Optimization Models and Algorithms for Decision Making in Agriculture

Growth and development are at the basis of our society. In every domain, progress is shaped by the ability to allocate limited resources, coordinate activities, and continuously improve performance while complying with technical, economic, and institutional constraints. As systems expand and become more interconnected, decision-making becomes harder: choices that were once simple and local turn into decisions with multiple objectives, long-term consequences, and non-trivial interactions. In this landscape, relying exclusively on intuition or experience is rarely sufficient. Effective decisions increasingly require analytical support, rigorous reasoning, and tools that can translate data and constraints into actionable plans. Agriculture exemplifies this challenge in a particularly clear way. It is a strategic sector for food security and economic stability, yet it operates under strong resource limitations and increasing pressure to meet sustainability goals. Farmers and stakeholders have to face with uncertainty driven by climate variability, biological dynamics, and market volatility, while respecting agronomic rules, operational constraints, and regulations. At the same time, the transition toward sustainable practices calls for decisions that explicitly account for environmental impacts, long-term soil health, biodiversity preservation, and responsible use of inputs (e.g. water, fertilizers). These requirements make many agricultural choices inherently multi-criteria and tightly constrained, often spanning multiple seasons and spatially distributed operations. The set of quantitative disciplines broadly referred to as Decision Science offers a coherent perspective to address such complexity by placing decisions, trade-offs, and measurable outcomes at the center of the analysis. Within this framework, Operations Research provides a methodological backbone for building decision-support systems grounded in mathematical modeling. By representing a decision problem through variables, constraints, and objective functions, Operations Research enables the systematic evaluation of alternative strategies and the identification of solutions that improve performance under realistic limitations. This work mainly adopts mathematical optimization methods, with a strong emphasis on combinatorial optimization. Many relevant agricultural decisions are discrete in nature---for instance selecting crops, assigning land to activities, scheduling operations, or designing service routes---and lead to large-scale optimization models where the number of feasible alternatives grows rapidly. In these settings, straightforward enumeration is computationally impractical, and effective decision support hinges on the design of appropriate formulations and efficient solution algorithms, including exact approaches and tailored heuristics able to deliver high-quality solutions within practical time limits. The core of this dissertation consists of two main chapters, each addressing an optimization problem in the agricultural domain. The first chapter investigates a crop planning problem in which crop rotations and sustainability-oriented constraints play a central role. The objective is to maximize the farmer’s profit over a multi-period planning horizon while ensuring agronomic feasibility and explicitly incorporating sustainability requirements arising from both public regulations and private schemes. The second chapter addresses a vehicle routing problem arising in fertilization operations in viticulture. In this context, fertilizer demand varies across vineyard plots, and routing decisions must account for operational constraints such as vehicle capacity limits, binary refilling at the depot, and the possibility of split deliveries. The objective is to minimize total travel distance while simultaneously constructing an operational schedule that supports efficient fertilization activities and an effective organization of working hours.