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Operations Research Problems

Raúl Poler, Josefa Mula and Manuel Díaz-Madroñero
Publication Date: 
Number of Pages: 
Problem Book
[Reviewed by
Donald L. Vestal
, on

A good mathematics textbook (in any subject) will give the reader three things: a history of the subject, the theory behind the subject, and then examples. In a subject as wide-ranging as Operations Research, however, this borders on impossible. There are books that attempt this: Hillier and Lieberman’s text, Introduction to Operations Research, is a 1000+ page textbook that still doesn’t cover everything (although it does cover a lot). There are a few books that focus on the (long) history of OR (for example, An Annotated Timeline of Operations Research: An Informal History, by Gass and Assad). And there are books like this that focus on examples.

This book has ten chapters, with each chapter devoted to a specific topic in OR: Linear Programming, Integer Programming, Non-Linear Programming, Network Modelling, Inventory Theory, Queueing Theory, Decision Theory, Games Theory, Dynamic Programming, and Markov Processes. Each chapter starts with an introduction that gives a brief overview of the theory and process involved in solving the given type of problem. Then the remaining sections are devoted to solving specific problems of that type, using 12 to 26 examples.

As the title of Chapter 8 (Games Theory) might suggest, this book is an English translation. As such, there are some odd phrasings that appear on occasion, such as using “–Infinite” to refer to negative infinity, “degenerated solutions” for degenerate solutions, or references to positive semi-defined matrices. Also, we have sentences which are missing periods, dollar signs that appear on the right of numbers (and then back on the left), and conditional probabilities written as P(s/i) instead of P(s|i).

But getting past those minor issues, there are some great problems here. As an example, here is a personal favorite:

“This problem intends to compare a McDonolds and a Burger-Kong. It is assumed that McDonolds has queues in operation, one for each cashier, and that customers aleatorily choose the queue when they enter, without considering the length of the queue and without being able to change queue. Burger-Kong also hast two cashiers, but a single queue where the customers at the front of the queue go to whichever cashier is available. Consider that one person arrives at both premises every minute and that the mean service time is 30s. Which method implies a longer waiting time and a longer service time for the customer?

A good problem source for Operations Research!

Donald L. Vestal is an Associate Professor of Mathematics at South Dakota State University. His interests include number theory, combinatorics, spending time with his family, and working on his hot sauce collection. He can be reached at Donald.Vestal(AT)

Linear programming
Integer programming
Non-linear programming
Network Modelling
Inventory theory
Queuing theory
Decision theory
Games theory
Dynamic programming
Markov processes