During WW2, the battle of Britain was a military campaign fought from July 1940 to June 1941 between Britain and Germany. It was conceived by the Germans after the fall of France. The battle was part of a strategy to downgrade Britain’s air defense capabilities in order to facilitate a Land invasion. We know now that The British were able to inflict an almost lethal blow to the Luftwaffe from which it never fully recovered. The question is how did they do it?
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With close to 1,000 men and about 200 operational research scientists, the British invented the Dowding System. This was a system made up of Radar stations, barrage balloons, fighter planes, search lights and observation posts amongst others. It could process huge amounts of information very fast. It gave Britain’s fighter defenses enough advanced warning to get ready for and intercept raids. It allowed Fighter Command to manage its valuable and relatively limited resources and making sure they were not wasted.The British had developed an air defense network that would give them a critical advantage in the Battle of Britain.
The Dowdy system
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Operations research
Developed during WW1 by military planners, OR is a subject that deals with the application of advanced analytical methods to help make better decisions. Operations research results arrive at optimal or near-optimal solutions to complex decision-making problems. It is considered an offshoot of applied mathematics. It makes use of methods from other mathematical sciences, such as mathematical modeling, mathematical optimization and statistical analysis operations.
The major disciplines in operational research are:
- Computing and information technologies
- Revenue management
- Simulation
- Manufacturing, service sciences, and supply chain management
- Policy modeling and public sector work
- Stochastic models
- Transportation
- Financial engineering
Weapon target assignment problem (Example)
Typical operation research in combinatorial optimization: this consists of finding an optimal assignment of a set of weapons of various types to a set of targets in order to maximize the total expected damage done to the enemy. Wikipedia example gives:
A commander has 5 tanks, 2 aircraft, and 1 sea vessel and is told to engage 3 targets with values 5, 10, and 20. Each weapon type has the following success probabilities against each target
One feasible solution is to assign the sea vessel and one aircraft to the highest valued target (3). This results in an expected survival value of 20(0.6)(0.5)=6} 20(0.6)(0.5)=6. One could then assign the remaining aircraft and 2 tanks to target #2, resulting in expected survival value of 10(0.4)(0.8)^{2}=2.56 10(0.4)(0.8)^{2}=2.56. Finally, the remaining 3 tanks are assigned to target #1 which has an expected survival value of 5(0.7)^{3}=1.715} 5(0.7)^{3}=1.715. Thus, we have a total expected survival value of 6+2.56+1.715=10.275} 6+2.56+1.715=10.275
Other application areas
Operations research is applied to manufacturing companies, airlines operations, service organizations, government, and the military. Some of the sectors include:
• Resource assignment: assigning crew to flights, trains or buses; employees to projects)
• Facility location: this means deciding most appropriate location for new facilities such as warehouse and factories
• Computer Network Engineering: involves packet routing and analysis.
• Hydraulics & Piping Engineering: the managing of water flow from reservoirs
• Health Services: managing information flow and supply chain management
• Game Theory: This involves identifying, understanding, and developing strategies adopted by companies
• Urban Design: effective City desin
• Telecommunications: packet routing, timing, and analysis.
• Scheduling: Time slot for airlines, trains, and buses.
Conclusion
Operations research was the key to Britain's survival during WW2. Today it has become a vital tool for just about every industry and service delivery. we salute the men and women who made this possible.
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