By Eline van Elburg
Harvesting machinery and auxiliary vehicles are used extensively in the Brazilian sugarcane industry. However, the use of such equipment takes up a large portion of the total sugarcane production costs and the efficiency is often very low. Harvesters are accompanied by carriers that receive the cut sugarcane. When full, the carriers are driven to transhipment sites outside the fields to unload after which they return to the harvesters. The time during which carriers are away from the harvester is denoted “servicing time”. Servicing has to happen as fast as possible, because harvesters cannot be left idle. As there are several harvesters and carriers working together, a logistical problem arises. This study developed a model that aims to increase the efficiency of the harvesting machinery by minimizing the servicing time of auxiliary equipment.
Three optimisation issues were considered. First, carriers need to take the optimal route from the location where their capacity is reached (starting node; SN) to a transhipment site (TSA). The second issue concerns the optimal allocation of SNs to specific TSAs, while considering a TSAs capacity. The third optimisation problem is finding the optimal n (n being a smaller subset) TSA locations given a set of potential TSA sites.
All three optimization issues belong to a class of mathematical problems called combinatorial optimization problems, and require optimization algorithms. Dijkstra’s algorithm, a shortest path algorithm, was used to calculate the optimal routes. For the second issue, simulated annealing (SA) was used. SA is a heuristic algorithm based on an analogy between the annealing of solids in physics and combinatorial optimization. For each iteration, a randomly chosen starting node was re-assigned to a different TSA and evaluated with the defined objective function. This objective function takes into account the time costs of the optimal routes calculated by Dijkstra’s algorithm and the capacity of the TSAs. Based on the cost value of the objective function, a re-assignment is accepted or not, and the iterations continue until certain stopping criteria have been met. For the third optimisation, an exhaustive search was implemented that uses the methods from the previous two optimisations to find the least-cost solution.
The developed model was applied to two different areas in São Paulo, Brazil. A random distribution of starting nodes was defined and the real TSA locations were used. For the third optimisation issue, several potential TSA locations, including the real ones, were chosen. The results were evaluated based on the value of the costs produced by the simulated annealing algorithm and the resulting network showing which SNs were assigned to which TSA.
The resulting networks look realistic, which implies that the model performs as expected. The value of the objective function tends to fluctuate strongly and the resulting network can often visibly be improved. This indicates that the optimization algorithm probably could be improved. When the model decides the optimal locations of the TSAs the value of the objective function decreases greatly.
The results show several practical applications of the model. One possibility would be an add-on for auto-guidance software for deciding to which TSA a full carrier should go. Also, the optimal TSA locations can be calculated before the harvest. This could potentially save a lot of time and thereby increase the efficiency of the sugarcane harvest, which results in a decrease of the costs.
Keywords: sugarcane; Saccharum spp.; path planning; agricultural machinery; harvesting operations; optimization; cooperating machines; Dijkstra’s algorithm; simulated annealing; machine efficiency.