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In designing the spreadsheet optimizer that is bundled with Microsoft Excel, we and Microsoft made certain choices in designing its user interface, model processing, and solution algorithms for linear, nonlinear, and integer programs. We describe some of the common pitfalls users encounter and remedies available in the latest version of Microsoft Excel. The Solver has many applications and great impact in industry and education.

T he algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for any gradient-based local solver for nonlinear programming (NLP) problems. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 155 smooth NLP and mixed integer nonlinear program (MINLP) problems due to Floudas et al. (1999), most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and 100 constraints. Global solutions to almost all problems are found in a small number of local solver calls, often one or two.

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Abstract:The interdisciplinary nature of water resources problems requires the integration of technical, economic, environmental, social, and legal aspects into a coherent analytical framework. This paper presents the development of a new integrated hydrologicagronomic-economic model in the context of a river basin in which irrigation is the dominant water use and irrigation-induced salinity presents a major environmental problem. The model's main advantage is its ability to reflect the interrelationships between essential hydrologic, agronomic, and economic components and to explore both economic and environmental consequences of various policy choices. All model components are incorporated into a single consistent model, which is solved in its entirety by a simple but effective decomposition approach. The model is applied to a case study of water management in the Syr Darya River basin in Central Asia. Integrated Hydrologic-Agronomic-Economic ModelingThe interdisciplinary nature of water resources problems requires the integration of technical, economic, environmental, social, and legal aspects into a coherent analytical framework ͑Serageldin 1995͒. A river basin is a natural unit for integrated water resources planning and management, since water interacts with and to a large degree controls the extent of other natural components such as soil, vegetation, and wildlife. Human activities, too, so dependent on water availability, might best be organized and coordinated within the river basin unit. Water resources management needs to focus on an integrated basin system, including water supply, water demand, and intermediate components. Accordingly, policy instruments designed to make more rational economic use of water resources are likely to be applied at this level. To provide an analytical framework at the basin scale, modeling techniques for integrated models have been studied and found to present opportunities for the advance of water resources management ͑McKinney et al. 1999͒.Irrigation is the dominant water use in many arid and semiarid river basins, and irrigation management plays a critical role in water management in these basins. An integrated hydrologicagronomic-economic model combines the management of surface and subsurface reservoir ͑supply͒ systems with irrigation and farming, evaluates irrigated crop yields, and derives reservoir operating policies. Some recent studies of such systems include Vedula and Mujumdar ͑1992͒, Dudley and Scott ͑1993͒, and Vedula and Kumar ͑1996͒, in which reservoir release and fieldwater allocation decisions are integrated in a modeling framework, taking into account soil moisture dynamics and crop growth at the field level. Reservoir inflow and precipitation can be considered stochastic, and water allocation among multiple crops is included ͑Vedula and Kumar 1997͒. Models in all these studies are applied to a single farm and a single reservoir, and result analysis is limited to reservoir operation and irrigation scheduling.Moreover, due to increasing water scarcity a...