The decline of the bee population poses threats to the production of considerable types of crops that require pollination. The prediction of the bee’s future population has therefore become a valuable research topic. For Problem one, we tried to solve it in mainly two ways: using the Grey Forecast Model and using differential equations. For data that were missing, we processed them by normalization at first and then regressed to find the abnormal data, and filled the missing data with average data after deleting abnormal data. For the Grey forecast, we use three types of models and compared their respective results with true values to pick the one with the most accurate output and use it to predict the population of bees. For the differential equation method, we simply express the rate of increase in population in terms of several variables (in the differential equation) and solve the equation to obtain the future population. For Problem two, we do a sensitivity test on the bee population. We applied the Random Forest model here to determine the importance of each variable. During the evaluation of the model, we test four sets of data and compare the Random Forest results with the true value. It turned out to be that the final model predicts the population precisely, which has proven that it is reliable. At last, we change the sensitivity of each variable for a 100% change and tell the importance of the variables. For Problem three, we get the model of the possibility of a plant being visited by a bee in a beehive system at any distance, and then we use this matrix to simulate the area and calculate the possibility at any point. After determining a possible lower bound, we can get the area that can reach the bound which is the area the current beehive system can serve. By changing the number and the positions of beehives, we can get the maximum area the system can serve at any time. We can also calculate the possibility considering the planting density and the population of bees so it can be related to problem 1. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.