This paper presents two facility location models for the problem of determining how to optimally serve the requirements for communication circuits between the United States and various European and Middle Eastern coun...
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This paper presents two facility location models for the problem of determining how to optimally serve the requirements for communication circuits between the United States and various European and Middle Eastern countries. Given a projection of future requirements, the problem is to plan for the economic growth of a communications network to satisfy these requirements. Both satellite and submarine cable facilities may be used. The objective is to find an optimal placement of cables (type, location, and timing) and the routing of individual circuits between demand points (over both satellites and cables) such that the total discounted cost over a T-period horizon is minimized. This problem is cast as a multiperiod, capacitated facility location problem. Two mathematical models differing in their provisions for network reliability are presented. Solution approaches are outlined and compared by means of computational experience. Use of the models both in planning the growth of the network and in the economic evaluation of different cable technologies is also discussed. [ABSTRACT FROM AUTHOR]
An important branch of mathematical programming is concerned with optimization in systems described by networks. This paper describes an integrated suite of advanced techniques for dealing with minimum cost network fl...
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An important branch of mathematical programming is concerned with optimization in systems described by networks. This paper describes an integrated suite of advanced techniques for dealing with minimum cost network flow formulations Written in Pascal and implemented on a microcomputer representative of current small computer technology (the APPLE II), this package places unprecedented modeling versatility and solution capability on the analyst's desktop. Able to solve small to medium size problems (3000 arcs or less) at reasonable speeds, programs to handle capacitated linear, nonlinear (convex separable), mixedinteger and elastic ranged linear models in addition to comprehensive control and data management routines are included. Problem size and solution speed benchmarks are given for a variety of models.
This is a comparison of two state-of-the-art large-scale nonlinear optimization systems exhibiting unprecedented problem solution capabilities both in size of problem handled and method of solution. These codes are MI...
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This is a comparison of two state-of-the-art large-scale nonlinear optimization systems exhibiting unprecedented problem solution capabilities both in size of problem handled and method of solution. These codes are MINOS, developed by B. A. Murtagh and M. A. Saunders, and XS, developed by G. G. Brown and G. W. Graves. The codes are evaluated with respect to their problem solving capabilities and potential for practical applica- tion by analysts. Computational results are presented for thirteen nonlinear and nonlinear mixedinteger test problems with from two to 793 variables (12 to 100 integer variables) and one to 401 constraints. Portions of this work were presented at the CORS/ORSA/TIMS joint meeting in Toronto, May 1981.
A methodology has been developed to include effectively water supply from groundwater in urban planning. The model LANDUSE for prediction of urban development and water demand is linked to the model WATSUP, an optimiz...
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A methodology has been developed to include effectively water supply from groundwater in urban planning. The model LANDUSE for prediction of urban development and water demand is linked to the model WATSUP, an optimization oriented finite element based water supply model for prediction and optimization of future water supply configurations. The nonlinearity of the objective function due to nonlinear head losses has been circumvented by means of empirical relationships for head losses and design criteria for pump and pipe sizes. The requirement that some decision variables such as the number of wells, equalizing reservoirs, etc. be integer variables leads to a mixed integer programming formulation. A two level coordination scheme is used in locating an optimal number of facilities such that cost is minimized and a safe exploitation of aquifer in the future is guaranteed. The methodology is applied to an actual situation in West Lafayette, Indiana.
A supervised discriminant mixed integer programming algorithm (DISMIP) is described which achieves either linear or non-linear separation, without assuming any specific probability distribution. This system offers gre...
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The ordinary knapsack problem is to find the optimal combination of items to be packed in a knapsack under a single constraint on the total allowable resources, where all coefficients in the objective function and in ...
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The ordinary knapsack problem is to find the optimal combination of items to be packed in a knapsack under a single constraint on the total allowable resources, where all coefficients in the objective function and in the constraint are constant. In this paper, a generalized knapsack problem with coefficients depending on variable parameters is proposed and discussed. Developing an effective branch and bound algorithm for this problem, the concept of relaxation and the efficiency function introduced here will play important roles. Furthermore, a relation between the algorithm and the dynamic programming approach is discussed, and subsequently it will be shown that the ordinary 0–1 knapsack problem, the linear programming knapsack problem and the single constrained linear programming problem with upper-bounded variables are special cases of the interested problem. Finally, practical applications of the problem and its computational experiences will be shown.
A model is presented for overall energy planning of an urban region with respect to the preference of energy forms. The region is divided into subareas depending on land use and their locations. Electrical and heating...
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A model is presented for overall energy planning of an urban region with respect to the preference of energy forms. The region is divided into subareas depending on land use and their locations. Electrical and heating demands are forecasted for each subarea and the region as a whole. The energy systems are described by plant and network capacities and linearized cost functions. The objective is to find appropriate energy forms in each subarea to minimize the annual costs. This approach will be used to analyze the economical aspects of different trends in energy consumption, land use potientials and system performance. Finally, the model can be used to analyse the consequences of the uncertainties in cost parameters and demand forecasting.
First, this paper presents the results of experiments with algorithmic techniques for efficiently solving medium and large scale linear and mixed integer programming problems. The techniques presented here are either ...
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First, this paper presents the results of experiments with algorithmic techniques for efficiently solving medium and large scale linear and mixed integer programming problems. The techniques presented here are either original or recent. The solution of a great number of problems has shown that efficient problem solving requires automatic adaptation of algorithmic techniques upon problem characteristics. We show when a given technique should be used for a particular problem. The last part of this paper describes an attempt to provide a powerful mathematical programming language, allowing an easy programming of specific studies on medium-size models such as the recursive use of LP or the build-up of algorithms based on the simplex method. All these features have been implemented in the IBM Mathematical programming System, MPSX/370, and its feature MIP/370. Extensive numerical results and comparisons on real-life problems are provided and commented upon.
Optimization of the program of installation of reprocessing plants is mathematically formulated as problem of mixed integer programming, which is numerically solved by the branch-and-bound method. A new concept of qua...
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Optimization of the program of installation of reprocessing plants is mathematically formulated as problem of mixed integer programming, which is numerically solved by the branch-and-bound method. A new concept of quasi-penalty is used to obviate the difficulties associated with dual degeneracy. The finiteness of the useful life of the plant is also taken into consideration. It is shown that an analogous formulation is possible for the cases in which the demand forecasts and expected plant lives cannot be predicted with certainty. The scale of the problem is found to have kN binary variables, (k+2)N continuous variables, and (k+3)N constraint conditions, where k is the number of intervals used in the piece-wise linear approximation of a nonlinear objective function, and N the overall duration of the period covered by the installation program. Calculations are made for N=24 yr and k=3, with the assumption that the plant life is 15 yr, the plant scale factor 0.5, and the maximum plant capacity 900 (t/yr). The results are calculated and discussed for four different demand forecasts. The difference of net profit between optimal and non-optimal installation programs is found to be in the range of 50-100 M$. The pay-off matrix is calculated, and the optimal choice of action when the demand cannot be forecast with certainty is determined by applying Bayes' theory. The optimal installation program under such conditions of uncertainty is obtained also with a stochastic mixed integer programming model.
A mixed-integer linear programming approach to the planning of electrical-power networks is described. The method is based on an interpretation of fixed-cost transportation-type models, and includes both network secur...
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A mixed-integer linear programming approach to the planning of electrical-power networks is described. The method is based on an interpretation of fixed-cost transportation-type models, and includes both network security and costs of network losses. Both single-period and multitime-period planning problems are considered. A large general-purpose mathematical programming system is used to obtain solutions using branch-and-bound algorithms, and the practical aspects of organising the problems and controlling the branch-and-bound tree search within a modern m.p.s. package are discussed. Three case studies are presented for illustration: the optimal design of a 132 kV subtransmission system, the optimal time-phased design of the same system over. eight years, and the optimal layout and cable selection for a new housing-estate low-voltage network. The paper concludes by indicating potential further applications of the method for scheduling, for example, new plant at substations.
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