A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

A mathematical programming model applied to the study of water markets within the Spanish agricultural sector

Spanish irrigated agriculture uses about 80% of all the nation's available water resources. The need to increase the economic efficiency of current uses of water in the agricultural sector is perceived as the top priority of the country's national water policy. In Spain surface water is centrally allocated among competing users based on allocation criteria dictated by the Water Law. The complete absence of price or market signals is a major obstacle to induce irrigators to use water more efficiently. Water markets within the agricultural sector is a promising, though scarcely analyzed in Spain, solution to increase its economic efficiency. This research is an attempt to evaluate probable water transfers among farmers and irrigation districts as well as water price equilibria resulting from different water market arrangements. Three interconnected mathematical programming models permit the simulation of water use at the farm level and water market arrangements in the Guadalquivir Valley (Spain). Results show that water markets would be highly dependent on the level of transaction costs and on the relative reductions of water allotments due to nonoverlapping drought cycles among water districts.     

Applying stochastic goal programming: A case study on water use planning

A decision support model to help public water agencies allocate surface water among farmers and authorize the use of groundwater for irrigation (especially in Mediterranean dry regions) is developed. This is a stochastic goal programming approach with two goals, the first concerning farm management while the other concerns environmental impact. Targets for both goals are established by the agency. This model yields three reduction factors to decide the different reductions in available surface water, standard groundwater and complementary groundwater that the agency should grant/authorize for irrigation, this depending on if it is a dry or wet year. In drought periods, the model recommends using more groundwater (in percentage) than in wet periods. A case study using year-to-year statistical information on available water over the period 1941–2005 is developed through numerical tables. A step-by-step computational process is presented in detail.     

A decision tool for optimal irrigated crop planning and water resources sustainability

In the present study, the conjunctive use policies of surface and ground water resources are developed for minimizing water shortage in an irrigation district subject to constraints on groundwater withdrawals and crop planning capacities. An integrated soil water balance algorithm is coupled to a non-linear optimization model in order to carry out water allocation planning in complex deficit agricultural water resources systems based on an economic efficiency criterion. Various options of conjunctive use water resources along with current and proposed cropping patterns have been explored by Koohdasht Irrigation District (KID), a semi-arid region in I.R. Iran. The analysis provides various scenarios, which can help managers in decision-making for the optimum allocation plans of water resources within the irrigation area. The results reveal that the proposed model, as a decision tool for optimal irrigated crop planning and water resources sustainability, may be used for maximizing the overall net benefits and global water productivity of an irrigation district considering an allowable annual recharge of groundwater. Findings indicate the importance of the conjunctive water management modeling, which can be easily implemented and would enhance the overall benefits from cropping activities in the study area.     

TREATMENT VERSUS PREVENTION OF NITROGEN FERTILIZER POLLUTION: AN INTER‐SECTORAL EXTERNALITY POLICY MODEL

Abstract This article presents an economic, hydrological, dynamic optimization model, which describes the negative external effects of nitrogen fertilizers on groundwater quality. The relative merits of treatment versus prevention of nitrogen pollution were analyzed. A dynamical water and nitrogen flow between land surface, the unsaturated zone, and groundwater was employed. A specific treatment technology, which gives rise to a discontinuous cost function, was also used. Applying the model to the coastal aquifer in Israel, our results showed that in a joint (agricultural and domestic) water source area that supplies a relatively small quantity of drinking water, it is more efficient to combine a policy that imposes restrictions on the use of nitrogen with a drinking‐water treatment process. However, when a relatively large quantity of drinking water is involved, imposing restrictions on the use of nitrogen only is more efficient. The paper, thus, is useful to planners of fast growing urban population centers with regard to regulation and can be used to calculate and evaluate specific policies.     

Optimal cropping patterns under water deficits

A mathematical programming model is proposed for optimal cropping patterns under water deficits in dry regions. Crops may be deliberately under-irrigated in order to increase the total irrigated area and possibly the profit. An operating policy will identify both the total area and the irrigation level allocated to a given selected crop taking into account the possible successors and predecessors of this crop. Both annual and seasonal crops are examined in the same study. The model starts by identifying the optimal operating policy for each grower in the region having a given stock of irrigation water. Then, in order to allocate water efficiently among growers, the model determines the global optimal cropping plan of the entire region. To solve efficiently the problem, a decomposition algorithm is developed. Also some useful economic interpretations are given.     

Modeling voluntary participation in a cost‐sharing agricultural water quality management program

This economic analysis of farmers' voluntary adoption of water quality management alternatives integrates three biophysical simulators to predict crop yields and soil erosion/water quality impacts under uncertain weather and market conditions. Farmers' willingness to costshare was used to estimate expectations of net returns and associated water and soil pollution based upon government costshare scenarios. Simulations integrated into mathematical programming results indicate that irrigation and nitrogen fertilizer applications do not alter water quality in the Gum Creek Watershed as much as generally anticipated. Under limited government payments, pollution abatement through reduction of irrigation and/or nitrogen fertilizer applications significantly reduces farmers' net revenues and hence, without threats of other regulatory means, more farmers opt out of a voluntary program. Abatement of nitrogen runoff and leaching should consider other management alternatives and include nonagricultural sources of pollution.     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

The economics of water resources for the generation of electricity and other uses

An optimal control approach is used to analyze the tradeoff between the use of water resources for electricity generation versus other economic uses (irrigation, industry, etc.). For that purpose, a dynamic model is presented which establishes relationships between economic growth, water resources management, and energy policy in the context of the aforementioned tradeoff, in an economy whose energy matrix is heavily dependent upon hydroelectric power. Among other results, the analysis establishes that in the market, the price of water for non-energy uses should be twice the price of the energy goods, indicating the necessity of substituting other sources of energy for hydroelectric power.     

春小麦水分敏感指数与有限水量生育期的最优分配

通过不同的受旱处理，确定了Jensen模型中的春小麦水分敏感指数。介绍了运用生态规划模型实现有限水量生育期最优分配的方法与步骤，并以辽西地区春小麦为例，确定了不同初始含水量和生育期可利用灌溉水量下的最优分配决策。     

IMPACTS OF WATER SUPPLY UNCERTAINTY AND STORAGE ON EFFICIENT IRRIGATION TECHNOLOGY ADOPTION

In the framework of a stochastic dynamic programming model, the paper investigates the impact of water supply uncertainty and storage at farm level on adoption of efficient irrigation technologies under a flexible water price regime. We find that even a flexible water pricing cannot guarantee higher adoption of efficient irrigation technology in all cases. Results of the paper indicate that if a farmer invests in water storage capacity, then the value of efficient usage of water increases, and the rate of adoption of efficient irrigation technology will be higher. It establishes a complementarity relationship between investments in storage capacity and adoption of efficient irrigation technology. The relationship becomes stronger with increasing variance in water supply. In a situation without any option to store water at the farm level, we find a negative relationship between investment in efficient irrigation technology and water variability. However, numerical analysis results suggest that a risk averse farmer may invest more in efficient irrigation only if the variance in water supply is very high.     

CONTROLLING GROUNDWATER QUALITY WITH ENDOGENOUS REGULATORY INSTRUMENTS

ABSTRACT. This research presents a competitive dynamic model that endogenously evaluates the economics of regulatory tax-policy options. This model is then applied to an irrigated corn production area west of Kearney, Nebraska, where the average groundwater contamination level from nitrates is reported to be 8.7 parts per million (ppm). Results indicate that no regulatory policies are necessary for maintaining potable groundwater quality with either a surge-flow irrigation system or a sprinkler irrigation system. In areas where conventional furrow irrigation technology is being used, higher net economic benefits result from the adoption of a variable-tax on nitrogen fertilizer use, followed by a constant-unit tax and a pollution tax.     

A multi-objective modeling approach for energetic material evaluation decisions

To develop ordnance for military applications requires a decision process of selecting materials. Once selected a performance evaluation of the material composite formulations energetic properties is required. Tailoring the composite materials for a particular ordnance application requires selecting reactants that seek an optimized combination of economic costs and performance properties (e.g., energy release, temperature, and gas generation). A successful energetic material evaluation must identify reactants offering a good fit with performance requirements and an overall materials selection strategy. To aid energetic material users in making complex reactant selection decisions we introduce a modeling approach that combines the concepts of thermodynamics, economic costs, and goal programming. This study is unique in its application of goal programming in exploring this type of decision situation. A case study is used to illustrate the modeling approach. The results demonstrate the efficacy of the approach for evaluating formulations where performance properties are important.     

A multiple objective programming approach for determining faculty salary equity adjustments

A multiple objective programming approach is proposed as a new analytical tool to fit a model which is used to project faculty salaries. The projected salaries are used as a basis to allocate the available budget for faculty salary equity adjustments. The model is also used to classify all faculty members into two categories with one category consisting of those faculty members being underpaid and the other consisting of those being overpaid. The multiple objective programming approach is much more powerful than regression analysis for this purpose because budgetary and policy restrictions can be included in the model as constraints. It is also more flexible than the goal programming approach because it has desirable solution properties. Salary data from a public university are used as an example to demonstrate the use of the approach. In addition, determinants of faculty salaries and variables to be included in the model are briefly discussed.     

Multi-choice goal programming with utility functions

Goal programming (GP) has been, and still is, the most widely used technique for solving multiple-criteria decision problems and multiple-objective decision problems by finding a set of satisfying solutions. However, the major limitation of goal programming is that can only use aspiration levels with scalar value for solving multiple objective problems. In order to solve this problem multi-choice goal programming (MCGP) was proposed by Chang (2007a). Following the idea of MCGP this study proposes a new concept of level achieving in the utility functions to replace the aspiration level with scalar value in classical GP and MCGP for multiple objective problems. According to this idea, it is possible to use the skill of MCGP with utility functions to solve multi-objective problems. The major contribution of using the utility functions of MCGP is that they can be used as measuring instruments to help decision makers make the best/appropriate policy corresponding to their goals with the highest level of utility achieved. In addition, the above properties can improve the practical utility of MCGP in solving more real-world decision/management problems.     

Modeling Optimal Allocation of Deficit Irrigation: Application to Crop Production in Saudi Arabia

We develop an integrated dynamic programming—linear programming (LP) model to solve for optimal land exploitation for a given crop. The model applies deficit irrigation in order to increase the irrigated area at the expense of reducing the crop yield per unit area. The dynamic program guarantees that deficit irrigation is considered only when it is economically efficient. Moreover, it provides the best irrigation level for each growth stage of the crop, accounting for the varying impact of water stress overtime. The LP provides the best tradeoff between expanding the irrigated area and decreasing water share per hectare. The model objective is to maximize the total expected crop yield. The model is particularly applicable for regions suffering from irrigation water scarcity, such as Saudi Arabia. The implementation was made for crops in Al-Jouf Region, north of Saudi Arabia     

Value-based DEA models: application-driven developments

Data envelopment analysis (DEA) is an approach based on linear programming to assess the relative efficiency of peer decision-making units (DMUs). Typically, each DMU is free to choose the weights of the factors used in its evaluation. However, the evaluator's preferences may not warrant so much freedom. Several approaches have been proposed to allow the incorporation of managerial preferences in DEA, but few address the additive DEA model specifically. This paper presents additive DEA models that use multi-criteria decision analysis concepts to incorporate managerial preferences, and presents the corresponding preference elicitation protocols. The models developed allow the incorporation of preferences at different levels: on valuing performance improvements, on introducing weight restrictions, and on finding adequate targets. These were application-driven developments, resulting from discussing modelling options and preliminary results with the top-level management of a retail chain in the context of an assessment of stores’ performance, also described in this paper.     

Accommodating diverse institutional investment objectives and constraints using non-linear goal programming

Institutional portfolio managers face a diverse mix of conflicting investment objectives and constraints such as risk and retum goals, institutional liability considerations, fund management legal restrictions, institutional cash flow requirments, and protfolio management performance targets. This paper argues that lexicographic goal programming can be used to keep track of an institution's complex investment goals and will provide a best possible solution for the institution's portfolio selection problem. Three examples illustrate the applicability of non-linear goal programming to institutions' differing investment requirements.     

DEVELOPMENT OF AN OPTIMAL WATER ALLOCATION DECISION TOOL FOR THE MAJOR CROPS DURING THE WATER DEFICIT PERIOD IN THE SOUTHEAST UNITED STATES

ABSTRACT. We developed a dynamic economic model to optimize irrigation water allocations during water deficit periods for three major crops grown in the humid southeastern United States. Analysis involved the use of crop simulation models to capture (a) the yield water relationship and (b) soil moisture dynamics from one week to another week. A hy‐drological model was used to find the water supply; combinations of hydrological and simulation models were used to find the optimal water allocation during each week in corn, cotton and peanuts. Results indicated that farmers should irrigate the most valuable crop first (peanuts) before applying water to other crops (corn and cotton). Results also showed that, because of restriction on total water supply, an increase in crop acreage did not increase the net revenue of the farm in a proportionate amount. Results should provide guidelines to water managers, engineers, policy makers, and farmers regarding an optimal amount of water allocation that will maximize net returns when water shortage is a serious concern.     

THE ECONOMICS OF DEFICIT IRRIGATION

Abstract Natural resource economists have paid great attention to irrigation water allocations among competing users. However, the intrauser allocation problem is greatly understudied. As irrigation becomes increasingly capital‐intensive, inefficient within‐field allocation and ill‐designed water‐conservation policy can bring considerable value loss to the water resource. We offer a comprehensive treatment of the economic problem of the intrauser allocation of a limited amount of irrigation water. A framework is provided for determining optimal irrigation intensity and extensity in both static and dynamic settings. An empirical application in West Texas cotton production demonstrates model implementation and offers new insights into the water‐saving potential of government‐sponsored cost‐share programs for promoting high‐efficiency irrigation adoption.