Advantages of combining linear programming and weighted goal programming for agriculture application

The aim of this paper is to present the basic characteristics of linear programing (LP) and weighted goal programming (WGP) to optimize processes on farms. Characteristics of both mathematical techniques are presented through the development of the crop planning model for solving some objective problems: maximizing financial results and minimizing different production costs on agricultural holdings. The model is structured from two sub-models, where the first based on linear programming and the second based on weighted goal programming are supported with penalty functions. The authors dispatch the weaknesses of LP with the application of WGP in the model and support this statement with results in this paper. The model was tested and validated on crop rotation with combinations of different field and vegetable crops in two different scenarios (WGPSC1 and WGPSC2) on a real agricultural holding in Slovenia. The results show that WGP combines more suitable crop rotation from an economic perspective than LP and provides a better solution for diversified and economically feasible crops that are included in the crop rotation. LP gives completely unacceptable results from the aspect of underachievement (for more than 100 %) of the maximum cropping area on a farm, while WGP completely satisfies all goals. From the obtained results in this paper, the authors identify several weaknesses of LP and present how it could be removed by applying the WGP technique.

[1]  June Jamrich Parsons,et al.  New Perspectives on Microsoft Office Excel 2003, Comprehensive, Second Edition (New Perspectives (Paperback Course Technology)) Package , 2005 .

[2]  R. Chambers,et al.  Expenditure Constraints and Profit Maximization in U.S. Agriculture , 1986 .

[3]  Saul I. Gass.  The setting of weights in linear goal-programming problems , 1987, Comput. Oper. Res..

[4]  Frederick V. Waugh,et al.  The Minimum-Cost Dairy FeedAn Application of “Linear Programming” , 1951 .

[5]  Tunjo Perić,et al.  Optimization of livestock feed blend by use of goal programming , 2011 .

[6]  I. M. Premachandra,et al.  Design of optimal food-based complementary feeding recommendations and identification of key "problem nutrients" using goal programming. , 2006, The Journal of nutrition.

[7]  Karmen Pažek,et al.  Application of weighted goal programming in the optimization of rations for sport horses , 2013 .

[8]  W B Roush,et al.  Multiple-objective (goal) programming model for feed formulation: an example for reducing nutrient variation. , 2002, Poultry science.

[9]  T. Ray,et al.  An improved evolutionary algorithm for solving multi-objective crop planning models , 2009 .

[10]  B. Khabiri,et al.  An Optimal Model using Goal Programming for Rice Farm , 2008 .

[11]  Stane Kavcic,et al.  Multi-step beef ration optimisation: application of linear and weighted goal programming with a penalty function , 2008 .

[12]  Carlos Romero,et al.  Relaxation of nutrient requirements on livestock rations through interactive multigoal programming , 1994 .

[13]  C. R. Taylor.  DUALITY, OPTIMIZATION, AND MICROECONOMIC THEORY: PITFALLS FOR THE APPLIED RESEARCHER , 1989 .

[14]  Dinesh K. Sharma,et al.  Fuzzy goal programming for agricultural land allocation problems , 2007 .

[15]  C. R. Taylor,et al.  Stochastic Dynamic Duality: Theory and Empirical Applicability , 1984 .

[16]  Carlos Romero,et al.  Multiple-criteria decision-making techniques and their role in livestock ration formulation , 1984 .