1. GLOBAL RESPONSE OF U.S. MILITARY CAPTAIN WIL GRANADOS CAPTAIN CLIFF WAKEMAN

2. BACKSTORY

3. REAL-WORLD PROBLEM  Conflict between North Korea and South Korea  China is in alliance with North Korea  US to send 500 companies to Eastern Asia  Conflict between Iran and Iraq  North African countries in alliance with Iran  US to send 1000 companies to Middle East  Tsunami devastated Pacific coastline of South America  US to send 250 companies to Southern South America

4. ANALYSIS QUESTIONS  What is the optimal minimum cost flow for our given scenario with no attacks?  What are the optimal attack plans on our network?  What are the optimal responses given the various attacks?  Is it possible to completely stop the US from supplying troops to the regions of interest?

5. THE WORLD

6. MCB PENDLETON MCB HAWAII MCB LEJEUNE AL UDEID AB INCIRLIK AB MCB OKINAWA PAYA LEBAR AB RAMSTEIN AB AUSTRALIA MALAYSIA EASTERN ASIA CHINA WESTERN ASIA MIDDLE EAST RUSSIA SOUTH AFRICA NORTH AFRICA EUROPE ANTARCTICA SOUTHERN SOUTH AMERICA NORTHERN SOUTH AMERICA CENTRAL AMERICA CARIBBEAN MEXICO CANADA GREENLAND ARCTIC REGION GLOBAL NODE LAYOUT

7. GLOBAL NETWORK

8. ABSTRACT NETWORK

9. NODES DATA  Supply for bases MCB_Pendleton600MCB_Lejeune600 MCB_Okinawa450Ramstein_AB450 MCB_Hawaii300Incirlik_AB300 Udeid_AB150Leber_AB150  Demand for regions Middle_East1000 Eastern_Asia500 Southern_SouthAmerica250  1 unit supply/demand = 1 company of Marines (~200 Marines)

10. ARCS DATA  Distance  scaled, relative, abstract map units (AMU)  Capacity  400 if Distance ≤ 20 AMU  300 if 20 AMU < Distance ≤ 40 AMU  200 if Distance > 40 AMU  CostFactor  1 if arc source node is a base  1.3 if arc source node is a region  Cost [MOE]  Distance × CostFactor × $100,000 / 27

11. MATHEMATICAL FORMULATION  Total cost = Primal objective value - nC max ∑(unsatisfied supply)  X and W interdictions derived in dual MIP

12. ATTACKS ON NETWORK  Alliance Attack  Country in alliance with aggressor, cutting off flow into region containing country  Resource Attack  Country attacking one of our bases, cutting off flow into or out of that base  Political Attack  Country forming pact with other country, forcing use of more expensive alternate routes

13. MODELING ATTACKS  Attacks on nodes  Manual setting of unusable region (alliance)  Optimal interdiction of bases (resources)  numberResourceAttacks ≤ 8  Attacks on arcs  Optimal interdiction of arcs (political)  numberPoliticalAttacks ≤ 8

14. SCENARIO 0 NO ATTACKS

15. MINIMUM COST FLOW WITH NO ATTACKS GLOBAL RESPONSE OF US MILITARY ****************************************** nCmax = 7670000 ****************************************** Solution to MinCostFlow with no network interdictions: MCB_Lejeune --> Northern_Sou --> 50.0 unit(s) MCB_Lejeune --> Southern_Sou --> 200.0 unit(s) Ramstein_AB --> Incirlik_AB --> 100.0 unit(s) Ramstein_AB --> Europe --> 50.0 unit(s) Ramstein_AB --> Middle_East --> 300.0 unit(s) Incirlik_AB --> Middle_East --> 400.0 unit(s) Udeid_AB --> Middle_East --> 150.0 unit(s) Lebar_AB --> Middle_East --> 100.0 unit(s) Lebar_AB --> Eastern_Asia --> 50.0 unit(s) MCB_Okinawa --> China --> 50.0 unit(s) MCB_Okinawa --> Eastern_Asia --> 400.0 unit(s) Northern_Sou --> Southern_Sou --> 50.0 unit(s) Europe --> Middle_East --> 50.0 unit(s) China --> Eastern_Asia --> 50.0 unit(s) Supply and demand not satisfied: MCB_Hawaii --> -300.0 unit(s) MCB_Pendleton --> -600.0 unit(s) MCB_Lejeune --> -350.0 unit(s) Total cost = $160,722,221 ****************************************** Political attack plan with 0 attack(s): ****************************************** Resource attack plan with 0 attack(s): ******************************************

16. MINIMUM COST FLOW WITH NO ATTACKS Solution to MinCostFlow with interdictions in place: MCB_Lejeune --> Northern_Sou --> 50.0 unit(s) MCB_Lejeune --> Southern_Sou --> 200.0 unit(s) Ramstein_AB --> Incirlik_AB --> 100.0 unit(s) Ramstein_AB --> Europe --> 50.0 unit(s) Ramstein_AB --> Middle_East --> 300.0 unit(s) Incirlik_AB --> Middle_East --> 400.0 unit(s) Udeid_AB --> Middle_East --> 150.0 unit(s) Lebar_AB --> Middle_East --> 100.0 unit(s) Lebar_AB --> Eastern_Asia --> 50.0 unit(s) MCB_Okinawa --> China --> 50.0 unit(s) MCB_Okinawa --> Eastern_Asia --> 400.0 unit(s) Northern_Sou --> Southern_Sou --> 50.0 unit(s) Europe --> Middle_East --> 50.0 unit(s) China --> Eastern_Asia --> 50.0 unit(s) Supply and demand not satisfied: MCB_Hawaii --> -300.0 unit(s) MCB_Pendleton --> -600.0 unit(s) MCB_Lejeune --> -350.0 unit(s) Total cost = $160,722,221 ****************************************** Primal objective = 9748222083.0 Dual objective = 9748222083.0 ****************************************** END OF OUTPUT

17. COMBAT TROOP MOVEMENT

18. SCENARIO 1 ALLIANCE ATTACKS ONLY Alliance Attack Country in alliance with aggressor, cutting off flow into region containing country

19. ALLIANCE ATTACKS  Alliance attacks  China  Northern_Africa  Remaining supply  MCB_Hawaii300  MCB_Pendleton 600  MCB_Lejeune 350  Total cost: $161,000,000

20. COMBAT TROOP MOVEMENT

21. SCENARIO 2 RESOURCE ATTACKS ONLY Resource Attack Country attacking one of our bases, cutting off flow into or out of that base

22. COMBAT TROOP MOVEMENT

25. MINIMUM COST FLOW WITH RESOURCE ATTACKS 13422 12293S So America 250 11148S So America 250Eastern Asia 500 S So America 250Eastern Asia 350Middle East 1000 8969Eastern Asia 350Middle East 1000none 6678Eastern Asia 350Middle East 850noneLebar 3273Eastern Asia 350Middle East 800noneUdeid Total Cost ($M) 602Eastern Asia 350Middle East 500noneHawaii Unsatisfied Demand 399noneMiddle East 50noneIncirlik nonePendleton 50noneRamstein Remaining Supply Pendleton 500Hawaii 300Pendleton Hawaii 300RamsteinLejeune LocationsOkinawa # Attacks12345678

26. OPERATOR RESILIENCE CURVE 399 602 6678 3273 8969 11148 12293 13422 161

27. SCENARIO 3 POLITICAL ATTACKS ONLY Political Attack Country forming pact with other country, forcing use of more expensive alternate routes

28. COMBAT TROOP MOVEMENT

31. 3963 Eastern Asia 500 2518Lebar 50 Eastern Asia 300Okinawa 450 2029Okinawa 300Lejeune 350 681S So America 250Lejeune 350Pendleton 600 293S So America 50Lejeune 600Pendleton 600Hawaii 300 261noneLejeune 400Pendleton 600Hawaii 300 Middle East - Eastern Asia 237noneLejeune 350Pendleton 600Hawaii 300 Western Asia - Eastern Asia Total Cost ($M)209noneLejeune 350Pendleton 600Hawaii 300 Antartica - S So America Udeid - Eastern Asia Unsatisfied Demand noneLejeune 350Pendleton 600Hawaii 300 N So America - S So America Russia - Eastern Asia Lejeune 350Pendleton 600Hawaii 300 Malaysia - Eastern Asia Caribbean - S So America Malaysia - Eastern Asia Remaining Supply Pendleton 600Hawaii 300 Lebar - Eastern Asia Central America - S So America Lebar - Eastern Asia Hawaii 300 Okinawa - China China - Eastern Asia Mexico - S So America China - Eastern Asia Locations Okinawa - Eastern Asia Lejeune - S So America Okinawa - Eastern Asia # Attacks12345678 MINIMUM COST FLOW WITH POLITICAL ATTACKS

32. OPERATOR RESILIENCE CURVE 209 237 293 261 681 2518 3963 161 2029

33. SCENARIO 4 ALLIANCE ATTACKS + RESOURCE ATTACKS

34. COMBAT TROOP MOVEMENT

37. MINIMUM COST FLOW WITH ALLIANCE ATTACKS AND RESOURCE ATTACKS 13422 12293S So America 250 11148S So America 250Eastern Asia 500 S So America 250Eastern Asia 350Middle East 1000 8972Eastern Asia 350Middle East 1000none 36666681Eastern Asia 350Middle East 850noneLebar Eastern Asia 350 Middle East 800noneUdeid Total Cost ($M) 719Middle East 50Middle East 500noneHawaii Unsatisfied Demand 415nonePendleton 150noneIncirlik nonePendleton 50Hawaii 300Pendleton Remaining Supply Pendleton 500Hawaii 300IncirlikLejeune Hawaii 300Ramstein LocationsOkinawa # Attacks12345678

38. OPERATOR RESILIENCE CURVE 161 719 6681 3666 8972 11148 12293 13422 415

39. SCENARIO 5 ALLIANCE ATTACKS + POLITICAL ATTACKS

40. COMBAT TROOP MOVEMENT

43. 3985 3963Eastern Asia 500 Lebar 50 2518Lebar 50Okinawa 450 1059Eastern Asia 300Okinawa 450Lejeune 350 Eastern Asia 100Okinawa 300Lejeune 350Pendleton 600 317Okinawa 100Lejeune 350Pendleton 600Hawaii 300 293noneLejeune 350Pendleton 600Hawaii 300 Incirlik - Middle East 261noneLejeune 350Pendleton 600Hawaii 300 Middle East - Eastern Asia Total Cost ($M)237noneLejeune 350Pendleton 600Hawaii 300 Udeid - Eastern Asia Unsatisfied Demand noneLejeune 350Pendleton 600Hawaii 300 Western Asia - Eastern Asia Lejeune 350Pendleton 600Hawaii 300 Russia - Eastern Asia Remaining Supply Pendleton 600Hawaii 300 Malaysia - Eastern Asia Hawaii 300 Lebar - Eastern Asia Locations Okinawa - Eastern Asia # Attacks12345678 MINIMUM COST FLOW WITH ALLIANCE ATTACKS AND POLITICAL ATTACKS

44. OPERATOR RESILIENCE CURVE 237 261 317 293 1059 2518 3963 3985 161

45. SCENARIO 6 RESOURCE ATTACKS + POLITICAL ATTACKS

46. MINIMUM COST FLOW WITH RESOURCE ATTACKS AND POLITICAL ATTACKS

47. SCENARIO 7 ALLIANCE ATTACKS + RESOURCE ATTACKS + POLITICAL ATTACKS

48. MINIMUM COST FLOW WITH ALLIANCE ATTACKS, RESOURCE ATTACKS, AND POLITICAL ATTACKS

49. WITH MORE TIME…  Add more bases  One node for each country  Multiple arcs based on mode of transportation  Adjust nodal reach based on resource limitations  Refine arc capacities and cost factors  Allow more resource and political attacks

51. DUAL FORMULATION