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A stochastic programming based analysis of the field use in a farm

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Abstract

The paper is devoted to the use of the arable land of a farms. The farm want to have certain amount of productions from some crops. This policy of the farm has two purposes. First some products, e.g. silo, are used on further production levels. Furthermore the diversification of the finished product decreases the financial risk of the farm caused by the unknown future behavior of the markets. The aim is to determine that use of the fields, which guarantees the highest probability of the satisfaction of demand. Crop rotation determining that which crops can be produced in a field gives a natural condition to be satisfied. The problem is modeled and solved by stochastic programming. The results based on the data of a farm are provided.

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Author information

Authors and Affiliations

  1. Dept. of Industrial Engineering, Eastern Mediterranean University, Famagusta, Northern Cyprus

    Béla Vizvári

  2. Dept. of Food Economics, Corvinus University, Budapest, Hungary

    Zoltán Lakner

Authors
  1. Béla Vizvári
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  2. Zoltán Lakner
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Corresponding author

Correspondence to Béla Vizvári.

Appendices

Appendix A

In the example of Sect. 4 the regression equations of the yields of the three crops are the followings.

where PDI t is the value of the Pálfai’s Drought Index t years earlier. E.g. PDI 0 is the index of the current year. If year=1986 and all PDI t =3.5 then the value of the right-hand sides equal to the expected value of the yield in the example.

Appendix B

The value of the PDI or any other drought index is a random variable if it is accepted that the weather is a random phenomenon. Its distribution function D(⋅) was estimated in (Vizvári et al. 2011) as

where the values of the parameters are: ν=4.12678063, σ=1.43656559, ρ=0.01546327.

Appendix C

Tables C.3 to C.7 contain the fields which can be used for the crops according to the current state of the crop rotation, and the expected values of the yields and the harvested products.

Table C.1 The fields of the farm
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Table C.2 Demands in metric ton
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Table C.3 Expected results from barley
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Table C.4 Expected results from feed barley
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Table C.5 Expected results from maize
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Table C.6 Expected results from sunflower
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Table C.7 Expected results from wheat
Full size table

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Vizvári, B., Lakner, Z. A stochastic programming based analysis of the field use in a farm. Ann Oper Res 219, 231–242 (2014). https://doi.org/10.1007/s10479-013-1335-2

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  • DOI: https://doi.org/10.1007/s10479-013-1335-2

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