Optimal workforce assignment to an assembly line
The problem of optimal workforce assignment to an assembly line is extremely important for industrial sector since labor cost takes a high portion of the total cost. Reduction of the labor cost can improve company’s profit and competitiveness. In a considered assembly line, a series of tasks must be executed by human operators. In such case, one of the most important questions that worry managers of an industrial company is the following. How many workers are needed in order to obtain the desired productivity?
An answer to this question can be quickly found by analyzing the tasks. However, since lower labor cost means higher profit margin and the possibility to reduce the selling price of the final product, it is interesting to find the minimal number of workers, which still satisfies the desired productivity.
In short, the problem under study can be described as follows. An assembly line consisting of several stations has different tasks to be executed by identical workers. The line is paced, which means that all unfinished products move towards the following workstation simultaneously after the same time interval. This time interval, called cycle time, is equal to the total processing time of the slowest, called “bottleneck”, station. Thus, the line’s cycle time equals the time spent to obtain a new unit of the final product. It is the cycle time that defines the line’s productivity. The smaller is the cycle time, the higher is the number of products manufactured per period of time. If the productivity is given, the cycle time can be easily calculated: total annual working time of the assembly line is divided by the desired annual productivity. The obtained value of the cycle time must not be exceeded at any station. If at some station the total processing time exceeds the cycle time – the line automatically produces less units of product per period of time.
The processing time of a task is inversely proportional to the number of workers assigned to it. It is a principle of the famous saying: “two heads are better than one”. If, for example, one worker can complete a certain task in 8 minutes, two workers would finish it in only 4 minutes, while three workers would do this task in, say, 3 minutes. Of course, there are certain limits determined by technological requirements and common sense. Some tasks must be done by at least two workers. At the same time, we cannot assign more than four workers to any task. Once a task is finished, a worker can move to another task at any station. One can notice that in order to respect the cycle time and therefore the line’s desired productivity, we may assign as many workers as possible to a task, because in such way the task will be finished earlier. There will be less chance to exceed the cycle time. But on the other hand, if we assign many workers to each task, the total number of workers employed in the line would be too big and, therefore, labor cost would be high as well. Assignment process is not obvious – there are many tasks, technological restrictions like precedence relations, and numerous combinations to consider. Our goal is to find such an assignment of workers to tasks, in which the total number of workers employed in the line is minimized.
In order to solve this problem, we used a mixture of an exact method and three heuristics. In short, exact methods guarantee the solution’s optimality but may take a lot of computational time. On the other hand, heuristics, while not guaranteeing the optimality, may find a good solution quickly. The methods were applied to both benchmark problem instances and an industrial case from the European project amePLM.
Our solution approach allows industrial managers to obtain an optimal or near-optimal assignment of workers to tasks of an assembly line. Computational experiments demonstrated that the instances with up to 20 tasks and 15 workers can be solved to optimality in a reasonable time on a standard computer. They also showed that the quality of the heuristic solutions for the industrial case with 170 operations is sufficiently good.
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