# Resource(s) use efficiencies and optimization techniques

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1 Resource(s) use efficiencies and optimization techniques L E C T U R E 8 S S R A N A S R S C I E N T I S T

2 Resources 2 land, water, nutrients, energy labour and capital

3 Efficiency Efficiency in any system is an expression of obtainable output with the addition of unit amount of input. The ratio of energy intake and energy of the produced biomass i.e. of input and output is called ecological efficiency. This can be studied at any trophic level. Resource use efficiency (fertilizer, water etc) is the output of any crop or any thing else per unit of the resource applied under a specified set of soil and climatic conditions. 3

4 Examples 4

5 Land use efficiency 5 Cultivated Land Utilization Index ( CLUI): Cultivated land utilization Index (Chuang, 1973) is calculated by summing the products of land area to each crop, multiplied by the actual duration of that crop divided by the total cultivated land times 365 days. Where, n total number of crops; a i area occupied by the ith crop, d i, days that the ith crop occupied and A = total cultivated land area available for 365 days. CLUI can be expressed as a fraction or percentage. This gives an idea about how the land area has been put into use. If the index is 1 (100%), it shows that the land has been left fallow and more than 1, tells the specification of intercropping and relay cropping. limitation of CLUI is its inability to consider the land temporarily available to the farmer for cultivation.

6 Fertilizer use efficiency (FUE) FUE is the output of any crop per unit of the nutrient applied under a specified set of soil and climatic conditions. The NUE/FUE can be expressed in several ways. Mosieretal. (2004) described 4 agronomic indices to describe NUE: partial factor productivity (PFP, kg crop yield per kg input applied); 6 agronomic efficiency (AE, kg crop yield increase per kg nutrient applied); apparent recovery efficiency (RE, kg nutrient taken up per kg nutrient applied); and physiological efficiency (PE, kg yield increase per kg nutrient taken up). Crop removal efficiency (removal of nutrient in harvested crop as % of nutrient applied) is also commonly used to explain nutrient efficiency.

7 Energy efficiency 7

8 Water use efficiency Crop water use efficiency Crop water use efficiency is a ratio between marketable crop yield and water used by the crop in evapotranspiration. WUE (kg/ha-mm) = Y/ETc Where, WUE = Water use efficiency in kg/ha-mm Y = Marketable crop yield in kg/ha ETc = Crop evapotranspiration in mm 8

9 Field water use efficiency Field water use efficiency is a ratio between marketable crop yield and field water supply which includes water used by the plant in metabolic activities, ET and deep percolation losses. WUE (kg/ha-mm) = Y/WR 9 Where, FWUE = Field water use efficiency in kg/ha-mm Y = Crop yield in kg/ha WR = Water used in metabolic activities, ET and deep percolation losses in mm

10 CROP Water Use Efficiency of Crops Water requirement (mm) 10 Grain yield (kg/ha) WUE (kg/hamm) Rice Sorghum Pearl millet Maize Groundnut Wheat Finger millet

11 Weed control efficiency 11 [Weed count or dry weight in weedy - weed count or dry weight in a treatment]/weed count or dry weight in weedy

12 Resource use efficiency 12 Resource use efficiency in agriculture is defined to include the concepts of technical efficiency, allocative efficiency and environmental efficiency (Haque 2006).

13 13 Public investment, subsidies and credit for agriculture are used in an efficient manner. There are large scale inter regional as well as inter farm variations in factor productivity due to varying influence of different factors in different regions. A number of management factors such as timeliness and method of sowing, transplanting, irrigation and application of right doses of inputs and input mix play an important role in influencing inter-farm variation in crop productivity.

14 14 Growing marginalization and fragmentation of land holdings coupled with rising incidence of informal tenancies and poor rural infrastructure such as road, electricity, markets and education affect factor productivity. The availability of good quality irrigation water coupled with flexibility of irrigation and drainage system and appropriate methods of application as well as pricing of irrigation water is crucial for sustainable use of land and water resources.

15 15 Technical efficiency is the ability of a firm to produce a given level of output with minimum quantity of inputs under a given technology. Allocative efficiency is a measure of the degree of success in achieving the best combination of different inputs in producing a specific level of output considering the relative prices of these inputs. Economic efficiency is a product of technical and allocative efficiency.

16 16 In one sense, the efficiency of a firm is its success in producing as large an amount of output as possible from given sets of inputs. Maximum efficiency of a firm is attained when it becomes impossible to reshuffle a given resource combination without decreasing the total output.

17 LINEAR PROGRAMMING 17 The word linear is used to describe the relationship among two or more variables which are directly proportional. For example, doubling (or tripling) the production of a product will exactly double (or triple) the profit and the required resources, then it is linear relationship. Programming implies planning of activities in a manner that achieves some optimal result with restricted resources.

18 18 Linear programming was developed by George B Dantzing (1947) during second world war. It has been widely used to find the optimum resource allocation and enterprise combination. Linear programming is defined as the optimization (Minimization or maximization) of a linear function subject to specific linear inequalities or equalities.

19 Maximize z Such that <bi i= 1 to m xj=0 cj=netincomefromjthactivityxj=levelofjth activity aij=amountofith resourcerequired forjthactivity bi = Amount of ith resource available. 19

20 Assumptions of Linear Programming 20 Linearity: It describes the relationship among two or more variables which are directly proportional. Additivity: Total input required is the sum of the resources used by each activity. Total product is sum of the production from each activity. Divisibility: Resources can be used in fractional amounts. Similarly, the output can be produced in fractions.

21 21 Finiteness of activities and resource restrictions: There is limit to the number of activities and resource constraints. Non negativity: Resources and activities cannot take negative values. That means the level of activities or resources cannot be less than zero. Single value expectations: Resource supplies, input- output coefficients and prices are known with certainty.

22 Advantages of L.P Allocation problems are solved. Provides possible and practical solutions.. Improves the quality of decisions. Highlights the constraints in the production. Helps in optimum use of resources. Provides information on marginal value products (shadow prices). 22

23 Linearity Limitations 23 Considers only one objective for optimization. Does not consider the effect of time and uncertainty No guarantee of integer solutions Single valued expectations.

24 24

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