Space minimization in agricultural production planning by column generation

We deal in this paper with an agricultural production planning problem where crops must be scheduled on land plots so as to satisfy crop demands every period of time and to minimize the overall surface of land used for cultivation. This problem can be formulated as a covering integer program with a huge number of variables. A resolution scheme based on column generation is thus proposed, where the resulting pricing problem is efficiently solved by dynamic programming. The numerical experiments show that the method is all the more so efficient and robust as the planning horizon is long and plot sizes are small

A computational study for the p-median Problem

Given a set of clients and a set of potential sites for facilities, the p-median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. In [Elloumi, S., A tighter formulation of the p-median problem, J. Comb. Optim., 19 (2004), 69?83], a new formulation of this problem was proposed that takes benefit from identical values in the distance matrix. This formulation, when directly used in a mixed integer linear programming software, was proved to perform better than other known formulations, on a large number of instances. Here, we propose to improve the performances of the new formulation by taking benefit from its structure in the solution of its LP-relaxation. Rows and columns are gradually added to the linear program until a condition on the optimal values of the variables is reached. A computational comparison is carried out on many classes of instances

hybridation de méthodes intérieures et de métaheuristiques pour la programmation linéaire en nombres entiers

PARIS-DAUPHINE-BU (751162101) / SudocSudocFranceF

A Branch-and-Price-and-Cut approach for Sustainable Crop Rotation Planning

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

A Branch-and-Price Algorithm for Sustainable Crop Rotation Planning

We deal with the agricultural problem of planning crops over a given time horizon and given land plots to meet the farmer?s needs over time. The MSCRP (Minimum-Space Crop Rotation Planning) focuses on building rotations that minimize the total area needed to meet demand. We show that the MSCRP problem is NP-hard and give a 0-1 linear formulation. We use Dantzig-Wolfe decomposition and column gen- eration. Finally, we study a branching scheme for solving the master problem by branch-and-price. Computational experiments show the efficiency of our approach on randomly generated instances