Improved mathematical model and bounds for the crop rotation scheduling problem with adjacency constraints

• Published in: European journal of operational research Vol. 278; no. 1; pp. 120 - 135
• Main Author: Regis Mauri, Geraldo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2019
• Subjects: Column generation; Combinatorial optimization; Crop rotation scheduling; Lagrangian decomposition; Lagrangian relaxation; Lagrangian decomposition; Column generation; Crop rotation scheduling; Combinatorial optimization; Lagrangian relaxation
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2019.04.016

•We propose a tighter model for a crop rotation problem of the literature.•Five relaxation methods are proposed to find bounds and solutions for the model.•A method previously presented in the literature is significantly outperformed.•A detailed set of instances based on real-world values is presented.•Optimal solutions are proven for almost all instances. The Crop Rotation Scheduling Problem (CRSP) consists of alternating crops in neighboring plots during a period of time in order to find a planting schedule that satisfies a particular objective subject to some constraints such as the non-simultaneous cultivation of crops from the same botanical family in neighboring plots. In this work, some assumptions are proposed to improve a mathematical model presented in the literature, making it more general and easier to be solved by a commercial solver. In addition, five different relaxation approaches are proposed to find bounds and solutions for the CRSP. A detailed set of instances is also proposed, and a column generation procedure presented in the literature is implemented in order to perform a fair comparison of results. Computational experiments were performed indicating the improvements provided by the new model and the capability of some relaxation methods to generate high-quality solutions and bounds for the CRSP.