Department of Industrial and Management Engineering
Project: Operation Research The Analysis of Problem P roblem Using: Network Optimization Models Special Case 9.1 Aiding Allies University of Turabo
Facilitator: Alexander X. Félix Rodríguez
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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. Commander Votachev and his two years dream of work and training revolutionaries east of the Ural Mountains has proved successful; his troops now occupy seven strategically important cities in the Russian Federation: Kazan, Perm, Yekaterinburg, Ufa, Samara, Saratov, and Orenburg. His siege is not yet over, however. He looks to the west. Given the political and economic 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, a meeting of the top security and foreign policy advisers of the United States is in progress at the White House. The President has recently been briefed about the communist revolution masterminded by Commander Votachev and is determining a plan of action. The President reflects upon a similar October long ago in 1917, and he fears the possibility of a new age of radical Communist rule accompanied by chaos, bloodshed, escalating tensions, and possibly nuclear war. He therefore decides that the United States needs to t o respond and to respond quickly. Moscow has requested assistance from the United States military, and the President plans to send troops and supplies immediately. The President turns to General Lankletter and asks him to describe the preparations being taken in the United States to send 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 with airfields: Boston and Jacksonville. The aircraft and ships will transfer all troops and cargo across the Atlantic Ocean to the Eurasian continent. The general hands the President a list of the types of aircraft, ships, and vehicles being assembled along with a description of each type.
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All aircraft, ships, and vehicles are able to carry both troops and cargo. Once an aircraft or ship arrives in Europe, it stays there to support the armed forces. The President then turns to Tabitha Neal, who has been negotiating with the NATO countries 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 the following ports and airfields in the NATO countries will be made available to the United States military. The President stands and walks to the map of the world projected on a large screen in the middle of the room. He maps the progress of troops and cargo from the United States to three strategic cities in the Russian Federation that have not yet been seized by Commander Votachev. The three cities are Saint Petersburg, Moscow, and Rostov. He explains that the troops and cargo will be used both to defend the Russian cities and to launch a counterattack 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 to unload. Palletized load system trucks brought over in the transports will then carry all troops and materials unloaded from the ships at the NATO ports to the three strategic Russian cities not yet seized by Votachev. All Starlifters that have traveled across the Atlantic must land at one of the NATO airfields for refueling. The planes will then carry all troops 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 Ship
C - 141 Starlifter Transport
150 240
400 MPH 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 Rotterdam, Netherlands
Berlin, Germany Istanbul, Turkey
The cities that need to be protected from Commander Votachev
City
Requirements
Saint Petersburg Moscow
320,000 Tons 440,000 Tons
Rostov
240,000 Tons 3
(A) Draw a network showing the different routes troops and supplies may take to reach the Russian Federation from the United States.
The military analyzing and verifying the distances in kilometers of their NATO Airfields and ports all around the United States, Europe and Russia From
To - (Ports)
Length of Route
USA
Boston
Napoli
7,950Km
Boston
London
6,200Km
Europe
Boston Boston
Hamburg Rotterdam
8,250Km 6,900Km
Boston Boston
Berlin Istanbul
7,250Km 8,300Km
USA Europe
Jacksonville Jacksonville
Napoli Hamburg
9,400Km 9,800Km
Jacksonville Jacksonville
London Berlin
7,900Km 9,200Km
Jacksonville
Rotterdam
8,900Km
Jacksonville
Istanbul
10,100Km
From
To - (Airfields)
Length of Route
From: (Ports) & (Airfields)
To: Russia
Length of Route
Europe
Berlin
St. Petersburg
1,280Km
Russia
Hamburg Istanbul
St. Petersburg St. Petersburg
1,880Km 2,040Km
London Rotterdam
St. Petersburg St. Petersburg
1,980Km 2,200Km
Napoli
St. Petersburg
2,970Km
Berlin Hamburg
Moscow Moscow
1,600Km 2,120Km
Istanbul London
Moscow Moscow
1,700Km 2,300Km
Rotterdam
Moscow
2,450Km
Napoli
Moscow
2,890Km
Europe
Berlin
Rostov
1,730Km
Russia
Hamburg
Rostov
2,470Km
Istanbul London
Rostov Rostov
990Km 2,860Km
Rotterdam
Rostov
2,760Km
Napoli
Rostov
2,800Km
Europe Russia
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The Network is showing the different routes that troops and supplies will take Berlin St. Petersburg
Hamburg
Boston Istanbul Moscow London
Jacksonville Rotterdam
Rostov Napoli
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(B) Moscow and Washington do not know when Commander Votachev will launch his next attack. Leaders from the two countries have therefore agreed that troops should reach each of the three strategic Russian cities as quickly as possible. The President has determined that the situation is so dire that cost is no object — as 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 on the number of troops and amount of cargo that can be transferred between any cities. The President has been given the following information about the length of the available routes between cities: Given the distance and the speed of the transportation used between each pair of cities, how can the President most quickly move troops from the United States to each of the three strategic Russian cities? Highlight the path(s) on the network. How long will it take troops and supplies to reach Saint Petersburg? Moscow? Rostov?
From: Boston – United States
Berlin St. Petersburg
Hamburg
Boston Istanbul
Moscow London
Jacksonville Rotterdam
Rostov Napoli
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From: Jaksonville – United States
Berlin St. Petersburg
Hamburg
Boston Istanbul Moscow London
Jacksonville Rotterdam
Rostov Napoli
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Finding the best and shortest path to get to their NATO bases Problem B
From: Boston, United States
Starlifter First leg
Second leg
Total km
Total miles
Hrs
Boston Boston
Berlin Berlin
Saint Petersburg Moscow
7250 7250
1280 1600
8530 8850
5300.542 5499.39
13.251355 13.748475
Boston
Berlin
Rostov
7250
1730
8980
5580.172
13.95043
Boston
Hamburg
Saint Petersburg
8250
1880
10130
6294.782
15.736955
Boston Boston
Hamburg Hamburg
Moscow Rostov
8250 8250
2120 2470
10370 10720
6443.918 6661.408
16.109795 16.65352
Boston
Istanbul
Saint Petersburg
8300
2040
10340
6425.276
16.06319
Boston
Istanbul
Moscow
8300
1700
10000
6214
15.535
Boston
Istanbul
Rostov
8300
990
9290
5772.806
14.432015
Boston Boston
London London
Saint Petersburg Moscow
6200 6200
1980 2300
8180 8500
5083.052 5281.9
12.70763 13.20475
Boston
London
Rostov
6200
2860
9060
5629.884
14.07471
Boston
Rotterdam
Saint Petersburg
6900
2200
9100
5654.74
14.13685
Boston Boston
Rotterdam Rotterdam
Moscow Rostov
6900 6900
2450 2760
9350 9660
5810.09 6002.724
14.525225 15.00681
Boston
Napoli
Saint Petersburg
7950
2970
10920
6785.688
16.96422
Boston
Napoli
Moscow
7950
2890
10840
6735.976
16.83994
Boston
Napoli
Rostov
7950
2800
10750
6680.05
16.700125
The Shortest Routes and Paths USA
Europe
Russia
Hrs
Boston Boston
Berlin London
Rostov Saint Petersburg
13.95043 12.70763
Boston
London
Moscow
13.20475
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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 Jacksonville
Hamburg Hamburg
Saint Petersburg Moscow
9800 9800
1880 2120
11680 11920
7257.952 7407.088
18.14488 18.51772
Jacksonville
Hamburg
Rostov
9800
2470
12270
7624.578
19.061445
Jacksonville
Istanbul
Saint Petersburg
10100
2040
12140
7543.796
18.85949
Jacksonville Jacksonville
Istanbul Istanbul
Moscow Rostov
10100 10100
1700 990
11800 11090
7332.52 6891.326
18.3313 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 Jacksonville
Rotterdam Rotterdam
Saint Petersburg Moscow
8900 8900
2200 2450
11100 11350
6897.54 7052.89
17.24385 17.632225
Jacksonville
Rotterdam
Rostov
8900
2760
11660
7245.524
18.11381
Jacksonville
Napoli
Saint Petersburg
9400
2970
12370
7686.718
19.216795
Jacksonville Jacksonville
Napoli Napoli
Moscow Rostov
9400 9400
2890 2800
12290 12200
7637.006 7581.08
19.092515 18.9527
The Shortest Routes and Paths USA Jacksonville
Europe London
Russia Rostov
Hrs 16.71566
Jacksonville Jacksonville
London London
Saint Petersburg Moscow
15.34858 15.8457
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(C) The President encounters only one problem with his first plan: he has to sell the military deployment to Congress. Under the War Powers Act, the President is required to consult with Congress before introducing troops into hostilities or situations where hostilities will occur. If Congress does not give authorization to the President for such use of 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 knows that Congress will not authorize significant spending for another country’s war, especially when voters have paid so much attention to decreasing the national debt. He therefore decides that he needs to find a way to get the needed troops and supplies to Saint Petersburg, Moscow, and Rostov at the minimum cost. Each Russian city has contacted Washington to communicate the number of troops and supplies the city needs at a minimum for reinforcement. After analyzing the requests, General Lankletter has converted the requests from numbers of troops, gallons of gasoline, etc., to tons of cargo for easier planning. The requirements are listed below. The President of the United States must satisfy each Russian city ’s military requirements at Minimum Cost.
Hamburg St. Petersburg
Rotterdam Boston Napoli Moscow London
Jacksonville Berlin
Rostov
Total cost of Operation Istanbul
$412,866,666 10
The second Part of the Network Hamburg St. Petersburg
Rotterdam Boston Napoli Moscow London
Jacksonville Berlin
Rostov
Total cost of Operation Istanbul
$412,866,666
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 for St. Petersburg is supplied from Jacksonville via London . The entire supply for Moscow is supplied from Boston via Hamburg . The 240,000 tons demanded by Rostov: o o o
60 are shipped from Boston via Istambul, 150 are shipped from Jacksonville via Istanbul 30 are shipped from Jacksonville via London .
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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 500 each (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 tons from Boston to Hamburg equals $ 125,000.
The Nodes, Net Flow, Supply & Demand representation table
Nodes
Net Flow
Supply / Demand
Boston
+500
+500
Jacksonville
+500
+500
Hamburg
0
0
Napoli
0
0
Rotterdam
0
0
London Berlin
0 0
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 travel between the United States and the Russian Federation, Tabitha Neal contacts each of the American cities and NATO countries to indicate the number of planes to expect at the airfields, the number of ships to expect at the docks, and the number of trucks to expect traveling across the roads. Unfortunately, Tabitha learns that several additional restrictions exist which cannot be immediately eliminated. Because of airfield congestion and unalterable flight schedules, only a limited number of planes may be sent between any two cities. These plane limitations are given below. In addition, because some countries fear that 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 objections mean that a limited number of trucks are able to travel between certain ports and Russian cities. These limitations are listed below. Tabitha learns that all shipping lanes have no capacity limits, owing to the American control of the Atlantic Ocean. The President realizes that because of all the restrictions he will not be able to satisfy all the reinforcement requirements of the three Russian cities. He decides to disregard the cost issue and instead to maximize the total amount of cargo he can get to the Russian cities. How does the President 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 the network. Part: A - Airplanes From
To
Maximum
Boston Boston
Berlin Istanbul
300 500
Boston
London
500
Jacksonville Jacksonville
Berlin Istanbul
500 700
Jacksonville
London
600
Berlin Istanbul
St. Petersburg St. Petersburg
500 0
London
St. Petersburg
1,000
Berlin Istanbul
Moscow Moscow
300 100
London
Moscow
200
Berlin Istanbul
Rostov Rostov
0 900
London
Rostov
100
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Maximum Flow: Part: A - Airplanes
Boston Berlin
St. Petersburg
Bostos
Istanbul
Moscow
Jacksonville London
Rostov
Jacksonville
Berlin
St. Petersburg
Bostos
Istanbul
Moscow
Jacksonville London
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Rostov
Algorithm: Maximum Flow: Part: A - Airplanes
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Part: B From
To
Maximum
Rotterdam Rotterdam
Moscow Rostov
600 Trucks 750 Trucks
Hamburg Hamburg
Moscow Rostov
700 Trucks 500 Trucks
Napoli
Moscow
1,500 Trucks
Napoli
Rostov
1,400 Trucks
Nodes: Nodes:
Rotterdam (Start) Napoli (Ends)
Maximum Flow: Part: B - Trucks
Moscow Moscow
Rotterdam
Hamburg
Rostov
16
Napoli
Rostov
Moscow
Rotterdam
Hamburg
Rostov
Algorithm: Maximum Flow: Part: B – Trucks
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Napoli
(e) Even before all American troops and supplies had reached Saint Petersburg, Moscow, and Rostov, infighting among Commander Votachev’s troops about whether to make the next attack against Saint Petersburg or against Moscow 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 President’s top prio rity is to help the Russian government to reestablish communications between the seven Russian cities and Moscow at minimum cost. The price of installing communication lines between any two Russian cities varies given the cost of shipping wire to the area, the level of destruction in the area, and the roughness of the terrain. Luckily, a city is able to communicate with all others if it is connected only indirectly to every other city. Saint Petersburg and Rostov are already connected to Moscow, so if any of the seven cities is connected to Saint Petersburg or Rostov, it will also be connected to Moscow. The cost of replacing communication lines between two given cities for which this is possible is shown 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 dangero us and notorious Russian Commander 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 Votachev’s troops about whether to make the next attack against Saint Petersburg or against Moscow, they split the revo lutionaries. 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 President’s top priority was to help the Russian government to reestablish communications between 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. Félix, ph.D for their support and insite in the project and for their advice and unconditional 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 Schaum’s out lines, New York, NY: McGraw-Hill
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