Solving the Crop Allocation Problem using Hard and Soft Constraints

Mahuna Akplogan, Simon de Givry, Jean-Philippe Métivier, Gauthier Quesnel, Alexandre Joannon, Frédérick Garcia
2013 Reserche operationelle  
Application tools for the crop allocation problem (CAP) are required for agricultural advisors to design more efficient farming systems. Despite the extensive treatment of this issue by agronomists in the past, few methods tackle the crop allocation problem considering both the spatial and the temporal aspects of the CAP. In this paper, we precisely propose an original formulation addressing the crop allocation planning problem while taking farmers' management choices into account. These
more » ... count. These choices are naturally represented by hard and soft constraints in the Weighted CSP formalism. We illustrate our proposition by solving a medium-size virtual farm using either a WCSP solver (toulbar2)oranILPsolver(NumberJack/SCIP). This preliminary work foreshadows the development of a decision-aid tool for supporting farmers in their crop allocation strategies. The design of a cropping plan is one of the first steps in the process of crop 2 production and is an important decision that farmers have to take. By cropping 3 plan, we mean the acreage occupied by all the different crops every year and 4 their spatial allocation within a farming land. The cropping plan decision can 5 be summarized as (1) the choice of crops to be grown, (2) determining of all 6 crops' acreage, and (3) their allocation to plots. Despite the apparent simplicity of 7 the decision problem, the cropping plan decisions depend on multiple spatial and 8 temporal factors interacting at different levels of the farm management. 9 The cropping plan decision-making combines long term planning activities with 10 managerial and operational activities to timely control the crop production pro-11 cess. Modeling a decision-making process supporting such farmers' decisions there-12 fore requires the planning of crop allocation over a finite time horizon, and the 13 need for replanning as the context changes (e.g., weather, prices). In this paper, 14 we precisely focus on the planning task seen as a spatio-temporal crop allocation 15 problem (CAP) whose relevance is assessed by a global objective function. In ad-16 dition to many approaches based on an optimization procedure, the objective of 17 our work is to propose new directions addressing the crop allocation problem while 18 taking farmers' decision factors into account. These factors are formalized as hard 19 and soft constraints in the WCSP framework. Our choice of physical constraints 20 and farmer's preferences is based on a survey of farmers' processes [11]. 21 Nevertheless, designing cropping plans with such an approach is still an open 22 question due to many other decision factors that could be taken into account to 23 solve the crop allocation problem. This preliminary work foreshadows the imple-24 mentation of a spatially explicit decision-aid tool, namely CRASH (Crop Rotation 25 and Allocation Simulator using Heuristics), developed for supporting farmers in 26 their crop allocation strategies. 27 The paper is organized as follows. In Section 2, we describe the crop allocation 28 problem. We introduce some specific definitions and emphasize the problem. Sec-29 tion 3 describes some existing approaches used to design cropping plans, showing 30 their main limitations. In Section 4, we introduce the Weighted CSP formalism. 31 Section 5 describes a WCSP formulation of the crop allocation problem. Its re-32 formulation as an integer linear program is given in Section 6. In Section 7,w e 33 illustrate our approach by solving a medium-size virtual farm using either the 34 direct WCSP formulation or a decomposed one, or the ILP reformulation. Finally, 35 we conclude in Section 8. 36 2. Crop allocation problem 37 2.1. Overview of the problem 38 We define the crop allocation problem as a spatio-temporal planning problem 39 in which crops are assigned to plots over a finite time horizon H (Fig. 1) . The On the largest instance, SCIP was more than three times faster than toulbar2 1 and used 160 MB of RAM compared to 803 MB for toulbar2, showing that our 2 decomposed formulation does not scale well compared to the ILP approach. 3 Let us consider the optimal solutions found by the decomposed approach. Fig-4 ure 7 represents for each instance the spatio-temporal crop allocation. The min-5 imum return times of crops are enforced. The temporal balance of winter rape is 6 enforced on block 2 and 4. Due to the historic values in block 3, the spatial balance 7 of maize is not enforced when the year t ∈{6, 8}. 8 7.4. Finding all the optimal solutions 9 We also measured the search effort done by toulbar2 on the decomposed for-10 mulation to find all the optimal solutions by setting the initial upper bound to the
doi:10.1051/ro/2013032 fatcat:erlmk7plifbijl4duf5xh7luwq