project 9.1 aiding allies
TRANSCRIPT
-
8/11/2019 Project 9.1 Aiding Allies
1/21
1
Department of Industrial and Management Engineering
Project: Operation Research
The Analysis of Problem Using: Network Optimization Models
Special Case 9.1 Aiding Allies
University of Turabo
Facilitator:
Alexander X. Flix Rodrguez
-
8/11/2019 Project 9.1 Aiding Allies
2/21
2
The Analysis of Problem Aiding Allies / The Battle of the Monopoly
The siege starts the following way in a cold night in October in Russia. CommanderVotachev and his two years dream of work and training revolutionaries east of the UralMountains has proved successful; his troops now occupy seven strategically importantcities in the Russian Federation: Kazan, Perm, Yekaterinburg, Ufa, Samara, Saratov, andOrenburg. His siege is not yet over, however. He looks to the west. Given the political andeconomic confusion in the Russian Federation at this time, he knows that his troops will be
able to conquer Saint Petersburg, Moscow and Rostov shortly. Across the Pacific Ocean, ameeting of the top security and foreign policy advisers of the United States is in progress atthe White House. The President has recently been briefed about the communist revolutionmasterminded by Commander Votachev and is determining a plan of action. The Presidentreflects upon a similar October long ago in 1917, and he fears the possibility of a new ageof radical Communist rule accompanied by chaos, bloodshed, escalating tensions, andpossibly nuclear war. He therefore decides that the United States needs to respond and torespond quickly. Moscow has requested assistance from the United States military, and thePresident plans to send troops and supplies immediately. The President turns to GeneralLankletter and asks him to describe the preparations being taken in the United States tosend the necessary troops and supplies to the Russian Federation.
General Lankletter informs the President that along with troops, weapons, ammunition,fuel, and supplies, aircraft, ships, and vehicles are being assembled at two port cities withairfields: Boston and Jacksonville. The aircraft and ships will transfer all troops and cargoacross the Atlantic Ocean to the Eurasian continent. The general hands the President a listof the types of aircraft, ships, and vehicles being assembled along with a description ofeach type.
-
8/11/2019 Project 9.1 Aiding Allies
3/21
3
All aircraft, ships, and vehicles are able to carry both troops and cargo. Once an aircraft orship arrives in Europe, it stays there to support the armed forces.
The President then turns to Tabitha Neal, who has been negotiating with the NATOcountries for the last several hours to use their ports and airfields as stops to refuel and
resupply before heading to the Russian Federation. She informs the President that thefollowing ports and airfields in the NATO countries will be made available to the UnitedStates military.
The President stands and walks to the map of the world projected on a large screen in themiddle of the room. He maps the progress of troops and cargo from the United States tothree strategic cities in the Russian Federation that have not yet been seized by CommanderVotachev. The three cities are Saint Petersburg, Moscow, and Rostov. He explains that thetroops and cargo will be used both to defend the Russian cities and to launch acounterattack against Votachev to recapture the cities he currently occupies.
The President also explains that all Starlifters and transports leave Boston or Jacksonville.All transports that have traveled across the Atlantic must dock at one of the NATO ports tounload. Palletized load system trucks brought over in the transports will then carry alltroops and materials unloaded from the ships at the NATO ports to the three strategicRussian cities not yet seized by Votachev. All Starlifters that have traveled across theAtlantic must land at one of the NATO airfields for refueling. The planes will then carry alltroops and cargo from the NATO airfields to the three Russian cities.
The US Government Capabilities and Intruments of War
Transportation Type Name Capacity Speed
Aircraft C - 141 Starlifter 150 400 MPH
Ship Transport 240 35 MPH
Vehicle Palletized Load 16,000 Kilograms 60 MPH
System Truck
The US NATO or Allies Ports and Airfields
Ports Airfields
Napoli, Italy London,UK
Hamburg, Germany Berlin, Germany
Rotterdam, Netherlands Istanbul, Turkey
The cities that need to be protected from Commander Votachev
City Requirements
Saint Petersburg 320,000 Tons
Moscow 440,000 Tons
Rostov 240,000 Tons
-
8/11/2019 Project 9.1 Aiding Allies
4/21
4
(A)Draw a network showing the different routes troops and supplies may take to reach theRussian Federation from the United States.
The military analyzing and verifying the distances in kilometers of their NATO Airfieldsand ports all around the United States, Europe and Russia
From To - (Ports)Length of
Route From To - (Airfields) Length of Route
USA Boston Napoli 7,950Km Boston London 6,200Km
Europe Boston Hamburg 8,250Km Boston Berlin 7,250Km
Boston Rotterdam 6,900Km Boston Istanbul 8,300Km
USA Jacksonville Napoli 9,400Km Jacksonville London 7,900Km
Europe Jacksonville Hamburg 9,800Km Jacksonville Berlin 9,200Km
Jacksonville Rotterdam 8,900Km Jacksonville Istanbul 10,100Km
From: (Ports) & (Airfields) To: Russia Length of Route
Europe Berlin St. Petersburg 1,280Km
Russia Hamburg St. Petersburg 1,880Km
Istanbul St. Petersburg 2,040Km
London St. Petersburg 1,980Km
Rotterdam St. Petersburg 2,200Km
Napoli St. Petersburg 2,970Km
Europe Berlin Moscow 1,600Km
Russia Hamburg Moscow 2,120Km
Istanbul Moscow 1,700Km
London Moscow 2,300Km
Rotterdam Moscow 2,450Km
Napoli Moscow 2,890Km
Europe Berlin Rostov 1,730Km
Russia Hamburg Rostov 2,470Km
Istanbul Rostov 990Km
London Rostov 2,860Km
Rotterdam Rostov 2,760Km
Napoli Rostov 2,800Km
-
8/11/2019 Project 9.1 Aiding Allies
5/21
5
The Network is showing the different routes that troops and supplies will take
Boston
Jacksonville
Berlin
Hamburg
Istanbul
London
Rotterdam
Napoli
St. Petersburg
Moscow
Rostov
-
8/11/2019 Project 9.1 Aiding Allies
6/21
6
(B) Moscow and Washington do not know when Commander Votachev will launch hisnext attack. Leaders from the two countries have therefore agreed that troops should reacheach of the three strategic Russian cities as quickly as possible. The President hasdetermined that the situation is so dire that cost is no objectas many Starlifters,transports, and trucks as are necessary will be used to transfer troops and cargo from the
United States to Saint Petersburg, Moscow, and Rostov. Therefore, no limitations exist onthe number of troops and amount of cargo that can be transferred between any cities. ThePresident has been given the following information about the length of the available routesbetween cities: Given the distance and the speed of the transportation used between eachpair of cities, how can the President most quickly move troops from the United States toeach of the three strategic Russian cities? Highlight the path(s) on the network. How longwill it take troops and supplies to reach Saint Petersburg? Moscow? Rostov?
From: BostonUnited States
Boston
Jacksonville
Berlin
Hamburg
Istanbul
London
Rotterdam
Napoli
St. Petersburg
Moscow
Rostov
-
8/11/2019 Project 9.1 Aiding Allies
7/21
-
8/11/2019 Project 9.1 Aiding Allies
8/21
-
8/11/2019 Project 9.1 Aiding Allies
9/21
9
Finding the best and shortest path to get to their NATO bases
Problem B From: Jacksonville, United States
Starlifter
first leg second leg Total km Total miles Hrs
Jacksonville Berlin Saint Petersburg 9200 1280 10480 6512.272 16.28068
Jacksonville Berlin Moscow 9200 1600 10800 6711.12 16.7778
Jacksonville Berlin Rostov 9200 1730 10930 6791.902 16.979755
Jacksonville Hamburg Saint Petersburg 9800 1880 11680 7257.952 18.14488
Jacksonville Hamburg Moscow 9800 2120 11920 7407.088 18.51772
Jacksonville Hamburg Rostov 9800 2470 12270 7624.578 19.061445
Jacksonville Istanbul Saint Petersburg 10100 2040 12140 7543.796 18.85949
Jacksonville Istanbul Moscow 10100 1700 11800 7332.52 18.3313
Jacksonville Istanbul Rostov 10100 990 11090 6891.326 17.228315
Jacksonville London Saint Petersburg 7900 1980 9880 6139.432 15.34858
Jacksonville London Moscow 7900 2300 10200 6338.28 15.8457
Jacksonville London Rostov 7900 2860 10760 6686.264 16.71566
Jacksonville Rotterdam Saint Petersburg 8900 2200 11100 6897.54 17.24385
Jacksonville Rotterdam Moscow 8900 2450 11350 7052.89 17.632225
Jacksonville Rotterdam Rostov 8900 2760 11660 7245.524 18.11381
Jacksonville Napoli Saint Petersburg 9400 2970 12370 7686.718 19.216795
Jacksonville Napoli Moscow 9400 2890 12290 7637.006 19.092515
Jacksonville Napoli Rostov 9400 2800 12200 7581.08 18.9527
The Shortest Routes and Paths
USA Europe Russia Hrs
Jacksonville London Rostov 16.71566
Jacksonville London Saint Petersburg 15.34858
Jacksonville London Moscow 15.8457
-
8/11/2019 Project 9.1 Aiding Allies
10/21
10
(C) The President encounters only one problem with his first plan: he has to sell themilitary deployment to Congress. Under the War Powers Act, the President is required toconsult with Congress before introducing troops into hostilities or situations wherehostilities will occur. If Congress does not give authorization to the President for such useof troops, the President must withdraw troops after 60 days. Congress also has the power to
decrease the 60-day time period by passing a concurrent resolution. The President knowsthat Congress will not authorize significant spending for another countrys war, especiallywhen voters have paid so much attention to decreasing the national debt. He thereforedecides that he needs to find a way to get the needed troops and supplies to SaintPetersburg, Moscow, and Rostov at the minimum cost. Each Russian city has contactedWashington to communicate the number of troops and supplies the city needs at aminimum for reinforcement. After analyzing the requests, General Lankletter has convertedthe requests from numbers of troops, gallons of gasoline, etc., to tons of cargo for easierplanning. The requirements are listed below.
The President of the United States must satisfy each Russian city s military
requirements at Minimum Cost.
Boston
Jacksonville
Rotterdam
Napoli
London
Berlin
Istanbul
St. Petersburg
Moscow
Rostov
Hamburg
Total cost of
Operation
$412,866,666
-
8/11/2019 Project 9.1 Aiding Allies
11/21
11
The second Part of the Network
The objective of this Algorithm network flow path is to satisfy all demands in the
network at minimum cost. The paths used to ship supplies to St.Petersburg, Moscow,
Rostov are highlighted on the following network diagram with arrows on top.
The entire supply forSt. Petersburgis supplied from Jacksonville via London.
The entire supply forMoscowis supplied from Boston via Hamburg.
The 240,000 tonsdemanded by Rostov:
o 60are shipped from Boston viaIstambul,o 150are shipped from Jacksonville via Istanbulo 30are shipped from Jacksonville via London.
Boston
Jacksonville
Rotterdam
Napoli
London
Berlin
Istanbul
St. Petersburg
Moscow
Rostov
Hamburg
Total cost of
Operation
$412,866,666
-
8/11/2019 Project 9.1 Aiding Allies
12/21
12
The Algorithm Procedures Model
This problem can be solved as a Minimum Cost Network Flow Problem. The two nodes
that are representing US cities are supply nodes with a suppply of 500each (we measure all
weights in 1000 tons). The three nodes representing the Russian Federation cities
St. Petersburg, Moscow and Rostov are demand nodes with demand of -320, -440, and 240,respectively.
All the nodes represening European airfields and ports are transshipment nodes. We
measure the flow along the arcs in 1000 tons. All arcs from European ports into
St. Petersburg have zero capacity. All the truck routes from the European point into Rostov
have a transportation limit of 2,500 that will be times 16 and that will equal 40,000 tons.
For all other nodes we determine natural act capacities based on the supplies and demands
at the nodes. We define the unit costs along the arcs in the network in $1000 per 1000 tons.
The cost of transporting 1 ton of material from Boston to Hamburg equals $3000 divided
by 240 that will equal $125. So the cost of transporting 1000 tonsfrom Boston to Hamburg
equals $ 125,000.
The Nodes, Net Flow, Supply & Demand representation table
Nodes Net Flow Supply / Demand
Boston +500 +500Jacksonville +500 +500
Hamburg 0 0
Napoli 0 0
Rotterdam 0 0
London 0 0
Berlin 0 0
Istanbul 0 0
St. Petersburg -320 -320
Moscow -440 -440
Rostov -240 -240
-
8/11/2019 Project 9.1 Aiding Allies
13/21
13
(d) Once the President releases the number of planes, ships, and trucks that will travelbetween the United States and the Russian Federation, Tabitha Neal contacts each of theAmerican cities and NATO countries to indicate the number of planes to expect at theairfields, the number of ships to expect at the docks, and the number of trucks to expecttraveling across the roads. Unfortunately, Tabitha learns that several additional restrictions
exist which cannot be immediately eliminated. Because of airfield congestion andunalterable flight schedules, only a limited number of planes may be sent between any twocities. These plane limitations are given below. In addition, because some countries fearthat citizens will become alarmed if too many military trucks travel the public highways,they object to a large number of trucks traveling through their countries. These objectionsmean that a limited number of trucks are able to travel between certain ports and Russiancities. These limitations are listed below. Tabitha learns that all shipping lanes have nocapacity limits, owing to the American control of the Atlantic Ocean. The President realizesthat because of all the restrictions he will not be able to satisfy all the reinforcementrequirements of the three Russian cities. He decides to disregard the cost issue and insteadto maximize the total amount of cargo he can get to the Russian cities. How does thePresident maximize the total amount of cargo that reaches the Russian Federation?Highlight the path(s) used between the United States and the Russian Federation on thenetwork.
Part: A - Airplanes
From To Maximum
Boston Berlin 300
Boston Istanbul 500
Boston London 500
Jacksonville Berlin 500Jacksonville Istanbul 700
Jacksonville London 600
Berlin St. Petersburg 500
Istanbul St. Petersburg 0
London St. Petersburg 1,000
Berlin Moscow 300
Istanbul Moscow 100
London Moscow 200
Berlin Rostov 0
Istanbul Rostov 900London Rostov 100
-
8/11/2019 Project 9.1 Aiding Allies
14/21
14
Maximum Flow: Part: A - Airplanes
Boston
Jacksonville
Bostos
Berlin
Istanbul
London
Jacksonville
St. Petersburg
Moscow
Rostov
Bostos
Berlin
Istanbul
London
Jacksonville
St. Petersburg
Moscow
Rostov
-
8/11/2019 Project 9.1 Aiding Allies
15/21
15
Algorithm: Maximum Flow: Part: A - Airplanes
-
8/11/2019 Project 9.1 Aiding Allies
16/21
16
Part: B
From To Maximum
Rotterdam Moscow 600 Trucks
Rotterdam Rostov 750 Trucks
Hamburg Moscow 700 Trucks
Hamburg Rostov 500 Trucks
Napoli Moscow 1,500 Trucks
Napoli Rostov 1,400 Trucks
Nodes: Rotterdam (Start)
Nodes: Napoli (Ends)
Maximum Flow: Part: B - Trucks
Moscow
Rotterdam
Moscow
Hamburg
Rostov
Napoli
-
8/11/2019 Project 9.1 Aiding Allies
17/21
17
Rostov
Algorithm: Maximum Flow: Part: BTrucks
Rotterdam
Moscow
Hamburg
Rostov
Napoli
-
8/11/2019 Project 9.1 Aiding Allies
18/21
18
(e)Even before all American troops and supplies had reached Saint Petersburg, Moscow,and Rostov, infighting among Commander Votachevs troops about whether to make thenext attack against Saint Petersburg or against Moscow split the revolutionaries. Troopsfrom Moscow easily overcame the vulnerable revolutionaries. Commander Votachev wasimprisoned, and the next step became rebuilding the seven cities razed by his armies. The
Presidents top priority is to help the Russian government to reestablish communicationsbetween the seven Russian cities and Moscow at minimum cost. The price of installingcommunication lines between any two Russian cities varies given the cost of shipping wireto the area, the level of destruction in the area, and the roughness of the terrain. Luckily, acity is able to communicate with all others if it is connected only indirectly to every othercity. Saint Petersburg and Rostov are already connected to Moscow, so if any of the sevencities is connected to Saint Petersburg or Rostov, it will also be connected to Moscow. Thecost of replacing communication lines between two given cities for which this is possible isshown below.
Table of Minimum Cost:To reestablish Comunication lines in the Russian Federation.
Between Cost to Reestablish
St. Petersburg Perm $185,000
Kazan Perm $150,000
Kazan Samara $95,000
Kazan Ufa $105,000
Perm Yekaterinburg $85,000
Samara Saratov $100,000
Moscow Saratov $140,000
Ufa Orenburg $75,000
Orenburg Rostov $120,000
Total: $1,055,000
-
8/11/2019 Project 9.1 Aiding Allies
19/21
19
The Minimum Spanning Tree Problem:To Reestablish Communication lines in the
Russian Federation. The analysis that was done by the method Minimum Spanning Tree
with in the Russian cities proved to be the key of success to reestablish all communication
after the aftermath.
The Cost to Reestablish the Communication Lines:
$1,055,000
-
8/11/2019 Project 9.1 Aiding Allies
20/21
20
Final Moments of The Battle of the Monopoly
Conclusion
The Battle for power and destruction was over for the Commander. It only took good
inteligence and swift trade crafe skills to bring down a dangerous and notorious RussianCommander to his knees. The objective was to simply take way the 3 mayor Russian cities
from the commander and corners him pushing him east towards Siberia and capturing him
at once.
Even before all American troops and supplies had reached Saint Petersburg, Moscow, and
Rostov, in fighting amongst Commander Votachevs troops about whether to make the next
attack against Saint Petersburg or against Moscow, they split the revolutionaries. Troops
from Moscow easily overcame the vulnerable revolutionaries. Commander Votachev was
imprisoned, and the next step became rebuilding the seven cities razed by his armies. The
Presidents top priority was to help the Russian government to reestablish communicationsbetween the seven Russian cities and Moscow at minimum cost.
-
8/11/2019 Project 9.1 Aiding Allies
21/21
21
Acknowledgement
The author and facilitator would like to give thank to the Institute of Industrial Engineers
(IIE) for the information that was provided and used to make this project a great success.
The author also would like to give thanks to two special people Prof. Ariel D. Machin, PE
and Alexis C. Flix, ph.D for their support and insite in the project and for their advice andunconditional support.
Reference:
Hillier & Lieberman, (2005). Introduction to Operation Research, New York, NY:
McGraw-Hill
Weida, Richardson & Vazsonyi, (2000). Operations Analysis Using Microsoft Excel,
California, CA: Pacific Grove
Richard Bronson & Govindasami Naadimuthu, (1997). Operation Research Schaums out
lines, New York, NY: McGraw-Hill