Energy-efficient automated vertical farms

Autonomous vertical farms (VFs) are becoming increasingly more popular because they allow to grow food minimising water consumption and the use of pesticides, while greatly increasing the yield per square metre compared with traditional agriculture. To meet sustainability goals, however, VFs must operate at maximum efficiency; it would be otherwise impossible to compete with the energy source powering plant growth in traditional agriculture: the sun. We introduce the Vertical Farming Elevator Energy Minimisation Problem (VFEEMP), which arises when minimising the energy consumption of automatic elevators servicing VFs. We prove that the decision problem associated with the VFEEMP is NP-complete. To solve the problem, we propose three Mixed-Integer Linear Programming (MIP) formulations together with valid inequalities, and a Constraint Programming model. We present a large set of instances, both synthetic and derived from real-life data, and we determine through extensive computational experiments which instance characteristics have an impact on the difficulty of the problem and which formulations are the most suitable to solve the VFEEMP.