Plant factory crop scheduling considering volume, yield changes and multi-period harvests using Lagrangian relaxation

Abstract

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.