Article
A MIP flow model for crop rotation planning in a sustainable development context
Annals of Operations Research (Impact Factor: 1.22). 10/2011; 190(1):149164. DOI: 10.1007/s1047900905530
Source: DBLP
ABSTRACT
We propose a MixedInteger Linear Programming model for a class of multiperiod crop rotation optimization problems with demand
constraints and incompatibility constraints between cultivation and fallow state on a land plot. This model is applied to
a case study on Madagascan farms in the scope of a sustainable development campain against deforestation, where the objective
is to better control agricultural space while covering seasonal needs of farmer. We propose an efficient upper bound computation
and study the variation of the minimum number of plots and total space needed in function of the unitary surface area of a
plot. Numerical results associated with the Madagascan case are reported.
KeywordsCrop rotation planning–Linear programming–Sustainable development
constraints and incompatibility constraints between cultivation and fallow state on a land plot. This model is applied to
a case study on Madagascan farms in the scope of a sustainable development campain against deforestation, where the objective
is to better control agricultural space while covering seasonal needs of farmer. We propose an efficient upper bound computation
and study the variation of the minimum number of plots and total space needed in function of the unitary surface area of a
plot. Numerical results associated with the Madagascan case are reported.
KeywordsCrop rotation planning–Linear programming–Sustainable development

 "In Alfandari et al. (2015), the authors use a BPC algorithm to solve a crop rotation problem that select plots from a candidate list in order to minimise the combined area of chosen plots while meeting a given demand. They deal with crops that have a single growing cycle (and therefore, one harvest period) and only two possible planting periods per year, following the same ideas proposed in Alfandari et al. (2011). These crop characteristics allow the feasible crop rotations to be expressed by means of a clever transition graph, so the subproblems can be solved by using a shortest path algorithm. "
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ABSTRACT: Crop rotation plays an important role in agricultural production models with sustainability considerations. Commonly associated strategies include the alternation of botanical families in the plots, the use of fallow periods and the inclusion of green manure crops. In this article, we address the problem of scheduling vegetable production in this context. Vegetables crop farmers usually manage a large number of crop species with different planting periods and growing times. These crops present multiple and varied harvesting periods and productivities. The combination of such characteristics makes the generation of good vegetable crop rotation schedules a hard combinatorial task. We approach this problem while considering two additional important practical aspects: standard plot sizes (multiples of a base area) and total area minimisation. We propose an integer programming formulation for this problem and develop a branchpriceandcut algorithm that includes several performanceenhancing characteristics, such as the inclusion of a family of subadditive valid inequalities, two primal heuristics and a strong branching rule. Extensive computational experiments over a set of instances based on reallife data validate the efficiency and robustness of the proposed method. 
 "A plot could be cultivated with several crops in the same period in this study. We direct the reader to Alfandari et al. (2011) for more details on the agricultural Madagascan con text. "
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ABSTRACT: In this paper, we study a multiperiodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received considerable attention in the literature in recent years. Crop cultivation and fallow periods must be scheduled on land plots over a given time horizon so as to minimize the total surface area of land used, while satisfying crop demands every period. This problem is proven strongly NPhard. We propose a 01 linear programming formulation based on cropsequence graphs. An extended formulation is then provided with a polynomialtime pricing problem, and a BranchandPriceandCut (BPC) algorithm is presented with adapted branching rules and cutting planes. The numerical experiments on instances varying the number of crops, periods and plots show the effectiveness of the BPC for the extended formulation compared to solving the compact formulation, even though these two formulations have the same linear relaxation bound. 
 "That is if one cultivates the same crop repeatedly on the same plot over the time, the yield decrease. The effect of crop rotation is taken into account in the papers (Alfandari et al. 2009; Castellazzi et al. 2008; Detlefsen and Jensen 2007; Dogliotti et al. 2003; ElNazer and McCarl 1986; Haneveld and Stegeman 2005; Mimouni et al. 2000; Santos et al. 2008; Vizvári et al. 2009). One can easily see that in our model the plot productivity functions do not depend on the crops cultivated previously on that plot. "
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ABSTRACT: This paper presents a multiobjective model for crop planning in agriculture. The approach is based on portfolio theory. The model takes into account weather risks, market risks and environmental risks. Input data include historical land productivity data for various crops, soil types and yield response to fertilizer/pesticide application. Several environmental levels for the application of fertilizers/pesticides, and the monetary penalties for overcoming these levels, are also considered. Starting from the multiobjective model we formulate several single objective optimization problems: the minimum environmental risk problem, the maximum expected return problem and the minimum financial risk problem. We prove that the minimum environmental risk problem is equivalent to a mixed integer problem with a linear objective function. Two numerical results for the minimum environmental risk problem are presented.
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