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Operational Research

Resources

Complement

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The OR Society
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Papers

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Others

Here are a few societies that I like (look at their blogs, magazines, and journals):

What is Operation Research (OR)?

What is O.R. >> http://www.theorsociety.com/Pages/Careers/WhatIsOR.aspx

https://www.youtube.com/watch?v=ILWbaWrjgU4

What is a system?

All of my exercises

https://github.com/sanchezcarlosjr/uabc/tree/main/essays/operations research

Optimization

ūüí°
This leads me to quote from Webster's dictionary of the English language (pre-1960), where we find that the verb 'to optimize' means "to view with optimism.‚ÄĚ

Knuth, D. E. (1973). The dangers of computer-science theory. In Studies in Logic and the Foundations of Mathematics (Vol. 74, pp. 189-195). Elsevier.

https://fmin.xyz/

Linear programming

Gurobi, Lindo, and Cplex

Terminology

Linear programming. Mathematical technique in which a linear function is maximized or minimized subject to linear constraints.

Objective function. Linear function to be maximized or minimized.

The Standard Maximum Problem. Find a x=(x1,...,xn)Tx=(x_1,...,x_n)^TÔĽŅ such that

Objetive¬†function:¬†Max¬†cTxFunctional¬†constraints:¬†Ax‚ȧbConstraints:¬†x‚Č•0\text{Objetive function: }\text{Max }c^Tx \\ \text{Functional constraints: } Ax\le b\\ \text{Constraints: }x \ge 0

Feasible set. Set of x=(x1,...,xn)x=(x_1,...,x_n)ÔĽŅ such that checks the functional constraints and constraints.

The Standard Maximum Feasible Set. Set of x=(x1,...,xn)x=(x_1,...,x_n)ÔĽŅ such that

Functional¬†constraints:¬†Ax‚ȧbConstraints:¬†x‚Č•0\text{Functional constraints: } Ax\le b\\ \text{Constraints: }x \ge 0

References

[1] ‚ÄúLINEAR PROGRAMMING. A concise introduction‚ÄĚ [Online]. Available: https://www.math.ucla.edu/~tom/LP.pdf.

Lagrange method

https://ebrary.net/134819/mathematics/constrained_optimization_method_lagrange_multipliers

Markov chains

Ergodic Markov Chains

Ergodic. Involving or relating to the probability that any state will recur; especially: having zero probability that any state will never recur.

: involving or relating to the probability that any state will recur especially: having zero probability that any state will never recur

Stability

Waiting Line systems and Queue theory

When you encounter systems displaying characteristics of waiting phenomena, like distributed systems and queues in real life, you often resort to applying queue theory. This approach entails evaluating and enhancing system performance by characterizing these phenomena through mathematical models and simulations.

More concretely, queue theory is used to model systems that exhibit concurrent access to a shared resource such as highway toll station, line at a restaurant, airport check, bandwidth, server, disk, memory,

Discrete-time Markov chains, Continuous-time Markov chains, Multi server and finite capacity queues.

Simulators

TODO

https://ccl.northwestern.edu/netlogo/