A plant factory is an environmentally controlled facility that can sustain stable crop cultivation while ensuring fast production and better crop quality by manipulating temperature, humidity, lighting, nutrient supply, and other cultivation factors. It requires better cultivation planning to fully utilise the facility since the set up and operating costs are high. This study aims to schedule crops in a commercial plant factory to maximise revenue by determining which crops are cultivated, the quantity, and at what time. The model considers not only crop market prices but also crop properties such as cultivation duration, volume change, multiple periods of harvests, and yield rates under different environmental settings. The problem is formulated as a mixed integer programming problem to find an optimal schedule. For a large size problem, Lagrangian relaxation with surrogate subgradient method is applied to obtain a good solution in a short time. The numerical results show that, compared to the integer program solver, the proposed method provides faster solutions with more than 80% efficacy when longer planning periods and multiple cultivation rooms are considered.

中文翻译：

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使用拉格朗日松弛考虑产量、产量变化和多期收获的植物工厂作物调度

植物工厂是一种环境受控的设施，可以通过控制温度、湿度、光照、养分供应和其他栽培因素来维持稳定的作物种植，同时确保快速生产和更好的作物质量。由于设置和运营成本很高，因此需要更好的种植计划才能充分利用该设施。本研究旨在通过确定种植哪些作物、数量和时间来安排商业植物工厂的作物产量，以最大限度地提高收入。该模型不仅考虑了作物市场价格，还考虑了作物特性，例如种植持续时间、产量变化、多个收获期以及不同环境设置下的产量。该问题被公式化为一个混合整数规划问题，以找到一个最佳计划。对于大尺寸问题，拉格朗日松弛与代理次梯度方法被应用于在短时间内获得良好的解决方案。数值结果表明，与整数规划求解器相比，当考虑更长的规划周期和多个培养室时，所提出的方法提供了更快的解决方案，效率超过 80%。