IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Optimering van wisselboustelsels

Listed author(s):
  • Visagie, S.E.
Registered author(s):

    Different types of crops are planted in winter grain regions. These crops can be planted in even more combinations. Crops that are planted on the same land in successive years do influence one another. In this situation the problem of which sequence of crops to plant arises. If appropriate assumptions are made, this problem can be solved with linear programming (LP). The complexity of this problem, however, increases dramatically with an increase in the number of crops as well as the number of years considered. Another problem with this formulation is how to choose the boundary conditions. Furthermore the solution to this problem is degenerate. In practice it is found that farmers prefer a cycle of crops in a rotary crop system, because it simplifies the management of the system. If the assumption is made that a farmer uses a cycle of at most three years, the problem of the boundary conditions is solved. If the dual formulation of this problem is considered it is evident that the problem has a specific structure. The structure of the problem as well as the fact that the solution to the problem is highly degenerate can be exploited to simplify the solution of the problem substantially. If the correct selection of solutions from this degenerate dual problem is chosen this selection can be used to formulate a simplified model in terms of strategies for the farmer. If the problem is formulated in terms of these strategies, the problem is further reduced to an LP with one constraint (the knapsack problem), which makes it possible to solve this problem by hand for a relative large number of crops in the rotary crop system. These strategies can also be used to solve a more generalised problem. Consider nature to be a player in Game Theory. The strategies of nature can be defined in many ways. The amount of rain per annum, for example, could be strategies used by nature to play a game against the farmer. The farmer in return can then use his strategies and the knowledge of Game Theory to maximise his profit. The problem can be generalised further if it is formulated in terms of Game Theory. In this generalisation the Game Theory model is expanded to incorporate a number of different situations with the use of extra constraints. The first of these situations is to incorporate other enterprises with the rotary crop system. The farmer could, for instance want the solution to contain at least a certain amount of feed for his cattle. The second situation is when the farmer has knowledge of the weather patterns, which implies for the Game Theory model that the farmer has knowledge of his opponentÂ’s strategies. Both these situations are incorporated in the model. Finally, a case study is presented in which the use of the model is demonstrated. Relevant data from the Swartland region are used. A dry year, an average year and a wet year were used as strategies for nature. The solutions drawn from these data were confirmed with a farmer from the region, who agreed that the solutions appear to be reasonable if it is compared to what is found in practice. The most frequently chosen strategies were the ones that contain wheat and clover. The solutions indicate that a farmer should plant less clover and more grain if it is a dry year, whilst it is better to increase the amount of clover planted if the rainfall is higher.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: no

    Article provided by Agricultural Economics Association of South Africa (AEASA) in its journal Agrekon.

    Volume (Year): 43 (2004)
    Issue (Month): 3 (September)

    in new window

    Handle: RePEc:ags:agreko:9483
    Contact details of provider: Web page:

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:ags:agreko:9483. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (AgEcon Search)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.