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     

A MODEL FOR ESTIMATING PREMIUMS TO REDUCE IRRIGATION ON FARMS

Abstract This paper aims to determine the minimum agri‐environmental premium per hectare that farmers should receive to reduce crop irrigation. To this end, the authors develop a mixed‐integer quadratic model using a new methodology based on traditional positive mathematical programming, which allows the inclusion in the model of crop variants that are not present in the baseline situation of the farms. What is shown is that the results obtained with this new methodology, using the cost average approach of calibration, are the same as those obtained with an empirical method, when there is no change of crop distribution after the changeover from irrigated to nonirrigated farms. The theoretical results are compared with those obtained using the calibration with exogenous elasticities and are illustrated numerically for a representative farm of an area around Spain's Tablas de Daimiel in which the use of groundwater for crop irrigation has led to the ongoing deterioration of wetlands that depend on the same source of water, endangering the region's environmental sustainability.     

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.     

Minimising the maximum relative regret for linear programmes with interval objective function coefficients

The minimax relative regret solution to a linear programme with interval objective function coefficients can be found using an algorithm that, at each iteration, solves a linear programme to generate a candidate solution and a mixed integer programme (MIP) to find the corresponding maximum regret. This paper first shows that there exists a regret-maximising solution in which all uncertain costs are at a bound, and then uses this to derive a MIP formulation that maximises the regret of a candidate solution. Computational experiments demonstrate that this approach is effective for problems with up to 50 uncertain objective function coefficients, significantly improving upon the existing enumerative method.     

A linear programming approach to water-resources optimization

A linear-programming model for use in analysis and planning of multiobjective water resources systems is described in this paper. A typical system consists of reservoirs, hydropower stations, irrigated land, artificial and navigation channels, etc., over a reach of a river or a river basin.The linear programming approach is studied and compared with other approaches: mixed integer-linear dynamic and nonlinear. The advantages and drawbacks of its use in a real case-study are also described.     

Analysis of lettuce evapotranspiration across soil water

In this study, we evaluated the lettuce accumulated evapotranspiration (ET) across four levels of irrigation, using a nonlinear mixed‐effects model. The plants were grown in protected environments and monitored over 23 consecutive days. When the moisture of the substrate in the vessels reached 50% of their maximum retention capacity, the water levels were elevated according to four treatments: , , , and . The model appeared to provide a good fit to the data and showed that the estimates of the maximum amount of accumulated ET were similar for the three treatments with soil water deficit and lower for . The results of the study supported the idea that optimization of the ET of lettuce plants could be achieved through irrigation with deficit, also indicating that the economical use of water was the most efficient way to boost agricultural production. Recommendations for resource managers

• The continued growth of the world population will result in a decrease of quality and availability of water and also an increase in demand for food. Therefore, sustainability will depend on high agricultural productivity with rational use of water.
• Considered the most efficient technology for boosting agricultural productivity, irrigation is also the largest water consumer in the world. With any kind of irrigation in the vegetable production area, the water intake for the plants must be treated with great caution.
• Both a lack or excess in water can decrease plant productivity. The amount of water available in the soil should be enough to maximize production. It is shown that high levels of irrigation are not necessary for this.
• It is important to balance the amount of irrigated water for an optimal level, in order that the production has its the production is maximized and valuable water resources are not wasted.

     

Models for petroleum field exploitation

This paper presents some models for an early evaluation of a petroleum field. Based on crude assumptions about a reservoir, our models suggest decisions concerning platform capacity, drilling programme and production. We start out with a simple production planning model using linear programming. By mixed integer programming techniques the model is gradually extended. The most sophisticated version of the model can propose platform capacity, where and when wells should be drilled, and the production from the wells. The models are tested on numerical examples, and the results are discussed. From the experiments we conclude that the problems are very hard to solve, and that the size of problems that can be solved is limited by the computational burden. Finally we give some ideas for future work that may provide better solution methods.     

Simulation and optimization for crop water allocation based on crop water production functions and climate factor under uncertainty

In this paper, the uncertainty methods of interval and functional interval are introduced in the research of the uncertainty of crop water production function itself and optimal allocation of water resources in the irrigation area. The crop water production functions in the whole growth period under uncertainty and the optimal allocation of water resources model in the irrigation area under uncertainty are established, and the meteorological factor is considered in the model. It can promote the practical application of the uncertain methods, reflect the complexity and uncertainty of the actual situation, and provide more reliable scientific basis for using water resources economically, fully improving irrigation efficiency, and keeping the sustainable development of the irrigated area. This approach has important value on theoretical and practical for the optimal irrigation schedule, and has very broad prospects for research and development to other related agriculture water management.     

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.     

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.     

Analysis of collaborative savings and cost allocation techniques for the cooperative carrier facility location problem

Transport companies may cooperate to increase their efficiency levels by, for example, the exchange of orders or vehicle capacity. In this paper a new approach to horizontal carrier collaboration is presented: the sharing of distribution centres (DCs) with partnering organisations. This problem can be classified as a cooperative facility location problem and formulated as an innovative mixed integer linear programme. To ensure cooperation sustainability, collaborative costs need to be allocated fairly to the different participants. To analyse the benefits of cooperative facility location and the effects of different cost allocation techniques, numerical experiments based on experimental design are carried out on a UK case study. Sharing DCs may lead to significant cost savings up to 21.6%. In contrast to the case of sharing orders or vehicles, there are diseconomies of scale in terms of the number of partners and more collaborative benefit can be expected when partners are unequal in size. Moreover, results indicate that horizontal collaboration at the level of DCs works well with a limited number of partners and can be based on intuitively appealing cost sharing techniques, which may reduce alliance complexity and enforce the strength of mutual partner relationships.     

Conservation laws for a class of soil water equations

In this paper, we consider a class of nonlinear partial differential equations which model soil water infiltration, redistribution and extraction in a bedded soil profile irrigated by a line source drip irrigation system. By using the nonlocal conservation theorem method and the partial Lagrangian approach, conservation laws are presented. It is observed that both approaches lead to the nontrivial and infinite conservation laws.     

Optimisation of sludge treatment and transport

In this paper we describe some work carried out in the UK into improving the effectiveness of a waste treatment and distribution network. Sludge is the name given to (treated) waste water and sewage. It is collected at small facilities and requires further treatment before it can be disposed of. We develop a linear programming model for the problem of effectively treating and distributing sludge. This model has been implemented in a large UK regional water company, Yorkshire Water.     

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.     

OPTIMIZING THE PERFORMANCE OF IRRIGATED AGRICULTURE IN EASTERN ENGLAND UNDER DIFFERENT WATER PRICING AND REGULATION STRATEGIES

Irrigation water shortage is becoming an increasingly serious problem in agricultural production. Growing pressure on water resources is leading to increasing restrictions on abstraction for irrigation and consideration of the use of economic instruments, such as increased abstraction charges and/or tradable licences, to restrict demand and encourage wiser use of water. We evaluate irrigation using selected economic, social, and environmental indicators of performance, including the value of water used for irrigation. A linear programming model is developed and used to simulate possible responses by irrigators and the impact on irrigation performance of intervention measures, namely abstraction quota restrictions and volumetric pricing that might be used to ration water and/or increase water use efficiency. Through the use of parametric programming a scenario analysis is performed to a case study in eastern England with regard to perturbations of irrigation water under alternative policy instruments.     

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.     

Design of a wind farm collection network when several cable types are available

In this article we consider a real-world problem submitted to us by the Hatch company. This problem consists of designing a collection network for a wind farm, assuming that the locations of the turbines and the potential cables are known, several cable types are available, and the cost of the energy that dissipates through the cables is known. We propose a mixed integer quadratic programme to model the network design problem and then linearize the quadratic programme because the latter is too difficult to solve using a standard mathematical programming software. We describe several classes of inequalities that strengthen the resulting mixed integer linear programme. Finally we use real-world data supplied by Hatch to carry out computational experiments with several versions of our model.     

Extending the mixed algebraic-analysis Fourier–Motzkin elimination method for classifying linear semi-infinite programmes

Motivated by a recent Basu–Martin–Ryan paper, we obtain a reduced primal-dual pair of a linear semi-infinite programming problem by applying an amended Fourier–Motzkin elimination method to the linear semi-infinite inequality system. The reduced primal-dual pair is equivalent to the original one in terms of consistency, optimal values and asymptotic consistency. Working with this reduced pair and reformulating a linear semi-infinite programme as a linear programme over a convex cone, we reproduce all the theorems that lead to the full eleven possible duality state classification theory. Establishing classification results with the Fourier–Motzkin method means that the two classification theorems for linear semi-infinite programming, 1969 and 1974, have been proved by new and exciting methods. We also show in this paper that the approach to study linear semi-infinite programming using Fourier–Motzkin elimination is not purely algebraic, it is mixed algebraic-analysis.     

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 three‐phase procedure for designing an irrigation system's water distribution network

This paper focuses on the design of an irrigation network included in a public project to build a distributing water system for agricultural purposes. We begin by outlining the issue. We then present a procedure composed of three sequential modules to tackle this complex problem. The first module provides the design of the network links by heuristically constructing a short length Steiner forest. In the second module, the flows for every arc of this network are calculated. The last one determines the size of the pipes and pumps by solving a mixed binary linear programming problem. A real experiment is reported. Although further improvements are required, the results confirm the adaptability of the overall procedure to assist agricultural engineers in preparing their projects.