production minimize J = t f t=1 x Bc t Interdependent matrix Vector of direct impacts (proportional) Allocation to industry at time t subject to c i t + 1 = c i t exp t k i z i t k General z General t 2 Effectiveness of allocation General allocation at time t i = {Fish, Real Estate, Amusements, Accommodations, Oil} t f t=1 z Fish t + z RealEstate t + z Amuse t + z Accom t + z oil t + z General t Z c 0 = c Overall budget 17

18 Dynamic allocation 18

19 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 19

20 This work was supported by the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation, under award MacKenzie, C. A., H. Baroud, and K. Barker, 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 20

21 End of Presentation contact: 21