Fuzzy linear programming for integrated farming systems in multi-objective environment

Crop production alone from predominantly small farms in India is quite inadequate to sustain the farm families. They have to depend on other land based enterprises, viz. crop, livestock, fishery, poultry, duckery, agroforestry etc. to meet the multifarious needs of farm family. Integrated Farming Systems (IFS) provides scope to integrate different enterprises with the objectives to generate additional farm income and employment, and improve the socio-economic condition of small and marginal farmers. IFS operate under different physical, biological, socioeconomic and technological environments. Designing a suitable IFS becomes complex due to the presence of uncertainties such as productivity, market prices of farm produce, non-availability of capital and labour at appropriate time. In the present study, Fuzzy Linear Programming (FLP) is used for developing suitable compromise integrated farming system models for farmers in north Indian situations under multi-objective environment. Based on the socio-economic survey, three objectives, capital requirement (CR), labour employment (LE) and farm income (FI) are considered for development of model. All three objective functions are represented by linear membership functions in fuzzy multi-objective framework. It is observed from compromise solution obtained by FLP that capital requirement, labour employment, farm income are 493 071, 897 man-days, 604 860, respectively with degree of satisfaction (λ)0.462. Analysis of compromise solution in multi-objective environment also indicated that capital requirement, labour employment and farm income have differed considerably as compared to individual optimal solutions obtained by solving linear programming individually for each objective function. Sensitivity analysis studies indicated that effect of linear/nonlinear membership functions is having significant effect on degree of satisfaction.