Farming optimization J. Boshoff, F. Farming optimization De Villiers, A. Roux, M. M. Sejeso, A. D. The price of success and the route to success Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- tavhatsindi, S. J. Boshoff F. De Villiers A. Roux M. M. Sejeso A. T. Sepuru, B. Seota, C. D. Maphiri M. O. Olusanya E. M. Thulare T. Nhangumbe Mutavhatsindi S. T. Sepuru B. Seota C. Nhangumbe Industrial Representative: Dr Norman Hoeltz Supervisor: Prof. Montaz Ali 1 / 33
Introduction Farming Objective optimization J. Boshoff, F. Provide smallholder and urban farmers with integrated solution De Villiers, A. Roux, M. M. combining the following aspects: Sejeso, A. D. Maphiri, M. Predictive pricing model O. Olusanya, E. M. Thulare, “Uber” for smallholder and urban agriculture T. Mu- tavhatsindi, S. T. Sepuru, B. Seota, C. Nhangumbe Figure: Aparate 2 / 33
Predictive pricing model Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. Helping farmers to decide: O. Olusanya, E. M. Thulare, What to grow in the first instance (single produce, mix of T. Mu- tavhatsindi, S. produce) T. Sepuru, B. Seota, C. Nhangumbe When to grow the produce When to harvest and sell their produce 3 / 33
Pricing data Farming optimization J. Boshoff, F. The following data is given: De Villiers, A. Roux, M. M. Historical monthly market prices for each produce over the Sejeso, A. D. Maphiri, M. last years O. Olusanya, E. M. Thulare, Historical daily market prices for each produce over the T. Mu- tavhatsindi, S. last 90 days T. Sepuru, B. Seota, C. Nhangumbe Growing guides to determine the time from planting to harvest Fruit and vegetable price trends Example of Monthly Market Information Report Vegetables 4 / 33
Time series plots Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- tavhatsindi, S. T. Sepuru, B. Seota, C. Nhangumbe Figure: Four different time plots 5 / 33
Seasonal plots Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- tavhatsindi, S. T. Sepuru, B. Seota, C. Nhangumbe Figure: Seasonal plots 6 / 33
ARIMA models Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- ARIMA models are struggling to model our commodity tavhatsindi, S. T. Sepuru, B. monthly average prices due to small data set. Seota, C. Nhangumbe 7 / 33
Forecasts Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- tavhatsindi, S. T. Sepuru, B. Seota, C. Nhangumbe Figure: forecast plots 8 / 33
Machine learning algorithms Farming optimization LSTM networks - type of Recurrent Neural Network J. Boshoff, F. De Villiers, A. specially designed to prevent the neural network output for Roux, M. M. Sejeso, A. D. a given input from either decaying or exploding as it cycles Maphiri, M. O. Olusanya, through the feedback loops. E. M. Thulare, T. Mu- SVR - uses a kernel function to transform a given data tavhatsindi, S. T. Sepuru, B. into a higher dimensional feature space to make it possible Seota, C. Nhangumbe to perform the linear separation FFNN - an artificial neural network wherein connections between the nodes do not form a cycle. As such, it is different from recurrent neural networks. The FFNN was the first and simplest type of artificial neural network devised. 9 / 33
Results for cabbages Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Table: Evaluation of the models for cabbages. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- Algorithm Training RMSE Testing RMSE tavhatsindi, S. T. Sepuru, B. LSTM 641.384 237.826 Seota, C. Nhangumbe SVR 664.997 237.989 FFNN 1199.857 859.124 ARIMA(2,0,1)(2,1,0)12 883.199 LSTM model is the best forecasting model for cabbage monthly average price. 10 / 33
Results for carrots Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Table: Evaluation of the models for carrots. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- Algorithm Training RMSE Testing RMSE tavhatsindi, S. T. Sepuru, B. LSTM 782.992 754.345 Seota, C. Nhangumbe SVR 779.796 755.541 FFNN 1500.923 1507.450 ARIMA(1,1,1)(1,1,0)12 944.169 LSTM model is the best forecasting model for carrots monthly average price. 11 / 33
Results for potatoes Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Table: Evaluation of the models for potatoes. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- Algorithm Training RMSE Testing RMSE tavhatsindi, S. T. Sepuru, B. LSTM 455.844 239.743 Seota, C. Nhangumbe SVR 456.753 260.213 FFNN 1337.049 1133.372 ARIMA(0,0,1)(2,1,0)12 336.984 LSTM model is the best forecasting model for potatoes monthly average price. 12 / 33
Results for strawberries Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Table: Evaluation of the models for strawberries. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- Algorithm Training RMSE Testing RMSE tavhatsindi, S. T. Sepuru, B. LSTM 16928.991 34146.637 Seota, C. Nhangumbe SVR 15764.179 30574.898 FFNN 33110.796 51201.785 ARIMA(2,0,1)(1,0,0)12 16251.967 SVR model is the best forecasting model for strawberries monthly average prices. 13 / 33
Conclusion and future work Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. LSTM has better forecasting capability for monthly O. Olusanya, E. M. Thulare, average price. T. Mu- tavhatsindi, S. Include more predictor variables in forecasting monthly T. Sepuru, B. Seota, C. average price such as temperature. Nhangumbe Hyper parameter tuning Ensemble Methods. 14 / 33
Route planning Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. O. Olusanya, E. M. Thulare, T. Mu- tavhatsindi, S. T. Sepuru, B. Seota, C. Nhangumbe Figure: Farm locations 15 / 33
The route to success Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. Objective O. Olusanya, E. M. Thulare, T. Mu- Develop route planning and optimization model including tavhatsindi, S. T. Sepuru, B. all farms and depots given Seota, C. Nhangumbe Increase economic viability for the transportation company regarding utilization of trucks, drivers and petrol 16 / 33
Model constraints Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. Max route length per day: 400km O. Olusanya, E. M. Thulare, T. Mu- Max time on the road: 8hrs / 480 mins tavhatsindi, S. T. Sepuru, B. Vehicles must return to the depot in the evening Seota, C. Nhangumbe Routes and travel time calculated based on average traffic time according to Google Maps API data 17 / 33
Model constraints Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Carrying capacities and vehicle types: Sejeso, A. D. Maphiri, M. Standard trucks (Vehicle 1: 1 ton, Vehicle 2: 2 ton) O. Olusanya, E. M. Thulare, Refrigerated truck (Vehicle 3: 0,5 ton) T. Mu- tavhatsindi, S. Vehicle type must match the produce transportation T. Sepuru, B. Seota, C. requirements Nhangumbe Include ramp-up/ramp-down time per farm visited: 15 minutes Include time taken to load cargo: 0.05 minutes per kg 18 / 33
Model constraints Farming optimization J. Boshoff, F. De Villiers, A. Roux, M. M. Sejeso, A. D. Maphiri, M. Relax requirement to visit every node exactly once: O. Olusanya, E. M. Thulare, allows us to find partial feasible routes when trucks are T. Mu- oversubscribed (in terms of distance, time or capacity); tavhatsindi, S. T. Sepuru, B. dropping a node from the routes carry a large penalty - Seota, C. Nhangumbe optimizer encouraged to include as many nodes as possible; penalties may be adjusted per node to prioritize nodes with certain characteristics. 19 / 33
Mathematical Model Model the problem as a graph G = ( F, E ) , with vertex set Farming optimization F = { 0 , 1 , . . . , n } with 0 := depot, and E is the set of edges. J. Boshoff, F. De Villiers, A. c ij - the distance of traversing the edge ( i, j ) ∈ E . Roux, M. M. Sejeso, A. D. d im - demand of produce m associated with farm Maphiri, M. O. Olusanya, i ∈ F − { 0 } E. M. Thulare, T. Mu- Q mk - capacity of produce m on vehicle k . tavhatsindi, S. T. Sepuru, B. Seota, C. We use the following notations for variables: Nhangumbe � 1 if vehicle k travels directly from i to j x ijk = 0 otherwise � 1 if vehicle k pick produce m form farm i y imk = 0 otherwise 20 / 33
Mathematical Model Objective: minimize the total distance travelled by the vehicles Farming optimization v n n J. Boshoff, F. � � � min c ij x ijk De Villiers, A. Roux, M. M. j =0 i =0 Sejeso, A. D. k =1 Maphiri, M. subject to O. Olusanya, E. M. Thulare, T. Mu- n n tavhatsindi, S. � � x 0 jk ≤ 1 ∀ k ; x i 0 k ≤ 1 ∀ k (1) T. Sepuru, B. Seota, C. Nhangumbe j =0 i =0 n v � � x ijk ≥ 1 ∀ j (2) i =0 k =1 n n � � x ijk = x jik ∀ j ; ∀ k (3) i =0 i =0 � � x ijk ≤ | S | − 1 ∀ k ; S ⊆ F − { 0 } (4) i ∈ S j ∈ S 21 / 33
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