INTRODUCTION:

In small-scale agriculture, the farming system integrates both production and consumption activity. In both small and large production resources are allocated to attain various goals. Low-resource farmers, like other decision makers, are goal oriented in the sense that they manage the resources at their disposal in an attempt to achieve a set of desired goals [5]. It is general assumption of the economists that the limited resources are allocated in such a way that profit can be maximized. In smallholder agriculture, farmers can desire to maximize profit, but at the same time maintain or conserve the land for future generations, maximum utilization of family labour can also be important. Better predictions can be made regarding producer’s actions when multiple goals are considered [1].

Therefore multiple goals of smallholders need to be taken into consider in research. Some of goals of smallholder may be complementary while others may be competitive. “Utility” can be achieved through attainment of the goals.

Utility is defined as the satisfaction one receives from consuming a good or a service or engaging in some activity. Many different goals besides maximizing profit or minimizing the cost of production can add to the utility a smallholder receives from an activity. Therefore the concept of Utility maximization rather than profit maximization is crucial for smallholders in agriculture. By having multiple goals, smallholder is assumed to satisfy as many goals as possible. The producers first try to the most important goal or goals, and then less important goals are pursued.

The objective of the study is to determine optimal crop combination under limited land resources to meet the goals of the smallholder of the study area. Three goals which had been taken for analyzing the optimal crop combination are: i) Minimum food production (To have Minimum food from farming throughout the year), Income for satisfying daily minimum requirement (To have enough monetary income for satisfying daily minimum needs), Minimisation of hired labour( To minimize the use of hired labour through maximum utilization of family labour).

On the basis of these objectives the optimality of the system had been assessed. The production system are said to be optimal only if it is capable of achieving aforementioned goals.

The application of Goal programming in the solution of problems in agriculture planning was studied by different researchers.Charnes et al. [3] discussed executive compensation method which contained the roots of GP.Charnes and Cooper[4] devised a procedure to incorporate multiple objectives within the Linear Programming framework. Their approach involves use of positive and negative deviational variables that add to or subtract from constraints to remove the infeasibilities. The optimal solution is the one which minimizes the sum of the deviations.Ijeri [8] introduced the concept of pre-emptive priorities in which Lexicographic ordering of goals was incorporated in Goal Programming model. Goals are grouped into various priority levels and program results are based on the condition that lower priority goals cannot degrade the solution of higher priority levels.Lee[9] modified the simplex method necessary to solve ‘priority’ linear programming models.Bazaraa et al[2] formulated a multi-regional single time period linear goal programming model for agricultural planning in a developing economy. In addition to specifying different levels of input and output for each activity, explicit crop interdependencies which account for rotational requirements has also been described.Gass [6] explains how a worthwhile link can be established between the Analytical Hierarchy Process (AHP) and GP. In fact, the weights derived from the pairwise comparison of AHP can be incorporated directly into a WGP model.Tamiz et al [13] presented a review of the current literature on the branch of multi-criteria decision modeling known as Goal Programming (GP).In depth investigations of the two main GP methods, lexicographic and weighted GP together with their distinct application areas is reported. Romero and Rehman [11] modeled a real decision-making problem in agriculture involving several objectives and goals through the use of goal programming formulation and its variants.

2.Description of the study area:

Situated in Northern part of India, the state of Bihar has a geographical area of about 94.2 thousand square km. It is naturally divided by river Ganges into two parts, the north Bihar and the south Bihar. With an area of 53.3 thousand km North Bihar has been divided into two main agro- climatic zones Zone-I( North West Alluvial Plain), Zone- II( North East Alluvial Plain). The climate of Bihar is mostly sub-tropical as it is located between 25 to 27 degree North latitude. The soil of the northern plain consists mostly of sandy loam to heavy clay. However the majority type belongs to loam category which is good for crop cultivation. The natural precipitation varies from 990 to 1700 mm.

There are mainly two crop seasons in the state- Kharif and Rabi. Rice, wheat and pulses are grown in all the districts however the choice of the crop and crop rotation varies across the agro climatic zone. Food-crop production remains a major component of all production activities in the agricultural sub-sector of Bihar. Food-crop production comes under different agricultural systems, most commonly as mixed farming, mixed cropping or mono croppingFarms are variously referred to as smallholder farms, small-scale farms, low-resource farms or small farms. About 94 per cent of the crops grown by all size holdings belong to the food grains category. Rice and wheat, which together account for about 83 per cent of the cropped area, dominate the cropping pattern.

In Bihar, smallholder farmers generally practice subsistence farming where they need to produce a continuous, reliable and balanced supply of foods, as well as cash for basic needs and recurrent farm expenditure. These farms are characterized by low level of operation, illiteracy of operators, and a labour intensive production technology. There is also complete reliance on household resources. It is also believed that a sizeable proportion of farm output is retained for family consumption and planting purposes. In the absence of adequate technological inputs to increase agricultural productivity through technical innovations, the smallholders resort to some other strategies to improve their chances of at least providing enough food for themselves. In addition to an intensive and more frequent cultivation of the farmlands which are subdivided into very small plots the farmers adopt a multi cropping system to maximize returns from every unit of land. Also, crop choice is concentrated on those ones, which involve less expense in materials and labour input but promise higher productivity.

3.Methodology:

Sampling technique has been employed for analysis of the study.The population of the study consists of all smallholder farmers of north Bihar. In this study smallholder is defined as the farmer who have land less than two hectare. The basic sampling unit for the study is the Household. The list of food crops farmers compiled by the agricultural officer of the selected villages formed the sampling frame for the study. Keeping the fact in view that a large segment of the population is illiterate Interview method is adopted for collecting the data. Frequent interviews were conducted during 2010 production season for over 6 months period which started in November 2010 and lasted till March 2011 after all the crops were harvested for collecting the data. The socio- economic characteristics of the farmers and production activities in terms of input, output, and their prices constitutes the bulk of the data collected.

The sampling technique employed is the Multistage Cluster sampling technique. The whole North Bihar is divided into different clusters on the basis of district. Among these clusters one cluster has been selected at random. The selected cluster is further divided into different blocks. From these blocks thirteen blocks are randomly selected. Lastly from each block 20 farmers are selected randomly, giving a sample size of 260 farmers.

4.4 Variables of the model:

The variables used in the WGP and LGP models are:

X1=Rice in kharif, X2=Wheat in rabi, X3 =Til in kharif, X4=Maize in rabi, X5=Pulses in rabi , X6=Potatos in rabi

X7=Tilhan in rabi, X8=urd in kharif

4.5Crop Combinations to be entered in the model:

On the basis of crops most frequently grown by the smallholders of the study area, 23 crop combinations have been entered in the model. These crop combinations are: Wheat/Maize, Wheat/Pulses, Wheat/Potato, Wheat/Tilhan, Wheat/Maize/Pulse, Wheat/Maize/Tilhan, Wheat/Pulses/Tilhan, Wheat/Maize/Potato, Wheat/Pulses/Potato, Wheat/Maize/Pulses/Potato,Wheat/Maize/Pulses/Tilhan, Wheat/Maize/Potato/Tilhan,Maize/Pulses/Potato,Maize/Pulses/Tilhan, Maize/Potato/Tilhan, Maize/Tilhan, Maize/Pulses, Maize/Potato,Pulses/Potato,Potato/Tilhan,Pulses/Tilhan,Rice/Maize,Rice/Urd,Rice/Til.

5. CONCLUSION:

Out of twenty five crop combinations only four crop combinations could be developed for kharif season. Crop combinations of kharif seasons entered in both LGP and WGP models are Rice/Maize, Rice/Til, Rice/Urd, and Rice/Til/Urd. All the crop combinations of this season invariably include rice as one of the crops. It is quite obvious as rice is a major part of the staple diet of the smallholder. Results of the both model do not find any crop combination of the kharif season as an optimum one.

Twenty one crop combinations have been developed for rabi season. Among them seven crop combinations are found to be optimum. Optimal crop combinations of rabi season achieving all the three goals of the smallholder for WGP model are Wheat/Potato, Wheat/maize/Potato, Wheat/Pulses/Potato,Wheat/Maize/Pulses/Potato, Wheat/Maize/Pulses/Tilhan,maize/Pulses/Potato, Maize/Potato/Tilhan.

Ms- excel solution of wheat/ Potato crop combination of rabi season suggest to grow wheat at 0.77ha and potato at 0.58 ha.Values of all deviational variables of objective function are zero which means all three goals have fully been achieved. Moreover, there is an over achievement in minimum food requirement and minimum income requirement goal by 18.38 qt and Rs. 4131.34 respectively. The solution of wheat/Maize/ Potato crop combination of rabi season suggests to grow only wheat and potato at 0.76 and 0.58 ha of land. There is an over achievement of minimum food requirement and minimum income requirement goal by 18.38 qt and Rs. 4131.97 respectively. The solution of wheat/Pulses/ Potato crop combination of rabi season says to grow wheat, pulses and potato at 0.11, 0.73 and 0.51 ha of land respectively.There is an over achievement of minimum income requirement goal by Rs.98.08 qt and 81.51 manday of family labour is saved. The solution of wheat/Maize/Pulses/ Potato crop combination of rabi season suggests to grow wheat, maize, pulses and potato at 0.25, 0.29, 0.30and 0.50 ha of land respectively. There is an over achievement of food goal as well as income goal by 3.9 qt and Rs.7.04 .Eight man days of family labour is also saved.MS-Excel solution of the WGP model with Wheat/Maize/Potato/Tilhan crop combination of rabi season suggests to cultivate wheat, Potato and Tilhan at 0.70, 0.38 and 0.26 ha of land respectively. An over production of wheat is observed by 16.57qt.Approximately 13 mandays of family labour is saved and over- achievement of income is observed by Rs.13.07.MS-Excel solution of the WGP model with Maize/Pulses/Potato crop combination of rabi season shows that present combination is an optimal one.It suggests to cultivate Pulses and Potato at 0.74 and 0.61 ha of land respectively. This will achieve both minimum income requirement as well as minimum use of hired labour goal. An over-achievement of income is observed by Rs.99.06 and 91.31 unit of family labour has been saved. MS-Excel solution of the WGP model with Maize/Potato/Tilhan crop combination of rabi season suggests to grow potato and Tilhan at 0.24 and 1.11 ha of land. This is an optimal crop combination as both the goals have been fully achieved. Income is over-achieved by Rs. 106.82 and 94.85 manday of family labour has been saved.MS-Excel solution of the WGP model with Maize/Potato crop combination of rabi season observs an optimum solution since all the deviational variables of objective function have value zero. The solution suggests to grow both Maize and Potato at 0.40 and 0.95 ha of land repectively. Minimum use of hired labour goal is over- achieved by Rs.12350.49. Full utilization of family labour is also observed.MS-Excel solution of the WGP model with Pulses/Potato crop combination of rabi season observes an optimal solution and 0.75 and 0.65 ha of land are allocated for Pulses and Potato respectively.MS-Excel solution of the WGP model with Potato/Tilhan crop combination of rabi season observs an optimal combination of crop with 0.23 ha of potato and 1.12 ha of tilhan. Family labour is saved by 94.97 manday.

Results of both WGP and LGP model do not provide any optimum crop combination in kharif season. Main reason behind this is that a large part of the land of study area is low land which remains submerged in water due to heavy monsoon. Although it is is very much suitable for growing rice but smallholders hardly find any other crop suitable for growing in this season. However, rabi season do observe seven optimal crop combinations which are same both for WGP and LGP model. An average rural household can practice any one of these crop combinations as per their hectare allocation. Out of these seven crop combinations five combinations include wheat as one of crops to be shown with other crops. However, two crop combinations do not include wheat but they are still providing optimal combination. Moreover, four crop combinations are pulses-based ensuring satisfaction of the protein requirements essential for doing physical labour. High labour cost and low return on food crops prevent a number of crop combinations to be helpful in achieving their basic goals.

The striking fact to be noted is that all optimum crop combinations of rabi season have potato as one of the crop to be sown. This is due to the fact that according to the data of the study potato is a high return crop with moderate labour requirement.

This fact suggests that although farmers of the study area do subsistence farming but they should encourage cultivating some cash crop for maximizing their return. It will take care of their food goal as well as income goal. For this adequate credit and marketing facilities should be provided to them by the government with rigorous check on the activities of middleman.

An average rural household can practice any one of these crop combinations as per their hectare allocation. Out of these seven crop combinations five combinations include wheat as one of crops to be shown with other crops. However, two crop combinations do not include wheat but they are still providing optimal combination. Moreover, four crop combinations are pulses-based ensuring satisfaction of the protein requirements essential for doing physical labour. High labour cost and low return on food crops prevent a number of crop combinations to be helpful in achieving their basic goals.

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Received on 12.01.2013 Accepted on 10.02.2013

Research J. Science and Tech 5(1): Jan.-Mar.2013 page 72-76