Project 9.1 Aiding Allies

8/11/2019 Project 9.1 Aiding Allies

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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


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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.


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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


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(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


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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


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(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


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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


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(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


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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


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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


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(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


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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


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Algorithm: Maximum Flow: Part: A - Airplanes


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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


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Rostov

Algorithm: Maximum Flow: Part: BTrucks

Rotterdam

Moscow

Hamburg

Rostov

Napoli


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(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


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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


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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.


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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

Project 9.1 Aiding Allies

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