Hello welcome to the part 1 of our introduction to operations research **operations research uses, operations research history** lecture in this lecture we will be talking about the history of operations research **operations research uses, operations research history** operations research **operations research uses, operations research history** today modeling and operations research **operations research uses, operations research history** the mathematical techniques for operations research **operations research uses, operations research history** the different phases of operations research **operations research uses, operations research history** study and the structure of mathematical models. So let’s begin so what is operations research **operations research uses, operations research history** operations. Research **operations research uses, operations research history** is the application of methods of science to complex problems arising in the direction and management of large number of men machines materials and money in industry business government and defense also operations research **operations research uses, operations research history** is the application of scientific methods techniques and tools to the problems involving the operations of a system so as to provide those in control of the system with optimum solution to the problem operations research **operations research uses, operations research history** can be traced back to world war ii when a group of scientists was hired by the government of england in order to research **operations research uses, operations research history** on the military operations of the english military so basically the group of scientists wanted to identify or wanted to optimize their radar operation and also their bomber operation with the success of the english group of scientists. The americans also hired their own group of scientists in order to research **operations research uses, operations research history** on complex logistical problems. Invention of new flight patterns planning c mining and effective utilization of electronic equipment both countries really used up their group of scientists and was able to profit in the in their operations for the military with the success of the military operations. The industry then followed in using operations research **operations research uses, operations research history** this is to sought out solutions to their complex executive type problems to serve the overall objectives of their organizations and utilization of the effective tools the first mathematical technique in operations research **operations research uses, operations research history** is called the simplex method of the linear programming. This was created by george b danzig in his dissertation or his phd thesis to give you a little story.

While george b dansek was a phd student. He came in late to one of his classes as he came in. He saw different problems that was written by his professor on the board and he thought these are his homeworks he wrote them all down and then by the next meeting he answered two. If i’m not mistaken out of the three problems but then he didn’t realize that these are actually not the homeworks but these are actually mathematical problems which have not been solved yet and when his professor or his advisor saw these they realized that he was able to come up one of the best solutions in solving linear programs and that is the simplex method and then these homeworks became his dissertation or his phd visas operations research **operations research uses, operations research history** today is not only used by military but also been used in business applications in hospitals in financial institutions libraries city planning transportation systems and even crime investigations so what are the different models. In operations research **operations research uses, operations research history** first we have iconic models iconic models are basically prototypes or real life samples of what the real life problem is for example a toy plane a toy plane is an iconic model of the real plane which is a very big one and since we wanted only to play on a smaller version then we create toy plane this is an iconic model. Another model is the analog models analog models are kind of abstract representation of a real system for example graphs and then we have symbolic or mathematical model an lp or a linear program which is written here is an example of a mathematical model it basically models the real system through mathematical equations and mathematical functions then with the advancement of technology there are two other models which have been created currently one is heuristics and the other one is simulation. Heuristics is basically rule of thumb or other techniques which have not been used before and may be used or may be useful in the future those are heuristics for example and different problems on scheduling.

One heuristic would be to schedule first. Those with shortest processing time that is a heuristic then. Simulation models are digital representations which imitate the behavior of a system using a digital computer the statistics describing the different measures of performance of the system are accumulated as the simulator advances on the computer. So what are the mathematical techniques for operations research **operations research uses, operations research history**. We have the following linear programming or lp then we also have dynamic programming then we have non-linear programming stochastic programming and also integer programming as we go through our different lectures. We will be talking about each one of them in depth for now we will focus on linear programming. So what are the different phases in order to do operations research **operations research uses, operations research history** study first we have to define the problem. This is very crucial and very critical. We have to understand the problem at its core in order for us to know what we want to solve and know what kind of problems we will encounter in the future then. We have the construction of the model. This is the part where we’re going to use mathematical models in order to replicate our real system so this is the part where we construct our linear program or our integer program. Then we have the solution of the model. This part is basically solving our model that we constructed from the previous stage. Then we have the validation model validation of the model is basically to validate if our solution to the model is actually correct. This is basically done through implementing our solution to a prototype system then we have the implementation of the final results where we have to implement our solutions to the real system now we will talk about the structure of mathematical models. This is an example of a linear program and a linear program is composed of the following elements. Each element will be explained individually on the part 2 of our lecture first we have the objective function.

Then we have decision variables and then the different parameters and the different constraints again. We have an objective function. We have decision variables we have the different parameters and then the set of constraints so that ends our lecture for today tune in for the part two. This is bonkly for dcranelia. Thank you very much for watching.

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