Abstract
This research aims at solving the special case of multistate assignment problem. The problem includes many special characteristics which are not normally included in the assignment problem. There are many types and conditions of vehicles included in the planning and different road conditions of traveling, which would have different effects on fuel consumption, which is the objective function of the study. The proposed problem is determined as a large and complicated problem making the optimization software unable to find an optimal solution within the proper time. Therefore, the researchers had developed a method for determining the optimal solution by using particle swarm optimization (PSO) in which the methods were developed for solving the proposed problem. This method is called the modified particle swarm optimization (modified PSO). The proposed method was tested with three groups of tested instances, i.e., small, medium, and large groups. The computational result shows that, in small-sized and medium-sized problems, the proposed method performed not significantly different from the optimization software, and in the large-sized problems, the modified PSO method gave 3.61% lower cost than the cost generated from best solution generated from optimization software within 72 hours and it gave 11.03% better solution than that of the best existing heuristics published so far (differential evolution algorithm).
Highlights
An appropriate vehicle was assigned to transport the chickens directly from its farms to the egg farms, for the purpose of finding the answer with the lowest assignment cost. e mathematical models for the Mathematical Problems in Engineering multistage assignment problem were developed which are suitable for the case study. en, the estimating methods to find the optimal answer were developed by employing the particle swarm optimization (PSO)
Conclusion and Suggestions e case study problem was the assignment consisting of the main costs incurred from chicken transportation and depended on the difference of truck types using to deliver throughout the road conditions, which affected the fuel costs as well
In which problem-solving with the exact method either the branch and bound method or the Lingo program could not be conducted in a short time. erefore, problem-solving using alternative methods or the heuristics method was the appropriate choice for resolving this problem. e heuristics used in this study would use the particle swarm optimization (PSO) method
Summary
Assignment problem (AP) means the problem of the task allocation to an agent. Each job is different and each employee has different expertise, resulting in unequal time spent in working, and the cost of assigning jobs to each one is different as well. erefore, the problem is how to assign the task so that the total cost shall be the lowest, with an important condition that the assignment must be one on one basis. Multistage assignment problem was studied by considering the appropriate vehicle type suitable for chicken transportation straight from the chicken farms to the egg farms, and the limitations are listed as follows:. Erefore, the researcher aims to study the multistage assignment problem by considering the appropriate vehicle type to transport chickens straight from the chicken farms to the egg farms for the cheapest total cost. This assignment is the multilevel assignment beginning by assigning the truck type, which. Each type of truck has a different capacity to transport chickens and different fuel consumption rate, resulting in different assignment costs. When considering the fuel used in both directions, which is 2.688 liters and 2.548 liters, it can be seen that the route from Farms 6–3 is longer than the route from Farms 2–6, but less fuel is used
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