# Optimization Model for Selective Harvest Planning Performed by Humans and Robots
## 1 Introduction
Once the technical feasibility of robotic harvesters has been proven, successful implementation and commercialization will depend on their integration into the production cycle [28], similarly to milking robots: after the technical feasibility of the milking robot had been successfully demonstrated, different operational research aspects were investigated at various levels, including optimal allocation in a robotic milking barn [29], the design and layout of an optimal barn [30], and prediction of the milking robot utilization [29]. One of the operational aspects of a harvesting robot is harvest planning, which includes scheduling, routing, and resource allocation to ensure high quality of the final products [1]. The agricultural environment is characterized by several variabilities and challenges, deriving from its unstructured and dynamic make-up and the biological nature of the product [27; 31; 32]. Fruit and vegetable crops vary widely in physiology and management practices, which may involve multiple harvests in a single season [33]. In particular, in high-value crops, harvesting is performed several times along a production season. These crops are generally non-staple crops, such as fruit, vegetables, ornamentals, and spices [34]. For such crops, the decision to harvest a specific fruit/vegetable depends on the fruit/vegetable maturity level, the harvesting capacity, and market demand. In this work, we aimed to develop a model for selective harvesting based on the maturity of the fruit, where harvesting can be performed by human workers or robots, with each type of harvester having different abilities to identify maturity. The model formulation and analyses are demonstrated in numerical studies using sweet pepper harvesting as a case study. We determined the optimal harvest production order to maximize farmers' profit. The production order defines how many peppers of each maturity level to harvest on each specific harvest day along the harvesting season. The production order defines the harvesting capacity needed, i.e., the number of workers/robots required to achieve this production. Usually, different types of workers are available for harvesting, and in the future, robotic harvesters might also be integrated into the harvesting process [14; 23]. The factors that determine the type of worker include costs (salary), the number of peppers each worker can harvest each day, and the worker's ability to classify the peppers into different maturity classes. For example, an inexperienced worker is able to classify peppers into only two maturity classes--mature and immature. An experienced worker can classify the pepper into four maturity classes--immature, partly mature, mostly mature, and must be harvested [35]. Therefore, more experienced workers, who are better able to estimate the pepper maturity level, will harvest the fruit at the best fit time, resulting in an overall higher pepper weight (since the fruit will stay longer on the plant and continue to develop). A robotic harvester will be able to non-destructively classify the exact maturity level [24; 36; 37; 38; 39] and will have a higher harvest capacity than a human worker, but will also have _higher costs_[23]. Only a few previous studies have investigated and analyzed the economic effect of robotic harvesting, focusing on the machine cost per area unit, compared to human workers [1; 40]. This work extends the literature by _estimating the selective robotic harvester quality savings_, taking into consideration both the cost (comparing robot costs to manual costs) and the effect of maturity classification using a robotic harvester (the quality effect). The remainder of this paper is organized as follows: Section 2 gives the relevant background and previous research. Section 3 describes in detail the basic formulation of the harvesting problem, and Sections 4 and 5, respectively, present expansions of the basic formulation and numerical studies. Finally, Section 6 concludes the paper.