Formulating Linear and Integer Linear Programs: A Rogues' Gallery (original) (raw)

Formulating Integer Linear Programs: A Rogues' Gallery

INFORMS Transactions on Education, 2007

The art of formulating linear and integer linear programs is, well, an art: It is hard to teach, and even harder to learn. To help demystify this art, we present a set of modeling building blocks that we call "formulettes." Each formulette consists of a short verbal description that must be expressed in terms of variables and constraints in a linear or integer linear program. These formulettes can better be discussed and analyzed in isolation from the much more complicated models they comprise. Not all models can be built from the formulettes we present. Rather, these are chosen because they are the most frequent sources of mistakes. We also present Naval Postgraduate School (NPS) format; a define-before-use formulation guide we have followed for decades to express a complete formulation.

The Science and Art of Formulating Linear Programs

1987

This paper describes the philosophy underlying the development of an intelligent system t o assist in the formulation of large linear programs. The LPFORM system allows users t o state their problem using a graphical rather than an algebraic representation. A major objective of the system is to automate the bookkeeping involved in the development of large systems. It has expertise related t o the structure of many of the common forms of linear programs (e.g. transportation, product-mix and blending problems) and of how these prototypes may be combined into more complex systems. Our approach involves characterizing the common forms of L P problems according to whether they are transformations in place, time or form. W e show how LPFORM uses knowledge about the structure and meaning of linear programs t o construct a correct tableau. Using the symbolic capabilities of artificial intelligence languages, we can manipulate and analyze some properties of the L P prior t o actually generating a matrix.

Integer Programming: Theory and Practice

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Review of "Integer Programming” by Conforti et al

2015

Please scroll down for article-it is on subsequent pages With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

Coefficient Strengthening: A Tool for Formulating Mixed Integer Programs

SSRN Electronic Journal, 2000

Providing a good formulation is an important part of solving a mixed integer program. We suggest to measure the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation. Sequentially strengthening coefficients can then be used as a tool for improving formulations. We believe this method could be useful for analyzing and producing tight formulations of problems that arise in practice. We illustrate the use of the approach on a problem in production scheduling. We also prove that coefficient strengthening leads to formulations with a desirable property: if no coefficient can be strengthened, then no constraint can be replaced by an inequality that dominates it. The effect of coefficient strengthening is tested on a number of problems in a computational experiment. The strengthened formulations are compared to reformulations obtained by the preprocessor of a commercial software package. For several test problems, the formulations obtained by coefficient strengthening are substantially stronger than the formulations obtained by the preprocessor. In particular, we use coefficient strengthening to solve two difficult problems to optimality that have only recently been solved.

Modelling Integer Programming with Logic: Language and Implementation

Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2000

The classical algebraic modelling approach for integer programming (IP) is not suitable for some real world IP problems, since the algebraic formulations allow only for the description of mathematical relations, not logical relations. In this paper, we present a language L + for IP, in which we write logical specication of an IP problem. L + is a language based on the predicate logic, but is extended with meta predicates such as at least(m; S), where m is a non-negative integer, meaning that at least m predicates in the set S of formulas hold. The meta predicates facilitate reasoning about a model of an IP problem rigorously and logically. L + is executable in the sense that formulas in L + are mechanically translated into a set of mathematical formulas, called IP formulas, which most of existing IP solvers accept. We give a systematic method for translating formulas in L + to IP formulas. The translation is rigorously dened, veried and implemented in Mathematica 3.0. Our work follows the approach of McKinnon and Williams, and elaborated the language in that (1) it is rigorously dened, (2) transformation to IP formulas is more optimised and veried, and (3) the transformation is completely given in Mathematica 3.0 and is integrated into IP solving environment as a tool for IP.

Integer-Programming-Problem-Formulation

OP Papers, 2011

Integer linear programming is a very important class of problems, both algorithmically and combinatorially.Following are some of the problems in computer Science ,relevant to DRDO, where integer linear Programming can be effectively used to find optimum solutions. * Computer Scientist, Defence R&D Org., Min of Defence, Delhi-110054. email:akdhamija@dipr.drdo.in, dhamija.ak@gmail.com, a k dhamija@yahoo.com.

Free modelling languages for linear and integer programming

MSOR Connections, 2007

This paper illustrates the use of a mathematical programming language when teaching Linear and Integer Programming models on Operational Research courses. Such languages have often required expensive optimization software, but fortunately, the worldwide scope of the internet has put powerful free optimization tools within the reach of anyone with a PC connected even briefly to the internet. An effective example that the University of the West of England uses in its postgraduate MSc Statistics and Management Science is the NEOS server. This freely-accessible tool permits the submission of large-scale managerial optimization problems over the internet in a wide-variety of formats and sends the results back by email, often very quickly.