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  • Articles  (8)
  • integer programming  (8)
  • 2020-2022
  • 1985-1989  (8)
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  • Articles  (8)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 12 (1988), S. 217-239 
    ISSN: 1572-9338
    Keywords: Propositional logic ; resolution ; integer programming ; theorem proving ; artificial intelligence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper illustrates how the application of integer programming to logic can reveal parallels between logic and mathematics and lead to new algorithms for inference in knowledge-based systems. If logical clauses (stating that at least one of a set of literals is true) are written as inequalities, then the resolvent of two clauses corresponds to a certain cutting plane in integer programming. By properly enlarging the class of cutting planes to cover clauses that state that at least a specified number of literals are true, we obtain a generalization of resolution that involves both cancellation-type and circulant-type sums. We show its completeness by proving that it generates all prime implications, generalizing an early result by Quine. This leads to a cutting-plane algorithm as well as a generalized resolution algorithm for checking whether a set of propositions, perhaps representing a knowledge base, logically implies a given proposition. The paper is intended to be readable by persons with either an operations research or an artificial intelligence background.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 15 (1988), S. 269-287 
    ISSN: 1572-9338
    Keywords: Production scheduling ; integer programming ; simulation ; flexible manufacturing ; hierarchical modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This study reports the development of a production scheduling system for the integrated management of production in large-scale, high-volume electronic assembly lines. The development of the system incorporates control and planning considerations by addressing the interaction of various subsystems. Stochastic and deterministic aspects of the problem environment are appropriately handled via relevant simulation and analytic models. By effecting a hierarchical breakdown of the problem environment, the system produces information used in practical decision making for production planning and scheduling. Procedures used encompass and address considerations for management of work-in-process, optimization of the various subsystems' performance, minimization of setup time effect, and inventory carrying costs.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 31 (1987), S. A55 
    ISSN: 1432-5217
    Keywords: integer programming ; greedy method ; Hilbert basis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird eine Version des Greedy-Algorithmus zur Lösung ganzzahliger linearer Optimierungsprobleme benutzt, die kein Rucksackproblem als Relaxation verwendet. Das Verfahren basiert auf der natürlichen partiellen Ordnung von Vektoren. Ziel der Arbeit ist es, eine möglichst große Problemklasse zu beschreiben, für die die Greedy-Lösung optimal ist. Die Ergebnisse verallgemeinern Sätze einer früheren Arbeit von Magazine, Nemhauser und Trotter und zeigen gleichzeitig einen Bezug zwischen zwei verschiedenen Gebieten der Kombinatorik auf: des Greedy-Verfahrens und von Hubert-Basen.
    Notes: Abstract A version of the greedy method not using any knapsack relaxation of the integer programming problem is considered in this paper. It is based on a natural partial ordering of the vectors. Our aim is to determine a large class of problems where the greedy solution is always optimal. The results generalize some theorems of an early paper of Magazine, Nemhauser and Trotter and at the same time show a connection between two different notions of combinatorics: the greedy method and the Hilbert basis.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 6 (1986), S. 291-310 
    ISSN: 1572-9338
    Keywords: Capacitated location-routing ; integer programming ; algorithm ; least cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In location-routing problems, the objective is to locate one or many depots within a set of sites (representing customer locations or cities) and to construct delivery routes from the selected depot or depots to the remaining sites at least system cost. The objective function is the sum of depot operating costs, vehicle acquisition costs and routing costs. This paper considers one such problem in which a weight is assigned to each site and where sites are to be visited by vehicles having a given capacity. The solution must be such that the sum of the weights of sites visited on any given route does not exceed the capacity of the visiting vehicle. The formulation of an integer linear program for this problem involves degree constraints, generalized subtour elimination constraints, and chain barring constraints. An exact algorithm, using initial relaxation of most of the problem constraints, is presented which is capable of solving problems with up to twenty sites within a reasonable number of iterations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 30 (1986), S. A79 
    ISSN: 1432-5217
    Keywords: Aggregation of constraints ; integer programming ; linear and nonlinear constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Die Zusammenfassung von Restriktionen ist eine Technik zur Lösung ganzzahliger Optimierungsaufgaben. Es wird ein Resultat von Zionts modifiziert. Ohne diese Modifikation gibt es nämlich ein Gegenbeispiel zur Behauptung. Ferner wird ein Satz von Bradley über die Zusammenfassung nichtlinearer Funktionen etwas verallgemeinert.
    Notes: Abstract To aggregate constraints is a technique for solving the integer programming problem. In this note we modify a result of Zionts (1974); without this modification, there is a counterexample for Zionts' result. Further, we give an elegant theorem which considers the aggregation of nonlinear constraints.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 3 (1985), S. 277-300 
    ISSN: 1572-9338
    Keywords: Clustering ; integer programming ; flexible manufacturing ; group technology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Parts grouping into families can be performed in flexible manufacturing systems (FMSs) to simplify two classes of problems: long horizon planning and short horizon planning. In this paper the emphasis is on the part families problem applicable to the short horizon planning. Traditionally, parts grouping was based on classification and coding systems, some of which are reviewed in this paper. To overcome the drawbacks of the classical approach to parts grouping, two new methodologies are developed. The methodologies presented are very easy to implement because they take advantage of the information already stored in the CAD system. One of the basic elements of this system is the algorithm for solving the part families problem. Some of the existing clustering algorithms for solving this problem are discussed. A new clustering algorithm has been developed. The computational complexity and some of the computational results of solving the part families problem are also discussed.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 4 (1985), S. 253-283 
    ISSN: 1572-9338
    Keywords: Mathematical programming ; integer programming ; general multiple-choice knapsack problem ; knapsack problem ; capital budgeting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A common problem frequently faced by business firms and individual investors is to select a few investment opportunities from many available possibilities. This problem, in its simplest form, can be modeled as a 0–1 knapsack problem. In a more general investment scenario, however, we obtain a model which is a general knapsack problem with a multiple-choice constraint. To solve this problem, an efficient enumerative algorithm is developed. The algorithm includes an efficient procedure to solve the LP-relaxed problem, a reduction algorithm which may allow the initial fixing of some of the variables, and various other implicit enumeration criteria derived from the group problem. Extensive computational experience illustrates the efficiency of the algorithm and related results.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 5 (1985), S. 557-573 
    ISSN: 1572-9338
    Keywords: Modeling ; micro-computers ; integer programming ; nonlinear programming ; heuristics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We describe the development and successful implementation of a decision support system now being used by several leading firms in the architecture and space planning industries. The system, which we call SPDS (spatialprogrammingdesignsystem) has the following characteristics: (i) user-friendly convenience features permitting architects and space planners to operate the system without being experienced programmers; (ii) interactive capabilities allowing the user to control and to manipulate relevant parameters, orchestrating conditions to which his or her intuition provides valuable input; (iii) informative and understandable graphics, providing visual displays of interconnections that the computer itself treats in a more abstract methematical form; (iv) convenient ways to change configurations, and to carry out ‘what if’ analyses calling on the system's decision support capabilities; (v) a collection of new methods, invisible to the user, capable of generating good solutions to the mathematical programming problems that underlie each major design component. These new methods succeed in generating high quality solutions to a collection of complex discrete, highly nonlinear problems. While these problems could only be solved in hours, or not at all, with previously existing software, the new methods obtain answers in seconds to minutes on a minicomputer. Major users, including Dalton, Dalton, Newport, and Marshal Erdwin, report numerous advantages of the system over traditional architectural design methods.
    Type of Medium: Electronic Resource
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