In this paper, we study a multi-periodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received increased 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 N P -hard. We propose a 0-1 linear programming compact formulation based on crop-sequence graphs. An extended formulation is then provided with a polynomial-time pricing problem, and a Branch-and-Priceand-Cut (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.
This problem was proven to be strongly NP-hard in REF and was reformulated as a 0/1 LP compact formulation based on crop-sequence graphs, then as an extended formulation with a polynomial-time pricing problem and a Branch-and-Price-and-Cut algorithm with adapted branching rules and cutting planes.
A branch-and-price-and-cut approach for sustainable crop rotation planning
Eur. J. Oper. Res.
Eur. J. Oper. Res.
Mathematics Computer Science