Rock Street, San Francisco

According to Analytics Vidhya, 2017, linear
programming is a simple technique where we depict complex
relationships through linear functions and then find the optimum points. The real relationships might be much
more complex but we can simplify them to linear relationships. Linear
programming is the process of taking various linear inequalities relating to
some situation, and finding the “best” value obtainable under those
conditions. A typical example would be taking the limitations of materials and
labor, and then determining the “best” production levels for maximal
profits under those conditions. Applications of linear programming are everywhere
around you. You use linear programming at personal and professional fronts. You
are using linear programming when you are driving from home to work and want to
take the shortest route. Or when you have a project delivery you make
strategies to make your team work efficiently for on time delivery.

Example
of Linear Programming

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10        U
5   V       12

S2                                      w      4

T     10           X           20               Z

For instance a DHL delivery man
has 8 packages to deliver in a day. The warehouse is located at point A. The 8
delivery destinations are given by S, T, U, V, W, X, Y and Z. The numbers on
the lines indicate the distance between the cities. To save on fuel and time
the delivery person wants to take the shortest route. So, the delivery person
will calculate different routes for going to all the 8 destinations and
then come up with the shortest route. This technique of choosing the shortest
route is called linear programming .In this case, the objective of the delivery
person is to deliver the parcel on time at all 8 destinations. The process of
choosing the best route is called Operation Research. Operation research is an
approach to decision-making, which involves a set of methods to operate a
system. In the above example, my system was the Delivery model. Linear
programming is used for obtaining the most optimal solution for a problem with
given constraints. In linear programming, we formulate our real life problem
into a mathematical model. It involves an objective function, linear
inequalities with subject to constraints. Is the linear representation of the 8
points above representative of real world? Yes and No. It is oversimplification
as the real route would not be a straight line. It would likely have multiple
turns, U turns, signals and traffic jams. But with a simple assumption, we have
reduced the complexity of the problem drastically and are creating a solution
which should work in most scenarios.

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