Mathematical Programming Systems Research Articles

Optimisation of repair and maintenance costs for electrical equipment in agricultural enterprises

Application of mathematical methods of cost optimization for repair and maintenance of electrical equipment of agro-industrial enterprises is one of the important and promising directions for increasing the efficiency of electrical equipment operation management in agriculture. Mathematical programming systems use graphical and related attributive information in solving optimization problems. As graphical information in these systems we used maps, plans, diagrams, schedules of preventive measures from which the list of equipment for certain types of repair and maintenance, their labor intensity for individual objects, types of equipment and in total for the enterprise are established. Databases of electrical equipment are used as attributive information to describe electrical equipment of agro-industrial enterprises. Due to joint processing of graphical and attributive information in optimization systems, all stages of work with spatial data are more operative. Beginning from spatial data search, selection and analysis we can make a specific decision during the operation control of electrical equipment. This article considers maintenance and repair operation (MR) as a task of mathematical programming with cost optimization and deals with three approaches to the organization of this task. The expediency of using each method of solution is analyzed. The structural schemes, equations describing mathematical models, advantages and disadvantages of the presented models are given. We marked prospect of using linear programming programs for the decision of the given optimization problem by means of the inverse matrix method, i.e. the modified simplex method and computing algorithm with a standard sequence of operations.

Review of Service Restoration for Distribution Networks

With the rapid deployment of the advanced metering infrastructure (AMI) and distribution automation (DA), self-healing has become a key factor to enhance the resilience of distribution networks. Following a permanent fault occurrence, the distribution network operator (DNO) implements the self-healing scheme to locate and isolate the fault and to restore power supply to out-of-service portions. As an essential component of self-healing, service restoration has attracted considerable attention. This paper mainly reviews the service restoration approaches of distribution networks, which requires communication systems. The service restoration approaches can be classified as centralized, distributed, and hierarchical approaches according to the communication architecture. In these approaches, different techniques are used to obtain service restoration solutions, including heuristic rules, expert systems, metaheuristic algorithms, graph theory, mathematical programming, and multi-agent systems. Moreover, future research areas of service restoration for distribution networks are discussed.

A strategic planning approach for protecting environmentally sensitive coastlines from oil spills: Allocating response resources on a limited budget

Oil exploration and production in the Gulf of Mexico (GOM) reached an all-time high in 2017 and projections for 2018 and 2019 suggest that production will continue to increase. As extraction activities continue their movement to deep and ultra-deep water environments, operational complexities that increase the risks associated with uncontrolled release events remain omnipresent. In addition to oil spills posing a critical threat to sensitive coastal environments, the geographic and economic implications of spill response need consideration. Specifically, given limited budgets, human resources and equipment, regional stakeholders must identify locations that improve the strategic value for siting spill mitigation resources. Not only can this help to improve the efficiency of spill response, an improved combination of equipment storage locations can help reduce the social and environmental costs of spills over time. The purpose of this paper is to detail an innovative strategic planning approach to protect sensitive coastlines from oil spills. Using a combination of mathematical programming and geographic information systems (GIS), we explore a range of alternative, geographic configurations of spill response resources, attempting to improve their overall proximity to environmentally sensitive shoreline areas using a case study in coastal Alabama, Mississippi and Florida.

Database structures for mathematical programming models

In the design and use of large-scale mathematical programming systems, a substantial portion of the effort has no direct relation to the variables and constraints, but is instead concerned with the description, manipulation and display of data. Established principles of database design do not apply directly to mathematical programming, however, because there are significant differences of organization and content between the data for an optimization model and the data for a conventional database application such as payroll or order entry. The goal of this work is thus to derive and elucidate fundamental principles of database construction for the specific case of large-scale mathematical programming. Alternative formulations of a steel mill planning model, combining aspects of production and network linear programming, are presented as an example; these formulations are shown to correspond to relational and hierarchical database schemes that have contrasting strengths and weaknesses. A particular implementation of a database system for steel optimization is then introduced and discussed, and a variety of promising generalizations are surveyed.

Power system restoration by joint usage of expert system and mathematical programming approach

AbstractWhen electric power supply interruption is caused by a fault, it is imperative to restore the power system promptly to an optimal target configuration after the fault. The problem of obtaining a target system is referred to as power system restoration. Both mathematical programming (MP) and expert systems (ES) have been used to solve restoration problems. However, existing approaches based on either MP and ES alone have inherent limitations stemming from their own paradigms. Mathematical progressing can obtain an optimal configuration under specified operational constraints, but requires a relatively long solution time. Although ES are effective in that they can utilize expert knowledge, maintenance of large‐scale ES requires inordinate effort.This paper proposes a new approach to power system restoration that utilizes both methodologies so as to exploit both systems' advantages. That is, a system under study is decomposed into a set of subsystems based on the knowledge of restoration experts, which is realized as an expert system. Then, MP is applied to each decomposed subsystem to obtain an optimal target configuration. A feasible operation sequence leading to the target configuration is generated by ES. This approach reduces significantly the computation time required to obtain target systems and is far less than would be the case if the total system is solved (as a unity). Moreover, the number of rules in the knowledge‐base are greatly decreased.

An interdisciplinary course in engineering synthesis

The interdisciplinary courseSynthesis of Engineering Systems has been offered by the Engineering Design Research Center over the last 3 years. Students are exposed to two major paradigms for design synthesis: mathematical programming and knowledge-based expert systems. The former emphasizes the mathematical formulation of optimization problems that involve discrete and continuous variables for the selection of topologies and parameters in engineering systems. The latter emphasizes representations and search techniques for processing qualitative knowledge for synthesis of designs by heuristic classification and hierarchical decomposition.

Constraint propagation, relational arithmetic in AI systems and mathematical programs

This paper explores the interrelationships between methods developed in mathematical programming to discover the structure of constraint (feasibility) sets and constraint propagation over networks used by some AI systems to perform inferences about quantities. It is shown that some constraint set problems in mathematical programming are equivalent to inferencing problems for constraint networks with interval labels. This makes the inference and query capabilities associated with AI systems that use logic programming, directly accessible to mathematical programming systems. On the other hand, traditional and newer methods which mathematical programming uses to obtain information about its associated feasibility set can be used to determine the propagation of constraints in a network of nodes of an AI system. When viewed from this point of view, AI problems can access additional mathematical programming analytical tools including new ways to incorporate qualitative data into constraint sets via interval and fuzzy arithmetic.

Constructing integer programming models by the predicate calculus

A modelling language for Integer Programming (IP) based on the Predicate Calculus is described. This is particularly suitable for building models with logical conditions. Using this language a model is specified in terms of predicates. This is then converted automatically by a series of transformation rules into a normal form from which an IP model can be created. There is also some discussion of alternative IP formulations which can be incorporated into the system as options. Further practical considerations are discussed briefly concerning implementation language and incorporation into practical Mathematical Programming Systems.

Computer solution of linear programs

PART I - BASIC THEORY AND METHOD: Linear programs and their solution The simplex method. PART II - PRACTICAL ASPECTS: Problem setup The basis matrix - fundamentals of numerical computation and numerical linear algebra The basis matrix - factorising and solving The basis matrix - updating and solving Selection strategies - choosing the entering and exiting variables Selection strategies - finding an initial feasible solution Practical implementation Mathematical programming systems in practice. PART III - OPTIMIZATION PRINCIPLE + SIMPLEX METHOD = LP ALGORITHM: The duality principle and the simplex method The decomposition principle and the simplex method The homotopy principle and the simplex method Bibliography Index.

Evelyn Martin Lansdowne Beale, 8 September 1928 - 23 December 1985

Evelyn Martin Lansdowne Beale was a talented mathematician at school and university. He became a pioneer in the development of linear programming methods at the Admiralty Research Laboratory (A.R.L.), Teddington. He then joined the Corporation for Economic and Industrial Research (C.E.I.R.) in 1961 in response to the challenge of applying operational research and mathematical programming to industrial problems. C.E.I.R. became Scicon (Scientific Control Systems Ltd) but Martin remained there, being its ‘Scientific Adviser' finally, a title that reflected his strong preference for advancing his subject in a benevolent way despite the commercial pressures of industry. Regularly on Mondays from 1967 he attended the Mathematics Department at Imperial College as a visiting professor. There, at conferences and in his published work, he communicated his extraordinary skill at extracting useful results computationally from mathematical models of real problems. Most of his papers on particular calculations and on particular techniques are substantial contributions to knowledge, but probably he will be remembered best for his constant and active interest in the development of mathematical programming systems for applying optimization algorithms painlessly in practice. He wrote (1961c)* that ‘The most important part of operational research is educated common sense, and computers have absolutely no common sense’, but he planned his systems so well that this defect of computers was negligible. There are no secrets of his success as he believed in open publication of useful discoveries. In all ways he was generous and kind, subject to high standards of honesty and academic integrity. He was devoted to his family and to the Christian faith.

Structural analysis of optimization problems formulated in planning languages

Computer-assisted model analysis, verification, and debugging is growing in importance. Most mathematical programming systems provide some debugging tools. This paper describes a typical structural analysis problem encountered in optimization models formulated in planning languages and states results that are useful in resolving it.

Solving large-scale mixed-integer programs with fixed charge variables

We consider large-scale mixed-integer programming problems containing fixed charge variables. In practice such problems are frequently approached by using commercial mathematical programming systems. Depending on the formulation, size and structure of the problem this approach may or may not be successful. We describe algorithms for preprocessing and optimization of such problems and discuss the design of an experimental software system based on MPSX/370. Numerical results for solving some large real life problems are also presented.

The Evolution of Mathematical Programming Systems

Computer programs to solve linear programming problems by the simplex method have existed since the early 1950s. They remain the central feature of today's mathematical programming systems. There has been a steady increase in the size of problem that can be solved: this has been due as much to a better understanding of how to exploit sparseness as to larger and faster computers. There has been a steady increase in the type of problem that can be solved: this has been due as much to new concepts, such as separable programming, integer variables and special ordered sets, as to new algorithms. There has been a steady increase in the extent to which the application of mathematical programming has become more automatic. This applies both to the use of computerized matrix generators and report writers and to the mathematical formulation itself, in that we rely less on the user producing a well-scaled linear programming problem and are starting on the process of automatically sharpening the formulation of integer programming problems.Important new work is being done on all these aspects of computational mathematical programming.

Integration of a primal simplex network algorithm with a large-scale mathematical programming system

In this paper we discuss the implementation of a primal simplex algorithm for network problems in the MPSIII mathematical programming system. Because of the need to interface with the rest of the MPS this implementation is unorthodox, but computationally effective, and has a number of advantages over “stand alone” network optimizers. It is argued that a similar approach is appropriate for other general-purpose mathematical programming systems, and has applications beyond pure network optimization.

On the solution of linear-programming problems with free (unrestricted) variables

This paper reviews the way free (unrestricted) variables are handled in the formulation and solution of linear-programming problems, and how such variables are processed in computerbased mathematical programming systems. Key theorems are proved that demonstrate the role of free variables in an optimal solution.

History of Mathematical Programming Systems

The systematic development of practical computing methods for linear programming (LP) began in 1952 at the Rand Corporation in Santa Monica, under the direction of George B. Dantzig. The author worked intensively on this project there until late 1956, by which time great progress had been made on first-generation computers. The work continued at CEIR, Inc., in Washington for some years and later in many places by many individuals and firms. By the late 1960s, elaborate systems of programs known as mathematical programming systems (MPS) had become a standard part of the available software for a number of computers, notably the IBM 360, GE 635, CDC 6600, and Univac 1108. The major MPSs underwent significant updating and extension during the mid-1970s taking on their present and probably final form, at least for big mainframes. Work still continues, however, and substantial improvements are being made in speed, reliability, supporting data management and control systems, and application techniques. Development of quite powerful microcomputer systems is now underway.

Large scale mathematical programming systems

This survey covers the state of the art of large scale mathematical programming systems (MPS's) for solving problems which can be modeled using linear programming or its extensions, such as mixed integer and some types of nonlinear programming. Such models occur frequently in chemical engineering and in other types of process, manufacturing and distribution applications.

Production and Sales Planning with Limited Shared Tooling at the Key Operation

The focus of this paper is multiperiod production and sales planning when there is a single dominant production operation for which tooling (dies, molds, etc.) can be shared among parts and is limited in availability. Our interest in such problems grew out of management issues confronting an injection molding manufacturer of plastic pipes and fittings for the building and chemical industries, but similar problems abound in the manufacture of many other cast, extruded, molded, pressed, or stamped products. We describe the development and successful application of a planning model and an associated computational approach for this class of problems. The problem is modeled as a mixed integer linear program. Lagrangean relaxation is applied so as to exploit the availability of highly efficient techniques for minimum cost network flow problems and for single-item dynamic lot-sizing type problems. For the practical application at hand, provably good solutions are routinely being obtained in modest computing time to problems far beyond the capabilities of available mathematical programming systems.

Mathematical programming systems, subsystems, and supersystems

Mathematical programming systems are becoming more difficult to define due to increasingly powerful abilities to interface different systems. The evolution and characteristics of the systems are described in terms of various real-world applications and specific implementations. A projection of past trends in development is made for a description of future system characteristics.

MP developments on burroughs computers

Mathematical Programming Systems that are available on Burroughs Computers are described. Possible differences between these systems that use serial processing equipment and a future system that uses parallel processing equipment are considered.