Operational Research
Miguel Casquilho, PhD, Prof. ret., IST — Erdős no.: 4  Orcid & Google Scholar Scopus     APDIO

The problems below are, essentially, academic exercises in OR that are freely accessible for resolution. These have evolved, since 1998, and are now in a systematic[2], simple style.

These problems provide answers to various subjects in "Operational Research" (and some related topics). As these problems were conceived for use with my support, in classes, some of them may be unclear —this is not an "online course"[1] !—, but, every problem, for ease, has default data embedded. Suggestions for clarification are welcome (here), as well as additional cases by colleagues.

For students, I suggest that they also solve any problem by themselves, namely by programming in their preferred language.

For the interested users, contact me for further scientific work leading to possible publication.
Miguel Casquilho


▸Linear Programming (LP)
• LP, revised simplex • LP, tableaux • LP using (IBM) CPLEX

• LP (ditto) from COO[4] data matrix

• MIP using (IBM) CPLEX (Mixed Integer Progr.)

• TP (using CPLEX) (Transportation Problem)

• Transshipment problem (conversion to a TP)

 • Assignment Problem
▸Networks
• Shortest path (Dijkstra)

• Traveling Salesman Problem

    
▸Monte Carlo

• Random number generation (RNG) uniform

 • RNG binomial, Poisson

• RNG Gaussian, Exponential, Beta

  

• Transformation by inversion

• Simulate Exp., Gaussian, triangular

• Parabolic distribution

• "Raised" cosine distribution

• Acceptance-rejection (AR) triangular distr.

• AR cosine, "hat" optimization

• RNG Gaussian (inv. Box-Muller, r. polar)

• Comparison, Gaussian: inv., Box-Muller, rej. polar

• Sum of 2 Gaussians (!)

• Product of 2 uniforms (analytical)

• Volume of spheres

 

• Throwing (n) dice

• Interdistance in an n-cube

• Distance to point in a circle

• Distance to point in a rectangle

▸Queueing
• Find s in an M/M/s system • Queue variables • Queue simulation  
▸Inventory theory

• EOQ, economic order quantity

• EOQ, Random demand, holding & shortage costs

    

Related topics

• Student's t distribution

• (Chi-square) χ² distribution

• Is a chi-square a Gaussian ?!

    

• Optimal facility location

•  → Ditto (Python)

    

All the web pages have a (clickable) W3C icon at the lower left corner to permit checking the formal correctness of the HTML code for normal performance under any browser (some browsers, however, do not fully comply with the W3C standards). Add‑ins (such as JavaScript) are not used, so just the browser is necessary. (The links are always underlined[4].)

There are many other web pages in this site (Engineering, Statistics), but the cases above have been selected for adequacy.


References:

• [1] MOOC.org

• [2] Online calc (since 1999, in Hydraulics), Prof. Victor M. Ponce, San Diego State University (for a systematic style).

• [3] Should All Links be Underlined ? (=.pdf) ('usability.gov').

• [4] Storing a sparse matrix: coordinate list, Wikipedia.

• APDIO, INFORMS

• Wikipedia: Operations Research, Investigação operacional, Investigación de operaciones, Исследование операций

• HTML5 Entity Names by Alphabet.

• World Wide Web Consortium (W3C)

• Cool URIs don't change (but they do; hence, more stable Wikipedia's ones).
(CSS link checker)
 
 
Valid HTML 4.01! IST http://web.tecnico.ulisboa.pt/~mcasquilho/acad/apdio/index.php
Created: 2021-Jun — Last modified: 2021-08-04