Comparing an expected value with a multistage stochastic optimization approach for the case of wine grape harvesting operations with quality degradation

Abstract

Operations planning is an important step in any activity as it aligns resources to achieve economic production value. In agriculture operations where uncertainty is present, planners must deal with biological and environmental factors, among others, which add variability and complexity to the production planning process. In this work, we consider operations planning to harvest grapes for wine production where uncertainty in weather conditions will affect the quality of grapes and, consequently, the economic value of the product. In this setting, planners make decisions on labor allocation and harvesting schedules, considering uncertainty of future rain. Weather uncertainty is modeled following a Markov Chain approach, in which rain affects the quality of grapes and labor productivity. We compare an expected value with a multi?stage stochastic optimization approach using standard metrics such as Value of Stochastic Solution and Expected Value of Perfect Information. We analyze the impact of grape quality over time, if they are not harvested on the optimal ripeness day, and also consider differences in ability between workers, which accounts for the impact of rain in their productivity. Results are presented for a small grape harvest instance and we compare the performance of both models under different scenarios of uncertainty, manpower ability, and product qualities. Results indicate that the multi?stage approach produces better results than the expected value approach, especially under high uncertainty and high grape quality scenarios. Worker ability is also a mechanism for dealing with uncertainty, and both models take advantage of this variable.