In this paper, we study the problem of planning the growth of crops on shelves in vertical farming cabinets under controlled growth conditions. By adjusting temperature, humidity, light, and other environmental conditions in different parts of the cabinets, a planner must ensure that crop growth is able to satisfy some deterministic demand. We prove this problem to be NP-hard and propose an integer programming formulation able to capture real-life operational characteristics, including changes of growth conditions on a daily, shelf-by-shelf basis, over a planning horizon of months. We compare four objective functions from which a planner can choose, depending on the specific operations of the company. A computational study on realistic instances, which we make available as a public dataset, shows that the choice of objective function heavily influences both the difficulty of solving the model with a standard solver and the solution characteristics.
European Journal of Operational Research (2021). DOI: 10.1016/j.ejor.2021.01.034