Harvest Planning in Apple Orchards Using an Optimization Model

Abstract

During the 2010 season, Chile became the first apple exporter in the southern hemisphere and reached second place worldwide (11.4 % of the world market), right after China with 14.2 % (Bravo 2011). On the other hand, in the last few years, agriculture in Chile has lost competitiveness, mainly because of a 30 % decline of the US$, of a 300 % increase in the prices of goods such as fertilizers and pesticides (Contreras 2008), of a 10 % decrease of the availability of agricultural workforce, and finally of a 12 % increase of the workers' wages (Domínguez 2007;Alarc on 2008). These factors progressively led to a decrease in the growth rate of the agricultural sector during the period [2005][2006][2007][2008], being surpassed by the National GDP growth (Contreras 2008). For this reason, producers and exporters in the industry are focusing on improving practices and better allocate resources, in order to reduce the costs involved along the supply chain.In Chile, the apple (Malus domestica) is the second most planted fruit species in the country, covering about 13 % of the national fruit area. The Maule Region As such, Maule is the main region producing apples in Chile, and, therefore, an improvement of the productivity and quality of the fruit produced in the region would have a significant impact on its economy. In this sense, this research seeks to increase the amount of fruit that could be exported, which would generate major incomes for the regional agricultural sector.When harvesting apples, one of the main factors affecting the quality of the fruit (and therefore its export) is the fruit ripeness and this must be taken into account when planning the harvest and the efficient use of resources such as equipment (ladders, containers), machinery (tractors, cars, and collectors carriers), and of course workforce, which is critical in this process. Indeed, over the last 10 years, during the harvest season, it has been every year harder to find the required quantity of seasonal workers, creating a 10 % decrease of them (Contreras 2008), and a 12 % increase in their costs over the last 3 years (Alarc on 2008). The main problem with the lack of workers is that the fruit cannot be harvested at the right ripeness and therefore cannot be selected for export, as it should. This issue has reduced the profitability of the agricultural producer, even though apple plantings remained constant over the last 10 years and the yield per hectare increased by approximately 73 % (Maule Competitiveness Center 2010).This work proposes a mathematical programming model to support planning decisions in an orchard and minimizing the amount of resources used, ensuring the production of good quality fruit for export. Furthermore, this model provides a harvest schedule that minimizes the loss of fruit for not fulfilling the desired quality parameters for export. The constraints of the model seek to fulfill the demands from the fruit packing plants, respect the processing capacity of the plants, availability of production in orchards, and harvesti...

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