For more than forty years, approximate solutions for the classical pipe network analysis problem have been obtained by direct solution of the nonlinear stationary point conditions. We propose a revolutionary new approach involving optimization techniques for solving this well-known engineering problem. It is shown that the pipe network analysis problem may be described mathematically in terms of a nonlinear convex cost network flow problem. Three mathematical programming algorithms for solving this problem have been coded and are computationally compared with a code using the traditional Newton-Raphson technique. The computational experience demonstrates that this new approach provides an attractive alternative for solving this important problem.

A school may be viewed as an enterprise in which the professional staff provide the operating conditions for converting quantifiable resources or inputs into pupil learning (outputs). The resources are determined by budgets, teacher assignments, and student assignments while learning is determined by various outputs scored according to standardized tests such as the Iowa Test of Basic Skills. Following the work of Charnes, Cooper, and Rhodes (Charnes, A., W. W. Cooper, E. Rhodes. 1981. Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management Sci. 27 (6) 668--697.), we use a ratio definition of efficiency that takes account of all outputs and inputs without requiring a priori specification of weights. Instead a series of mathematical programs are applied to determine "virtual multipliers" from actual data. The multipliers produce values that can be regarded as the "most favorable weights" for each school being evaluated. If the resulting optimum virtual multipliers for a given school yield an efficiency ratio of one, then that school is said to be efficient. If the ratio is less than one then that school is said to be inefficient relative to the other schools in the analysis. The ratio is also accorded operational significance---it is not merely an index number---so that the resulting values and the associated virtual multipliers make it possible to locate where improvements may be made along with their relative magnitudes. This analysis was applied to 167 elementary schools in the Houston Independent School District. Of these schools, 78 were found to be inefficiently utilizing their resources as compared to the 89 efficient schools. Based on this pilot study, an Educational Productivity Council has been formed at the University of Texas at Austin to provide an annual analysis for all of its member schools. At present 285 Texas schools in 22 districts are scheduled for participation in the annual analysis as described in this investigation.mathematical programming: applications, education systems: planning, data envelopment analysis

This exposition presents a state-of-the-art survey of results and algorithms for linear multicommodity network flow problems.

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D esigning a wideband code division multiple access (W-CDMA) network is a complicated task requiring the selection of sites for radio towers, analysis of customer demand, and assurance of service quality in terms of signal-to-interference ratio requirements. This investigation presents a net-revenue maximization model that can help a network planner with the selection of tower sites and the calculation of service capacity. The integer programming model takes as input a set of candidate tower locations with corresponding costs, a number of customer locations with corresponding demand for traffic, and the revenue potential for each unit of capacity allocated to each demand point. Based on these data, the model can be used to determine the selection of radio towers and the service capacity of the resulting radio network. The basic model is a large integer program and requires a special algorithm for practical solution. Our algorithm uses a priority branching scheme, an optimization-gap tolerance between 1% and 10%, and two sets of global valid inequalities that tighten the upper bounds obtained from the linear programming relaxation. The algorithm has been implemented in software for the AMPL/CPLEX system and an empirical investigation has been conducted. Using over 300 problem instances with up to 40 towers and 250 service locations, various combinations of algorithm settings have been evaluated. Using the recommended setting results in a design tool that generally runs in under 20 minutes on a 667 MHz AlphaStation.

KORBX® (a registered trademark of AT&T) is AT&T's new system for solving large-scale linear programs. The system consists of both hardware, which uses parallel processing technology configured with 256 MB of memory, and software which exploits the design and resources of this modern hardware. The KORBX linear programming software system contains four algorithms which are variations of the interior point method of Narendra Karmarkar. The primal, dual, primal-dual, and power series algorithms were empirically evaluated on a set of linear programming application models being used by the staff of the Military Airlift Command at Scott Air Force Base. For calibration purposes, a set of smaller test problems were also run using MPSX and XMP; and some pure network problems were solved using NETFLO, MPSX, and XMP.

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