Parametric Optimization of Linear and Non-Linear Models via Parallel Computing to Enhance Web-Spatial DSS Interactivity

A web based Spatial Decision Support System (web SDSS) has been implemented in Thessaly, the most significant arable cropping region in Greece, to evaluate selected energy crop supply. The web SDSS uses an optimization module to support the decision process launching mathematical programming (MP) profit maximizing farm models. Energy to biomass raw material cost is provided in supply curve form incorporating physical land suitability for crops, farm structure, and Common Agricultural Policy (CAP) scenarios. To generate biomass supply curves, the optimization problem is parametrically solved for a number of steps within a price range determined by the user. The more advanced technique used to solve the MP model, the higher the delay of response to the user. In this paper, the authors examine how effectively the web SDSS response time can be reduced to the user requests using parallel solving of the corresponding optimization problem. The results are encouraging, as the total solution time drops significantly as the problem’s size increases, improving the users’ experience even when the underlying optimization models use advanced, time demanding modeling techniques. These statements are illustrated by comparing lp and non-lp agricultural sector models. DOI: 10.4018/jdsst.2012010102 IGI GLOBAL PROOF International Journal of Decision Support System Technology, 4(1), 14-30, January-March 2012 15 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. concern business decision support, whereas some deal with environmental issues involving also multi-criteria models often attempting to enhance public participation in local environmental decision making (Kingston et al., 2000). One of the most interesting classes of web-based decision support tools are the so-called Spatial DSS (SDSS). SDSS, as defined by Sugumaran and Sugumaran (2007), are “flexibly integrated systems built on a GIS platform to deal with spatial data and manipulations, along with an analysis module ... they support ‘what if’ analysis ... and help the user in understanding the results” (p. 850). With the development of the internet, Web-based SDSS have been developed, adding Internet interface programs to the computational models and geographic databases of the SDSS, in order to provide decision support through the Web based on relevant information. Bio-energy issues constitute by excellence spatially dependent problems requiring both detailed spatial information but also extensive model building. Unlike conventional energy carriers that have hierarchical structure, biomassto-energy production involves hundreds to often thousands of decentralised decision makers. This is considered one of the “grand challenges” for bio-energy assessment (McKone et al., 2011). As a matter of fact, bio-energy profitability is linked to the structure and perspectives of the arable cropping systems to supply considerable quantities of a bulky raw material to transformation plants also taking into account demand location and volume. Recent analyses of economic biomass potential are reported in regional (Hilst et al., 2010) or country level (Simon et al., 2010). Therefore, appropriate tools are necessary to enable comprehensive analysis and support decisions of policy makers, industry, researchers and farmers. For this purpose, a state-of-the-art modular SDSS that contains optimization models embedded in a GIS environment fed by technical, economic, and cartographic databases has been built to provide stakeholders with region specific biomass-to-energy supply information in Central Greece (Rozakis, 2010). A web-based interface built in open source software makes the SDSS tool available for collaborative decision-making allowing for an interactive process in real time. The tool operates on the Internet, where the user can have access to the dataset, enter selected parameters into the model, and enable spatial visualization and exploration of the results, injecting interactivity in the decision process. In order to adequately represent arable agriculture of the region under study, bottomup mathematical programming models have been used to estimate agricultural policy impacts and farmers’ supply response. Numerous gross margin maximizing Decision-Making Units (DMU), geographically dispersed decide whether or not to introduce energy crops in their crop mix using crop suitability maps and survey data at the farm level. Conventional linear programming (LP), traditionally used for this purpose, is gradually being dominated in the agricultural economics literature by alternative methods implemented also in the Greek context as multi-criteria (Manos et al., 2009) or interval linear programming (Rozakis, 2011) models and also positive models incorporating downward sloping demand (Rozakis et al., 2008) or increasing cost functions (Petsakos & Rozakis, 2010) in the objective function. These methods, broadening economic rationality, manage to transform the objective function so that optimal solutions include not only crop plans on the vertices of the feasible polyhedron but also points on hyper-plans enabling the model to approach observed levels of activities, thus outperforming their LP counterparts. Nevertheless there is a price to pay that is the increased complexity and consequently solution time span of such models. That may not be a problem when models are operated for research purposes, but it certainly is a serious drawback in business or policy-making oriented environments and especially in a context of interactive decision making such as the one previously described. Regional farm based sector models articulated in an angular structure are parametrically solved to explicit supply response to bio-energy market signals, in other words optimization is consecutively launched for different entry data IGI GLOBAL PROOF 16 International Journal of Decision Support System Technology, 4(1), 14-30, January-March 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. (data related models). Approximately resolution times are multiplied by the number of iterations. This penalizes nonlinear models since they require longer solving times than the corresponding linear model. However the modular structure of bottom-up arable agriculture models consists of numerous independent problems that constitute an embarrassingly parallelizable problem as each iterative solution is independent to anyone else. This feature makes the parallel solving of such problems quite interesting since lapse time for resolution is drastically reduced. Furthermore, the extensive use of Personal Computers (PCs) within the scientific community and tremendous increase in their CPU’s frequency, and the advent of multi-core CPUs and network technologies (intranets and internet) has rendered distributed computing infrastructures readily accessible even to modest research institutes (Creel, 2005). Parallel computing is implemented in this paper aiming at improving efficiency of the optimization process in the bio-energy assessment web-SDSS. Three model types are used namely an LP model and two nonlinear specifications that represent different degrees of structural complexity. The next section introduces the concept of parallel computing in the case of web accessible Decision Support Systems. The methodology of the optimization component and the model specification for arable agriculture in Thessaly, Greece, is then presented. Model parallelization, the implementation issues and the speedup results for a case study of integrating a web-SDSS with a parallel LP meta-solver follow. The paper is completed by concluding remarks and issues of further research work. PARALLEL COMPUTING FOR DATA RELATED MODELDRIVEN WEB-DSS Web-Based DSS deliver decision support information or decision support tools using a “thin-client”, that is a Web browser. A modeldriven web-DSS such as the one supporting biomass assessment, according to the typology of Power (2004) “uses formal representations of decision models and provide analytical support using tools of decision analysis, optimization, stochastic modeling, simulation, statistics and logic modeling”. A model-driven web-DSS should contain at least two components: The user interface component, which would be some kind of web application and the decision analysis component that would include the necessary software that will perform the decision analysis. The former component is the front-end which the user interacts with the web-DSS by feeding input to the latter component and obtaining results from it. Tolerable waiting time (TWT) is defined as the amount of time users are willing to wait before giving up on the download of the web page. There are several papers that attempt to measure TWT with time spans ranging from 4 to 41 seconds (Nah, 2004). For a web-DSS the above time values should not be considered literally, since the user is more dedicated to the purpose of obtaining the results (that is downloading the web page) than a user browsing or querying various sites. However the above range gives us an order of magnitude of the time a web-DSS system should respond and that it should not exceed one minute. Also it is deducted that for the same web-DSS, as the waiting time decreases, the user experience is improved and enriched. Given the high possibility that the computation procedures might be a major source of delaying the system’s response, we are looking for ways to decrease this delay. Implementing parallel computing solutions to our decision analysis can decrease the total waiting time for the user, thus moving the overall performance of the system towards a tolerable waiting time. There are cases where solving the decision problem in parallel is embarrassingly easy, for example when the decision process incorporates solving a Monte Carlo simulation, performing sensitivity analysis, solving different scenarios or when we have to solve multiple independent linear problems (data related problems). The models that we are using on our web-SDSS IGI GLOBAL PROOF International Journal of Decision Support System Technology, 4(1), 14-30, January-March 2012 17 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. (regional sector models in a farm basis) fall to the latter category. Migrating from an existing (serial) decision analysis component of a web-DSS to a parallel solution is not a trivial task since several issues have to be resolved. For example we are primarily concerned about the immediate distributed resources availability. Utilizing a batch processing distributed system is very likely to bring on delays. There is also an issue about the cost-benefit ratio of migrating to a parallel solution. The costs of adapting the serial implementation of the decision analysis process to a parallel system can be significant and for example it could include the development and the deployment of the software solution, the maintenance costs of the cluster, etc. On the other hand the benefit of using a parallel system is the decrease in the user waiting time, and this is greater as the problem size is increasing. METHODOLOGY FOR ESTIMATING BIOMASSTO-ENERGY SUPPLY Traditional Programming Techniques for the Agricultural Sector In the agricultural economics literature as Kutcher and Norton (1982) narrate, analysts tackled with the farm decision problem that is maximizing profits under constraints, aiming either to deriving the best plan or more usually to assist policy decision by illuminating the varied consequences of multiple choices. This kind of analysis was carried out by means of mathematical programming. At first such models simulated producers responses searching the optimal plan assuming parameters such as output prices fixed, specified in linear programming form. The elementary sub-model, is specified as follows: an individual farmer ( ) f is supposed to choose a cropping plan (x f ) and input use among technically feasible activity plans A x b f f f ≤ so as to maximize gross margin, gm . The optimization problem for the farmer f appears as seen in Box 1. The sector model contains f farm problems such as the one specified above. The basic farm problem is linear with respect to x , the primal n×1 vector of the n cropping activities. The m n × matrix A f and the m×1 vector b f represent respectively the technical coefficients and the capacities of the m constraints on production. The vector of parameters θ characterizes the f-th representative farm and includes yields for crop i ( ), yi f variable costs ( ), ci f prices dependent on quality ( ) pi f and subsidies linked to crop quantity( ) lsi f . Symbol κ stands for the vector of general economic parameters which includes prices not dependent on farm ( ) pi and subsidies specific to crop cultivated area( ) psi . The constraints can be distinguished in resource, agronomic, demand and policy ones. The model enables a comparative static analysis, but does not allow for farm expansion, as it takes as given land resource endowments and land rent of the base year. Different sets of parameters are applied to denote the policy context in vigor. Unlike the standard LP formulation, where input and output prices are assumed fixed and exogenous, price endogenous models are used in situations where this assumption is flawed or untenable. Consequently, LP models can be modified to include a response of the market (i.e., of the aggregate of producers) under the assumptions regarding market form and producer decision rules leading in non-linear programming (NLP) specifications (Bauer & Kasnakoglou, 1990). For instance, it is usual that the quantity of fodder crops produced affects the equilibrium price primarily due to the high transportation costs which restricts its consumption locally or to adjacent regions. As a result, and given the limited alternative uses of fodder crops, the analyst assumes that the price received by producers is determined by the total amount produced in the region. Price endogenous module for fodder crops renders the model quadratic belonging to the class of NLP. IGI GLOBAL PROOF 18 International Journal of Decision Support System Technology, 4(1), 14-30, January-March 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Model Validation A validation process is always required in order to assess model’s ability to predict farmers’ response to different market signals or policy shifts. For this purpose, observations for base year are compared to model results by examining appropriate distance measures. Among them the average absolute deviation (AAD) index is readily used, defined as the average absolute difference between the observed data and the land allocations generated by the model at the