Solving a special case of the generalized assignment problem using the modified differential evolution algorithms : a case study in sugarcane harvesting

We proposed and created a methodology to solve a real-world problem, which is a special case of the generalized assignment problem. The problem consists of assigning drivers to harvesters, which will then be assigned to harvest sugarcane in order to maximize daily profit. A set of drivers have various levels of experience. Therefore, a different capability to harvest sugarcane leads to a range of daily wages. Each harvester has different operating years and engine size, which affects its fuel consumption rate and capacity to harvest sugarcane, respectively. Assigning a worker to a harvester can improve the fuel consumption and efficiency of the harvester. We developed a mathematical model to reflect this problem and to solve it to find the maximum outcome using Lingo v.11 commercial optimization software. Since Lingo v.11 is limited to solving only small-size test instances, for medium to large test instances, four modified differential evolution (MDE) algorithms were used to solve the problem: MDE-1, MDE-2, MDE-3, and MDE-4. MDE-2 was found to be the best proposed heuristics because it has intensification and diversification ability. MDE has been tested with the case study. We tried to increase the daily profit by implementing three strategies: (1) change all harvesters that are more than five years old, (2) train drivers to reach maximum capacity, and (3) a combination of 1 and 2. Each strategy has a different investment. The breakeven point (number of days) to return the investment was calculated from the increase of daily profit. The computational results show that strategy 2 is the best because it has the quickest rate of investment return rate. However, this strategy has a disadvantage, since it is possible that drivers may leave the company if they have been highly trained. Moreover, strategy 1 has an acceptable break-even point at 392 days.