Operational Research

01) Introduction to Operational Research

Video Lecture PDF Notes Definition Operational Research is a scientific approach for decision making to analyzing a problem, developing the mathematical models to represent it and using various techniques to find the best solution. Purpose To solve complex problems Improve decision making Optimize resources (maximize efficiency using limited resources) Applications Business Management Transportation Health Care Government and Publice Services Finance Sub-disciplines Linear Programming Non-Linear Programming Quadradic Programming Integer Programming Dynamic Programming Transportation Theory Game Theory Queuing Theory Information Theory Revenue Management Financial Engineering History In 17th century, Mathematicians Blaise Pascal and Chritiaan Hygens solve the complex decision problems using game theory concepts and expected values. Others, Pierre de Fermet and Jacob Bernoulli solved these types of problems using combinatorial Reasoning. In 1840, Char...

Scope and Definition of Network Models

Scope of Network Models Pipeline Design : Agar kisi ko Gulf of Mexico se gas supply karni ho, toh sabse kam kharche wali pipeline banane ka model use kiya jata hai. Gulf of Mexico ek bara samundari hissa hai jo North America ke neeche mojood hai. Yeh America, Mexico aur Cuba ke darmiyan hai. Yeh ek bara pani ka ilaqa hai jo Atlantic Ocean se connected hai. Yahan par bohot zyada tel aur gas mojood hai, is wajah se yeh duniya ki economy ke liye important hai. Is Gulf se America aur Mexico dono apni oil aur gas ki zaroorat poori karte hain. Yeh bohot saari machliyon aur samundari zindagi ka bhi ghar hai. ek bara talab ya dariya jo sirf ek mulk mein nahi, balki alag alag mulkon ko connect karta hai. Shortest Route : Do shehron ke darmiyan sabse chhoti aur behtareen road ka pata lagana. Maximum Flow : Agar Wyoming ke coal mines se Houston tak coal le jana ho, toh sabse zyada coal kis tareeke se bheja ja sakta hai. Wyoming ke coal mines → Wyoming ek jagah hai America (USA) mein,...

02) Linear Inequalities and Feasible Solution

Video Lecture Pdf Notes Linear Inequalities Inequalities can expressed by following four symbols: < (less than), > (greater than), <= (less than or equal to) and >= (greater than or equal to) (i) ax < b(ii) ax + b ≥ c(iii) ax + by > c(iv) ax + by ≤ c Inequalities (i) and (ii) are in one variable while inequalities (iii) and (iv) are in two variables. The following operations will not affect the order (or sense) of inequality while changing it to a simpler equivalent form: (i) Adding or subtracting a constant to each side of it. (ii) Multiplying or dividing each side of it by a positive constant. Solution Region of Linear Inequalities in two variables The graph of a system of inequalities consists of the set of all ordered pairs (x, y) in the xy-plane which simultaneously satisfy all the inequalities in the system. To find the graph of such a system, we draw the graph of each inequality in the system on the same coordinate...

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01) Introduction to Operational Research

Scope and Definition of Network Models

02) Linear Inequalities and Feasible Solution

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