Discover the Untapped Power of Integer Programming with Laurence Wolsey

Have you ever faced a challenging optimization problem where variables can only take on whole numbers? If so, then you've encountered the fascinating world of Integer Programming.

What is Integer Programming?

Integer Programming (IP) is a branch of mathematical optimization where the decision variables are constrained to be integers. It is a powerful tool used in various industries and disciplines, including logistics, manufacturing, finance, and scheduling, to tackle complex problems.

Integer Programming

by Laurence A. Wolsey (2nd Edition, Kindle Edition)

5 out of 5

Language	:	English
File size	:	23607 KB
Text-to-Speech	:	Enabled
Enhanced typesetting	:	Enabled
Print length	:	356 pages
Screen Reader	:	Supported

FREE

Meet the Expert: Laurence Wolsey

In the realm of Integer Programming, one name stands out: Laurence Wolsey. With decades of expertise and numerous acclaimed publications, Wolsey has made significant contributions to the field.

Contributions to Integer Programming

Laurence Wolsey has been instrumental in advancing the theory and applications of Integer Programming. He has focused on developing efficient algorithms to solve complex IP problems and has pioneered techniques that allow real-world problems to be formulated as integer programs.

The Wolsey-Gomory Cutting Plane Algorithm

One of Wolsey's most renowned contributions is the development of the Wolsey-Gomory Cutting Plane Algorithm. This algorithm effectively cuts through the solution space, reducing it to a smaller, more manageable size, and enabling faster and more accurate computations.

Applications of Integer Programming

The applications of Integer Programming are vast and span across multiple industries. Some common examples include:

• Resource Allocation: Optimize the allocation of limited resources, such as personnel, machines, or materials, to maximize output.
• Vehicular Routing: Determine the most efficient routes for delivery vehicles to minimize time and costs.
• Portfolio Optimization: Allocate investments to different assets to maximize returns while considering risk and constraints.
• Production Planning: Optimize production schedules, considering factors such as demand, inventory, and production capacities.

Advantages and Challenges of Integer Programming

While Integer Programming offers powerful solutions, it also presents challenges. Some advantages and challenges of using IP include:

Advantages:

• Ability to model real-world problems more accurately
• Great flexibility in formulating a wide range of optimization problems
• Provides optimal or near-optimal solutions
• Offers insights into trade-offs between different objectives

Challenges:

• Significantly more computationally complex compared to linear programming
• Larger solution spaces lead to longer computing times
• Optimal solutions may require significant computing power

Integer Programming, with its ability to handle discrete variables, plays a vital role in solving complex optimization problems in various fields. Thanks to the groundbreaking contributions of Laurence Wolsey, the efficiency and effectiveness of Integer Programming have been greatly enhanced. So, if you find yourself facing a challenging optimization problem, remember that Laurence Wolsey's expertise in Integer Programming can unlock a world of solutions at your fingertips.

Integer Programming

by Laurence A. Wolsey (2nd Edition, Kindle Edition)

5 out of 5

Language	:	English
File size	:	23607 KB
Text-to-Speech	:	Enabled
Enhanced typesetting	:	Enabled
Print length	:	356 pages
Screen Reader	:	Supported

FREE

A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED

The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition. The revised second edition:

• Contains new developments on column generation
• Offers a new chapter on Benders’ algorithm
• Includes expanded information on preprocessing, heuristics, and branch-and-cut
• Presents several basic and extended formulations, for example for fixed cost
• network flows
• Also touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project 

Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.