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2022 | Buch

Building and Solving Mathematical Programming Models

50 Practical Examples


Über dieses Buch

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation.

The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension.

In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases).

As an ideal companion to the author’s previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.


Chapter 1. Introduction to Modeling Methodology
In this chapter, a summary of some relevant aspects of the methodology guiding the modeling of the 50 problems is given, noting all the references described in the methodology for the modeling of specifications and objective criteria. The chapter delves into important aspects necessary for modeling compound propositions.
José Manuel García Sánchez
Chapter 2. Building and Solving Models with LINGO
This chapter introduces the LINGO algebraic modeling language, used for solving all the models in the book. The chapter presents the most important characteristics, including all the options for the input and output data of a model. The chapter provides us with a simple framework to transform any model whose information has been expressed using the methodology described for the elements of a system.
José Manuel García Sánchez
Chapter 3. Low-Level Problems
Low-level problems offer an introductory view of modeling in mathematical programming. We work with simple systems where the elements do not offer difficulty in their definition. Only simple specifications are considered. All types of simple specifications will be seen. We do not consider propositional logic specifications in any problem, and the treatment of the data does not offer any difficulty.
We only work with decision variables, except for two problems that incorporate bound variables. In three of the problems, there are two different ways of raising the modeling of the problem.
José Manuel García Sánchez
Chapter 4. Low-Medium Level Problems
In this chapter, we present problems of a higher level than the problems of the previous chapter, although we continue with systems with a high degree of abstraction. The main difference is the introduction of binary logical calculations and, therefore, the introduction of logical propositions. In general, the goal is to continue learning modeling techniques.
José Manuel García Sánchez
Chapter 5. Medium-Level Problems
At this level we present eight problems, where we continue to increase the complexity of the scenarios to be modeled, introducing in some problems particular cases in variable costs, both in specifications and in the objective function, and more elaborate logic specifications. Also, in some models we increase the complexity in the treatment of the data.
José Manuel García Sánchez
Chapter 6. Medium-High Level Problems
Most of the components that may be required in modeling an optimization problem are presented in the problems in this chapter. The use of non-binary logical calculations appears for the first time. Most problems have a high level of information handling. Although they are in the medium-high level, probably for some user many of these problems can be of a higher level. It is difficult to classify the difficulty of some of the systems in which the optimization problem is developed.
José Manuel García Sánchez
Chapter 7. High-Level Problems
The high-level problems raise optimization problems in thirteen scenarios. This chapter presents the most innovative aspect of the book, within the field of operations research, as some of the problems have not been studied before.
José Manuel García Sánchez
Building and Solving Mathematical Programming Models
verfasst von
José Manuel García Sánchez
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