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  • Articles  (146)
  • linear programming  (146)
  • Mathematics  (142)
  • Energy, Environment Protection, Nuclear Power Engineering  (4)
  • 1
    Electronic Resource
    Electronic Resource
    A case study of resources management planning with multiple objectives and projects (1994)
    Springer
    Environmental management 18 (1994), S. 729-742 
    Details
    ISSN: 1432-1009
    Keywords: Analytic hierarchy process ; resource allocation ; linear programming ; Olympic National Park
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Each National Park Service unit in the United States produces a resources management plan (RMP) every four years or less. The plans commit budgets and personnel to specific projects for four years, but they are prepared with little quantitative and analytical rigor and without formal decision-making tools. We have previously described a multiple objective planning process for inventory and monitoring programs (Schmoldt and others 1994). To test the applicability of that process for the more general needs of resources management planning, we conducted an exercise on the Olympic National Park (NP) in Washington State, USA. Eight projects were selected as typical of those considered in RMPs and five members of the Olympic NP staff used the analytic hierarchy process (AHP) to prioritize the eight projects with respect to their implicit management objectives. By altering management priorities for the park, three scenarios were generated. All three contained some similarities in rankings for the eight projects, as well as some differences. Mathematical allocations of money and people differed among these scenarios and differed substantially from what the actual 1990 Olympic NP RMP contains. Combining subjective priority measures with budget dollars and personnel time into an objective function creates a subjective economic metric for comparing different RMP’s. By applying this planning procedure, actual expenditures of budget and personnel in Olympic NP can agree more closely with the staff’s management objectives for the park.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02394636
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  • 2
    Electronic Resource
    Electronic Resource
    Project analysis using a linear approach (P.A.U.L.A.) (1993)
    Springer
    Decisions in economics and finance 16 (1993), S. 73-86 
    Details
    ISSN: 1129-6569
    Keywords: project analysis ; linear programming ; internal financial law (IFL) ; financial leverage ; discounted cash-flows (DCF) decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Riassunto Si definisce un modello generale (PAULA) per la valutazione, selezione e gestione ottimale di progetti certi alternativi. Sfruttando i risvolti formali e finanziari dei problemi lineari associati (diretto e duale), si formulano poi due proposte per definire una legge finanziaria interna (IFL) ottimale, utili sia per abbattere la molteplicità intrinseca delleIFL, sia per evitare risultati economicamente arbitrari nel loro uso.
    Notes: Abstract We define a general model (called PAULA) for the valuation, optimal management and selection among mutually exclusive safe projects. By exploiting the formal and financial features of the associated linear problems (primal and dual), we put forward two proposals to define an optimal internal financial law (IFL). They may be used to reduce the multiplicity of the IFLs and to avoid economically arbitrary outcomes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02086763
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  • 3
    Electronic Resource
    Electronic Resource
    An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization (1989)
    Springer
    Stochastic environmental research and risk assessment 3 (1989), S. 17-29 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic optimization ; linear programming ; simplex method ; Karmarkar's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543425
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  • 4
    Electronic Resource
    Electronic Resource
    An algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations (1990)
    Springer
    Mathematical programming 47 (1990), S. 175-201 
    Details
    ISSN: 1436-4646
    Keywords: Optimization ; linear programming ; complexity ; polynomial time algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present an algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations wherem is the number of constraints, andn is the number of variables. Each operation is performed to a precision of O(L) bits.L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of $$\sqrt {m + n} $$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580859
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  • 5
    Electronic Resource
    Electronic Resource
    Making sparse matrices sparser: Computational results (1990)
    Springer
    Mathematical programming 49 (1990), S. 91-111 
    Details
    ISSN: 1436-4646
    Keywords: Sparse matrices ; linear programming ; bipartite matching
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Many optimization algorithms involve repeated processing of a fixed set of linear constraints. If we pre-process the constraint matrixA to be sparser, then algebraic operations onA will become faster. We consider the problem of making a given matrix as sparse as possible, theSparsity Problem (SP). In a companion paper with S. Frank Chang, we developed some theoretical algorithms for SP under a non-degeneracy assumption (McCormick and Chang, 1988). Here we investigate what must be done to make those algorithms applicable in practice. We report encouraging computational results in making linear programming constraint matrices sparser. We also find that the Simplex Algorithm can solve the reduced LPs faster. Comparisons are made to a heuristic algorithm for SP of Adler et al. (1989).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588780
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  • 6
    Electronic Resource
    Electronic Resource
    Interior point algorithms for linear programming with inequality constraints (1991)
    Springer
    Mathematical programming 52 (1991), S. 209-225 
    Details
    ISSN: 1436-4646
    Keywords: Karmarkar's algorithm ; linear programming ; projective algorithm ; conical projection ; interior methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Interior methods for linear programming were designed mainly for problems formulated with equality constraints and non-negative variables. The formulation with inequality constraints has shown to be very convenient for practical implementations, and the translation of methods designed for one formulation into the other is not trivial. This paper relates the geometric features of both representations, shows how to transport data and procedures between them and shows how cones and conical projections can be associated with inequality constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582888
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  • 7
    Electronic Resource
    Electronic Resource
    An interior point potential reduction algorithm for the linear complementarity problem (1992)
    Springer
    Mathematical programming 54 (1992), S. 267-279 
    Details
    ISSN: 1436-4646
    Keywords: Linear complementarity ; P-matrix ; interior point ; potential function ; linear programming ; quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The linear complementarity problem (LCP) can be viewed as the problem of minimizingx T y subject toy=Mx+q andx, y⩾0. We are interested in finding a point withx T y 〈ε for a givenε 〉 0. The algorithm proceeds by iteratively reducing the potential function $$f(x,y) = \rho \ln x^T y - \Sigma \ln x_j y_j ,$$ where, for example,ρ=2n. The direction of movement in the original space can be viewed as follows. First, apply alinear scaling transformation to make the coordinates of the current point all equal to 1. Take a gradient step in the transformed space using the gradient of the transformed potential function, where the step size is either predetermined by the algorithm or decided by line search to minimize the value of the potential. Finally, map the point back to the original space. A bound on the worst-case performance of the algorithm depends on the parameterλ *=λ*(M, ε), which is defined as the minimum of the smallest eigenvalue of a matrix of the form $$(I + Y^{ - 1} MX)(I + M^T Y^{ - 2} MX)^{ - 1} (I + XM^T Y^{ - 1} )$$ whereX andY vary over the nonnegative diagonal matrices such thate T XYe ⩾ε andX jj Y jj⩽n 2. IfM is a P-matrix,λ * is positive and the algorithm solves the problem in polynomial time in terms of the input size, |log ε|, and 1/λ *. It is also shown that whenM is positive semi-definite, the choice ofρ = 2n+ $$\sqrt {2n} $$ yields a polynomial-time algorithm. This covers the convex quadratic minimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586054
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  • 8
    Electronic Resource
    Electronic Resource
    Herd composition in an Aymara community of the Peruvian Altiplano: A linear programming problem (1991)
    Springer
    Human ecology 19 (1991), S. 369-387 
    Details
    ISSN: 1572-9915
    Keywords: Andes ; pastoralism ; Aymara ; linear programming ; utility theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Ethnic Sciences
    Notes: Abstract A model of herd management is presented for Aymara alpaca herders in the south central Andes. Linear programming methods and subjective utility values are used to model how pastoralists choose the size of their herd and the species they raise. These decisions are modeled in light of the land and labor resources available to pastoralists, and the products Andean herders must derive from their herds (meat, wool, and dung). The model predicts typical herd size in the community of Chinchillape, and has implications for social and economic changes seen in the Andes today. Specifically, pastoralists in Chinchillape are pursuing maximizing strategies, optimizing herd value by concentrating on alpacas, and decreasing the proportion of llamas in their herd in response to expanding transportation systems. Finally, results of the models indicate that sheep are a very poor option for Andean herders. This explains the reluctance of indigenous herders to adopt sheep herding in some areas of the Andes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00888983
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  • 9
    Electronic Resource
    Electronic Resource
    On greedy algorithms for series parallel graphs (1988)
    Springer
    Mathematical programming 40 (1988), S. 197-204 
    Details
    ISSN: 1436-4646
    Keywords: Greedy algorithms ; series parallel graphs ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This note describes some sufficient conditions for the maximum or minimum of a weighted flow (the weights are on paths, and are derived from weights on the edges of the path), of given volume in a series parallel graph to be found by a greedy algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580730
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  • 10
    Electronic Resource
    Electronic Resource
    Low order polynomial bounds on the expected performance of local improvement algorithms (1986)
    Springer
    Mathematical programming 35 (1986), S. 193-224 
    Details
    ISSN: 1436-4646
    Keywords: Local improvement ; average performance of algorithms ; linear complementarity ; linear programming ; extremal set theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a general abstract model of local improvement, applicable to such diverse cases as principal pivoting methods for the linear complementarity problem and hill climbing in artificial intelligence. The model accurately predicts the behavior of the algorithms, and allows for a variety of probabilistic assumptions that permit degeneracy. Simulation indicates an approximately linear average number of iterations under a variety of probability assumptions. We derive theoretical bounds of 2en logn and en 2 for different distributions, respectively, as well as polynomial bounds for a broad class of probability distributions. We conclude with a discussion of the applications of the model to LCP and linear programming.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580647
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