Solving a Special Case of the Generalized Assignment Problem Using the Modified Differential Evolution Algorithms: A Case Study in Sugarcane Harvesting

Abstract

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.

Adaptive Large Neighborhood Search to Solve Multi-Level Scheduling and Assignment Problems in Broiler Farms

“…GAPs are often solved with the exact method. Small problems, or problems with 200 jobs and 20 employees, are the biggest problems that can be solved by the exact method [2]. Therefore, the heuristics method has been used to solve GAPs [8].…”

“…Each time period has different demands, which behooves the decision-maker to assign the right amount to fulfill all of the demands. The study by Srivarapongse and Pijitbanjong did not discuss this [2]. Moreover, in this article, a new solving method based on an algorithm called Adaptive Large Neighborhood Search (ALNS) will be presented.…”

“…It has a higher number of broiler farmers when compared to other provinces in the region, because it is a province with an area and physical characteristics that are suitable for raising broilers. It is also close to the source of raw materials that are used for broiler-raising, meaning that the cost of raising them is lower than for other provinces in the region [2]. As a result, some of the farmers in the province have turned their attention to broiler farms.…”

“…As we previously mentioned, the problem is a combination of production scheduling and assignment. Srivarapongse and Pijitbanjong have previously discussed he assignment problem in the agricultural industry [2]. They presented a special case of the generalized assignment problem (S-GAP) of assigning the driver to the truck.…”

Modified Differential Evolution Algorithm for a Transportation Software Application

“…For example, Praseeratasan et al [41] proposed the adaptive large neighborhood search (ALNS) algorithm to solve real-world multilevel scheduling and assignment problems, in which ALNS is modified to solve the problem of a broiler farm. Theeraviriya et al [42] proposed the differential evolution (DE) algorithm to solve the location and routing problem; the innovation proposed in that study is that while considering the location and routing problem, fuel consumption is taken into account and DE is proposed to solve a special case of the generalized assignment problem [43]. Praseeratasan et al [44] proposed ALNS to solve a real-world production planning problem.…”