Modeling Of Real-world Problems Research Articles

Hybrid heuristic algorithms for Set Covering

The paper considers the minimal set covering problem. It is one of the most important discrete optimization problems because it serves as model for real-world problems, such as the best utilization of resources and workers in several fields. In general terms, there are a lot of tasks to do and a lot of resources for doing these tasks. One should find the subset of resources of minimal cost that fulfils all tasks. Of course, since the problem pertains to discrete optimization, the well-known operations research tool of integer programming is a natural choice. However, the problem is very hard to solve even by current supercomputers since the computing time grows exponentially with the problem size when a naive representation in the mathematical field of integer programming is adopted. Thus, a novel representation is described which combines two approaches for achieving good computation performance in large-size problems: first a linear programming model, then an improvement technique based on a simulated neural network. The linear programming relaxation model is new in that it uses a constraint matrix which is not problem instance specific as in the traditional model, and all problem specific data are incorporated in the objective function vector. Only two types of general constraints are used: choice constraints, which ensure each ‘job’ is covered, and exclusion constraints, which prevent redundant resources to be used. Significant test results and comparisons to other algorithms are reported. They show that the proposed new algorithm is effective in solving practical cases. In particular, it reports an average improvement in the execution time over the current best algorithms in solving hard problems while producing the same order of solution quality, i.e. optimality approximation. Minimal set covering (MSC) is a known NP-hard problem. It is the model of many important real-world problems and plays a central role in rostering (crew scheduling) problems. Large-size set covering problems (constraint matrix of about 10,000∗100,000 elements) are considered.First, the traditional model of MSC as integer program is recalled, then a new representation in linear programming (LP) is described. Finally, a new algorithm based on recurrent neural networks is introduced for the optimization of the pivot positions selection. This algorithm is combined with the LP algorithm to guarantee an optimal solution. The heuristic part serves for choosing the pivot positions in the Simplex algorithm for LP. The results of significant tests on real data are reported. They compare favourably with the best-known results on set covering, both in terms of execution time and solution accuracy.

Improving PRETREE's predictive capabilities

Compared to compensatory type choice models (e.g., logit), hierarchical choice models have been used much less frequently in the real world. This has happened even though there is a lot of evidence to suggest that the hierarchical structure is closer to the actual process by which individuals make choices. In this paper, we have considered one of the original hierarchical models (PRETREE). The PRETREE model has been heavily cited in the marketing and psychometric literatures. We wish to examine PRETREE at the aggregate level making n-way (market share) predictions. A primary strength of the PRETREE model was its apparent ability to capture violations of the property of the “independence of irrelevant alternatives” (IIA). We prove that there are limitations to this argument. We suggest a method to overcome these limitations; this change resulted in substantial improvement in the predictive abilities of the model, when the modified PRETREE is applied to real world data. The predictions are at an aggregate level on a hold-out sample. The above modification to PRETREE will hopefully not only renew but also increase interest in applying a hierarchical approach to modeling real-world problems on choice.

Proactive optimization of toxic waste transportation, location and technology

Abstract Many models of real world problems, such as the toxic waste transportation and location problem, produce solutions that “make the best of a bad situation”. Yet in many cases, giving the model better choices with which to work could produce far superior results. We introduce a framework for proactive optimization, defined as identification of the structural parameters within an OR problem that cause optimal solutions to be less than satisfactory, followed by an exogenous search for better options to add to the model. The proactive methodology is illustrated by a multiobjective, mixed-integer, location-allocation model with technology choice variables. A new technology, solar-driven waste detoxification, is compared with toxic waste incineration on three traditionally conflicting criteria: cost, a new risk measure (μg/m3 person hrs), and a new disequity measure (MinMaxSum kg∗km). The solar process is found to improve all three objectives considerably. Sensitivity analysis indicates the robustness of the results in terms of cost, risk, and sunlight availability.

Different kinds of models to integrate the OR-expert's knowledge into Decision Support Systems

This paper presents an approach to integrate OR-expert's knowledge about the modelling of real world problems into a Decision Support System (DSS). First, the problem of modelling is considered and a short survey over the structure of DSS is given. Then a model of different phases of interaction between a DSS and its user is discussed. In the framework of this phase model, different kinds of models are necessary to enable a DSS to perform the support of its user. These models, representing the OR-expert's knowledge, and their various interrelations are discussed. Finally, a prototype computer implementation of this approach is presented and further research topics are figured out.

Restricted planar location problems and applications

Facility location problems in the plane are among the most widely used tools of Mathematical Programming in modeling real-world problems. In many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden. We consider center and median problems where the forbidden set is a union of pairwise disjoint convex sets. As applications we discuss the assembly of printed circuit boards, obnoxious facility location and the location of emergency facilities.

Multiple criteria decision making: The case for interdependence

There has been a growing interest and activity in the area of multiple criteria decision making (MCDM), especially in the last 20 years. Modeling and optimization methods have been developed in both crisp and fuzzy environments. The overwhelming majority of approaches for finding best compromise solutions to MCDM problems do not make use of the interdependences among the objectives. However, as has been pointed out by Carlsson, in modeling real world problems (especially in management sciences) we often encounter MCDM problems with interdependent objectives. It is our intention in this paper to introduce measures of interdependences between the objectives, in order to provide for a better understanding of the decision problem, and to find effective and more correct solutions to MCDM problems.

Building Mathematical Models of Simple Harmonic and Damped Motion

Given the recent public mania over bungee jumping, stimulating students' interest in a model of that situation should be an easy “leap.” Students should investigate the connections among various mathematical representations and their relationships to applications in the real world, asserts the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Mathematical modeling of real-world problems can make such connections more natural for students, the standards document further indicates. Moreover, explorations of periodic real-world phenomena by all students, as well as the modeling of such phenomena by college-intending students, is called for by Standard 9: Trigonometry.

Combinatorial algorithms for some 1-facility median problems in the plane

Facility location problems in the plane are widely used tools of Operations Research in modeling real-world problems. In many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden. This paper investigates restrictions in 1-facility median problems in the plane. We introduce efficient algorithms for problems where the unrestricted problem can be solved in polynomial time. The algorithms are of a combinatorial nature and reduce the search for an optimal solution of the restricted problem to a finite number of candidates. The assumptions on the model are very weak. We only require that the forbidden area is a union of pairwise disjoint convex sets.

Causal independence for probability assessment and inference using Bayesian networks

A Bayesian network is a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real-world problems. When there are many potential causes of a given effect, however, both probability assessment and inference using a Bayesian network can be difficult. In this paper, we describe causal independence, a collection of conditional independence assertions and functional relationships that are often appropriate to apply to the representation of the uncertain interactions between causes and effect. We show how the use of causal independence in a Bayesian network can greatly simplify probability assessment as well as probabilistic inference.

Use of reason maintenance in model formulation

Studies of the process of model formulation by experts have shown the process to be an iterative one, in which the model is continuously refined until a complete and consistent representation emerges. It is also a highly unstable activity as the problem specifications, including the goal, may change both during and after the formulation. In order to be able to model real world problems, model formulation systems, which provide computer-based support for model formulation, should also be capable of dealing with changes to the problem. This paper presents the architecture of a model formulation system enhanced with reason maintenance capabilities, for dealing with changes in assumptions and specifications during formulation.

Book review: Queuing Networks- Exact Computational Algorithms: A Unified Theory Based on Decomposition and Aggregation by Adrian E. Conway and Nicolas D. Georganas (MIT Press 1989)

Queuing Network models are an approach to modeling real-world problems based on the abstractions of servers, queues, and routing between them. Product-form queuing networks have a particularly simple formula describing the state distribution, and have accrued a literature describing them.

Knowledge-based approaches for scheduling problems: a survey

Recent developments in artificial intelligence (AI) have led to the use of knowledge-based techniques for solving scheduling problems. The authors survey several existing intelligent planning and scheduling systems with the aim of providing a guide to the main AI techniques used. In view of the prevailing difference is usage of the terms planning and scheduling between AI and operations research (OR), a taxonomy of planning and scheduling problems is presented. The modeling of real world problems from closed deterministic worlds to complex real worlds is illustrated with a project scheduling example. Some of the more successful planning and scheduling systems are surveyed, and their features are highlighted. The AI approaches are consolidated into knowledge representation and problem solving in the project management context. >