Controlled environment agriculture (CEA) systems present an opportunity to overcome global food security challenges by decoupling crop growth from natural weather conditions [7, 8]. These systems involve growing crops in enclosed structures where technology is used to optimize growing conditions tailored to the needs of each plant. This approach enables increased efficiency, reduced resource use, year-round production, and scalability. Unfortunately, CEA systems are high-risk ventures due to the high capital and operating costs [3, 9] and uncertain market conditions, creating a significant challenge for implementation. As such, a CEA system may be economically feasible and optimal at the design stage but becomes infeasible at the operating stage. To properly assess the economic feasibility of CEA systems, a methodology that accounts for market uncertainty is required at the design stage. Such a robust design approach ensures that an optimal design is economically feasible at the operating stage.
Optimization plays a critical role in the design and operation of CEA systems by optimizing the economic performance of the entire system over its life cycle. However, very few existing approaches have implemented optimization methods that are sufficiently adaptable to the complexity of modern agriculture systems [4-6, 9]. Furthermore, only a limited number of these approaches incorporate uncertainty in the modeling stage, which is essential for assessing the long-term viability of these systems [4-6, 9]. To the best of our knowledge, only one method employs a deterministic global optimization approach to address these challenges comprehensively, accounting for uncertainty [9]. However, the modeling assumptions of Cetegen and Stuber [9], such as fixing and synchronizing crop growing periods, are relatively restrictive and may not accurately capture the flexibility of CEA systems to diverse crop choices. Additionally, the model of [9] does not exist in any publicly accessible repository. This motivates the need for further research and developments into CEA design approaches that can help to ensure sustainable production for future generations.
In this work, we present a software tool for the simultaneous design and scheduling of CEA systems under multi-period risk. We build upon the original semi-infinite programming (SIP) formulation developed in [9] to address the optimal design under uncertainty problem. This formulation optimizes the life cycle economic performance while accounting for uncertainty in the form of mean-variance risk when planning the crop rotations. Our novel developments enable us to incorporate the growth cycles specific to each crop in the system, a key enhancement that enables greater customization and system flexibility to yield more accurate results. This adaptation presents a significant advancement in the formulation and code implementation, as it enables the tool to more accurately reflect the behavior of different crops, enhancing its applicability to a variety of crop combinations. This tool allows users to tailor parameters to construct a personalized system and solve their problem to global optimality to determine economic feasibility in the face of worst-case market conditions. We will demonstrate our package’s capabilities to design robust CEA systems with crop growing/scheduling decisions made monthly. We demonstrate our approach on a nontrivial case study from [9] with the proposed increased modeling fidelity that results in an SIP with 99 upper-level decision variables and 24 semi-infinite constraints parameterized by a 64-dimensional uncertainty set.
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