Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> T HIS PAPER presents some aggregation results for linear programming models of the firm. It is assumed that the production decision problem for each firm in some regional, industrial, or typical firm aggregate can be represented by a linear programming model. By means of the duality theorem for dual linear programs, it is shown that under suitable conditions a single linear programming model for the aggregate is equivalent to a direct aggregation of the solutions of a set of individual firm models. Conditions sufficient for this equivalence are proportional variations of resources1 and behavioral "bounds"; proportional variation of net return expectations among all firms in the aggregate; and, finally, common technical coefficients which appear in the constraints on the firms' decisions. It is shown that imperfections in an atomistic market introduced by imperfect knowledge, uncertainty, or government policies may increase the number of aggregate models needed to describe an entire industry such as agriculture. An example is explored and implications of the model for equilibrium of an "open" economy sketched out. <s> BIB001 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> This paper attempts to indicate how spatial equilibrium models of the Enke-Samuelson variety may be handled as quadratic programming problems. Assuming the existence of linear regional demand and supply relations, models are formulated and algorithms specified which may be used to obtain directly and efficiently the interregional price and flow solutions for the single and multiproduct, n region cases. For each of the specifications the existence, uniqueness and convergence characteristics are investigated and the conditions for obtaining optimum solutions are noted. Illustrative numerical examples are given to reflect the structure of the programming formulation for several alternative spatial models. <s> BIB002 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> This paper shows how an approximate competitive market equilibrium may be computed as the solution to a linear programming model, when production possibilities are described by activity analysis vectors and demand functions are locally linear. Numerical examples show that the degree of approximation may be expected to be very small in many cases. Prices and quantities of goods and resources and also incomes are explicit in the primal. The defining characteristics of a market equilibrium are written as primal constraints. Linearizations of inherently nonlinear expressions are attained by use of grid linearizations and the associated interpolation variables. <s> BIB003 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> Serious aggregation errors may arise in mathematical programming sector models when aggregation is not properly done. Existing aggregation literature mostly focuses on exact aggregation of homogenous groups of firms. However, homogeneity rarely holds in real problem situations. Moreover, theoretical aggregation developments are generally based on the assumption of availability of full information about the firms to be aggregated. Such full information is hardly a plausible assumption when modeling the agricultural sector. This paper discusses an empirical aggregation approach based on decomposition theory, which may be particularly helpful while aggregating heterogenous firms under the absence of full information. Copyright 1989 by Oxford University Press. <s> BIB004 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> Abstract Current EC nitrogen legislation stipulates for the non-sensitive areas a preventive approach via the development of ‘best management practices’ (BMPs) within a context of voluntary implementation. Under existing technologies, the adoption of BMPs leads to economic losses. A crop simulation model (NTRM) and a mathematical mixed multi-objective programming model (NISE) are used to assess the effects of nitrogen price increase and drainage water reduction in inducing adoption of BMPs. The model shows that increasing nitrogen price cannot be used to stimulate farmers to adopt BMPs. On the other hand, imposing a tax on drainage water could lead to a reduction of up to 37% on the quantity of nitrogen leached with a decreased of only 1·5% in gross margin. However, above this level, drainage water is no longer a useful instrument to reduce and control nitrogen losses, and could lead to inefficient solutions in terms of gross margin and nitrates pollution. <s> BIB005 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> A farm-level risk programming framework is presented which evaluates income/ environmental risk tradeoffs. This framework uses a time-series of environmental risk indices to incorporate the stochastic, multiattribute characteristics of environmental outcomes associated with agricultural production practices. The model is applied to a representative farm in the Oklahoma Panhandle region of the Central High Plains. Results indicate that expected income is sensitive to nitrate loading restrictions, and relatively less sensitive to pesticide loading restrictions. Results also indicate that prescriptions derived using deterministic environmental risk measures may ignore significant probabilities of exceeding an environmental standard. <s> BIB006 </s> Operations Research Models and the Management of Agricultural and Forestry Resources: A Review and Comparison <s> 447 <s> Abstract Production of marketed commodities and protection of natural systems often conflict. A focus on only one goal can result in large losses in other goals and may result in inefficient and unsustainable outcomes. In this paper, we develop a method that combines economic and ecological models in a dynamic and spatial analysis to evaluate land use decisions and find cost-effective alternatives for which it is not possible to do better on one objective without harming another objective. The method is demonstrated using timber production and species conservation on a forested landscape over a 100-year planning horizon. Current land use strategies are simulated and compared with cost-effective alternatives. The approach is compared to a static reserve approach, similar to previous studies, and found to produce substantially more efficient management strategies for the case study landscape. <s> BIB007
covering OR applications in agriculture has declined slightly over the last decade or so, the use of OR models has grown, chiefly because of the impressive development of personal commercial software programs. Agricultural-Planning Problems (Farm Level)  work can be considered the starting point of linear programming (LP) models addressing agricultural decision making. Researchers formulated initial models at the farm level. The basic model has the following structure. The criterion function is usually gross margin (sales revenue minus variable costs). The feasible set represents the constraints that define the environment within which choices are made (for example, labor requirements, land available, and working capital requirements). Decision makers have used the basic model to (1) determine the optimum cropping pattern, (2) analyze the interdependence of parts of the farm, and (3) investigate the optimal sizes of different types of fixed equipment and machines to add to farm resources  . Researchers have also used LP models at the farm level to assess and to simulate the economic impact of some agricultural policies. These models are generally prospective; they try to predict the impact of policy changes on farmers' incomes and production patterns. LP models present difficulties; for example, an aggregation bias arises as one goes from farm level to regional-sector models, and identifying the real objectives farmers pursue is difficult. However, their current and future possibilities could be important. Lauwers et al. (1998) and van Huylenbroeck et al. (2001) , for example, demonstrate their potential. In some farm-planning situations, the values of the decision variables cannot be continuous (for example, the location of agricultural-processing activities) or such activities as milk production that must be undertaken at some minimum level if they are to be conducted at all. Such situations require integer or zero-one LP models. The intertemporality underlying many agricultural decisions sometimes demands the use of multiperiod LP models (Rae 1994) . To deal with the risk and uncertainty that farmers encounter in real situations, we must incorporate multiple criteria into LP models. Agricultural-Planning Problems (Regional-Sector Level) When the analysis moves from the farm to the regional sector, the definitions of the objective function of the model and the aggregation problem change. In the regional-sector context, the objective function used at farm level (for example, gross margin) is economically unjustifiable, because, among other things, changes in the supply of outputs affect prices. As  demonstrated, the objective function of this type of model maximizes social welfare, measured by the sum of consumer and producer surpluses. This type of objective function is full of economic meaning, as it leads to a partial equilibrium. This partial-equilibrium approach was a starting point for BIB002 empirical research. Moreover, it can be extended to a case of general equilibrium BIB003 . The partial-equilibrium method is based upon welfare economics and is beset with difficulties. Thus, the quantity and price vectors are endogenous to the model, which destroys the linearity of the objective function, creating a quadratic-programming problem. The improvement in nonlinear computer packages has reduced the impact of these difficulties.  published a good survey of applications of this type of partial-equilibrium models that lead to quadratic-programming formulations. The second issue is the aggregation problem. In fact, as all farms considered in a region or sector model are not alike, it is inappropriate to treat the region or sector as a single farm. Hence, we must use the appropriate aggregation rules to minimize the aggregation bias. BIB001 was the first to state conditions for exact aggregation that were rigorous but too strong.  and BIB004 proposed weaker conditions for aggregation. Modeling the Interaction Between Agriculture and the Environment Until recently, agricultural managers focused on increasing yields through the intensive use of agrochemicals, fertilizers, and other inputs. This practice had many unwanted environmental side effects, some of which made the continuation of many agricultural practices doubtful. Fortunately, researchers are developing models to evaluate the economic Downloaded from informs.org by [200.89.69 .180] on 20 July 2015, at 12:33 . For personal use only, all rights reserved. Interfaces 36(5), pp. 446-457, © 2006 INFORMS impacts of environmental effects to achieve sustainable agriculture. They usually use a crop-simulator model to predict the environmental effects of various management practices and then link to an optimization model to determine trade-offs between economic returns and environmental impacts. The final output is usually a sustainable compromise between economic achievements and environmental quality. Various researchers have conducted studies in this direction.  linked CERES, a cropsimulator model, to a dynamic optimization model to determine the optimum applications of water and fertilizers needed to maximize gross margin. BIB005 combined NTRM, a crop-simulator model, and a mathematical mixed multiobjective programming model to assess the effects of an increase in nitrogen prices and a reduction in drainage irrigated water, thus inducing the adoption of best management practices. Finally, BIB006 used the EPIC-PST simulation model to predict the environmental risks of using pesticides and nitrates. They combined the results with a Target MOTAD optimization model that minimizes the sum of negative deviations from a prefixed income target (Tauer 1983) . In this way, they evaluated the trade-offs between income and an index measuring the risks associated with using pesticides and nitrates. Including environmental constraints in agricultural programming models dates back to the early 1970s, but environmental concerns are increasingly important. Thus, the multiobjective modeling of joint production processes that combine private goods sold on the market place and public goods without established markets, such as environmental protection, is an important line of research BIB007 ).