European Business Schools Librarian's Group

ESSEC Working Papers,
ESSEC Research Center, ESSEC Business School

No WP1408: A Branch-and-Price-and-Cut Approach for Sustainable Crop Rotation Planning

Laurent Alfandari (), Agnès Plateau and Xavier Scheplerc
Additional contact information
Laurent Alfandari: ESSEC Business School, Postal: 1 AVENUE BERNARD HIRSCH, CS 50105 CERGY, 95021 CERGY PONTOISE CEDEX, FRANCE
Agnès Plateau: Conservatoire National des Arts et Métiers (CNAM), Postal: 292, rue Saint-Martin, 75141 PARIS Cedex 03, FRANCE
Xavier Scheplerc: Université du Havre, LITIS et LMAH, Postal: 25, rue Philippe Lebon, BP 540, 76058 LE HAVRE, FRANCE

Abstract: 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 NP-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.

Keywords: OR in agriculture; crop rotations; production planning; column generation; branch-and-price-and-cut

JEL-codes: Q10

22 pages, April 2014

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