شکل متمرکز است که در آن توابع -U این مقاله بر ارائه یک مدل جدید برای مسئله بالانس خط مونتاژ
هدف از جنس هزینه، ظرفیت و کیفیت به طور هم زمان در قالب یک مسئله بررسی می شود. بهعلاوه فرض
شده هر وظیفه به مجموعه ای از ابزارآلات نیاز دارد و کیفیت انجام وظایف توسط کارگرها نیز متفاوت
است؛ بنابراین هدف مدل این است که تجهیزات و کارگران بهنحوی به ایستگاه ها تخصیص یابند که
مجموع هزینهی تجهیزات حداقل شود و کیفیت انجام کار در بالاترین سطح ممکن قرار گیرد. علاوه بر این
دو هدف، تعداد ایستگاه ها نیز کمینه میشوند. به این منظور، ابتدا یک مدل برنامهریزی چندهدفه غیرخطی
آمیخته عدد صحیح ارائه می شود. سپس مدل، خطیسازی شده و برای حل مسئله، الگوریتم فراابتکاری
شبیهسازی تبرید و نیز دو حالت بهبودیافته ی آن به کارگیری می شود. دو الگوریتم پیشنهادی شامل یک
برنامه رمزگذاری و رمزگشایی جدید و نیز جستجوی محلی برای تخصیص کارگر به هر ایستگاه است.
برای تعیین حدود پارامترها در این سه الگوریتم از روش طراحی آزمایش استفاده شده و به ازاء ترکیب
پارامترها، حالت های مختلفی برای حل مسئله ایجاد شده است. سپس، بر اساس گراف های موجود در
ادبیات تحقیق مثال های عددی ایجاد و نتایج حل آنها با سه الگوریتم مقایسه و کارایی الگوریتم ها سنجش
می شوند. به علاوه، برای ارزیابی کارایی مدل و الگوریتم پیشنهادی در مسائل واقعی، مطالعه موردی در خط
مونتاژ قطعه نازل انجام گردید که در پالایشگاه های نفت کاربرد دارد. نتایج حل مطالعه موردی و بررسی
شاخص های عملکرد برای آن، بیانگر کارایی و عملکرد بهتر حالتهای بهبودیافته الگوریتم شبیهسازی
عنوان مقاله [English]
Providing a multi-objective programming model for U-shaped assembly line balancing with equipment assignment and task performing quality level
This paper focuses on a novel model of the U-shaped assembly line balancing problem, in which the objective functions include cost, capacity, and quality. It is assumed that each task requires a set of equipment. In addition, the quality of tasks performed by each worker varies. Hence, the purpose of the model is that the total cost of the equipment is minimized and the quality of the work is maximized. Additionally, the number of workstations is minimized. At first, a multi-objective non-linear mixed-integer programming model is provided. Then, the model is linearized, and simulated annealing (SA) algorithm and two of its modified modes have been proposed to solve the problem. The proposed algorithm includes a new encoding/decoding scheme, as well as a local search for assigning the worker to each station. To determine the parameters in three algorithms, the experimental design has been used and various modes have been created by combining the parameters. Moreover, numerical examples were established based on the graphs found in the literature and the solution is compared with three algorithms, revealing the efficiency of each algorithm. Additionally, a case study on the nozzle assembly line in oil refineries was conducted to evaluate the efficiency of the proposed model and algorithm. Results from the case study show that the modified SA algorithms performed better.
Nowadays, assembly lines play a crucial role in the production of standardized and high-volume products. If task allocation to workstations is done without considering the balance of the assembly line, it can lead to high levels of idle time in some workstations and decreased line efficiency. Therefore, assembly line balancing is an important stage in the production process to enhance production line productivity. This study focuses on the single-model U-shaped assembly line balancing problem. Assembly lines can be divided into four categories based on their layout, and in this research, the U-shaped assembly lines are specifically considered. The objectives of this problem include minimizing the number of workstations, minimizing equipment costs, and minimizing the level of work quality deviation at each workstation (equivalent to maximizing work quality). Additionally, constraints related to occurrence, precedence, and capacity, as well as limitations on tool and worker allocations, have been considered in the problem model. In terms of research gaps in this field, it should be noted that in previous studies on U-shaped assembly line balancing problems, objective functions combining cost, capacity, and quality have not been simultaneously addressed within a single problem. Furthermore, simultaneous allocation of workers (based on skill levels) and tools has not been studied in the context of U-shaped assembly line balancing problems.
Materials and Methods
In this study, a nonlinear mixed-integer multi-objective programming model is proposed for balancing a single-model U-shaped assembly line. The problem modeling assumes realistic conditions where each task requires a set of tools, and in this regard, the quality of task execution by workers is considered to be different. The modeling of quality in the assembly line balancing problem (as one of the objective functions) is approached differently compared to previous studies in this field, aiming to minimize the level of work quality deviation in all workstations. Additionally, for solving the problem, the allocation of workers and tools to the workstations is performed based on a neighborhood algorithm, which is a notable innovation in the research. In this study, a modified simulated annealing metaheuristic algorithm is developed with innovations in encoding and decoding procedures to solve the proposed model in three optimization scenarios. To compare the results of these algorithms, numerical examples based on graphs available in the research literature are solved using the three algorithms. Furthermore, a case study is conducted on the assembly line of component δ, which is used in oil refineries, to evaluate the efficiency of the proposed model and algorithm in real assembly lines.
Discussion and Results
In this study, to validate the proposed algorithms, 10 numerical examples of different sizes (small, medium, and large) were designed based on valid graphs available in the research literature. Then, for various parameter values, each problem was solved 10 times using each algorithm, and the results of each algorithm were analyzed. In these examples, the costs of tools and the data related to task quality were randomly generated. Additionally, workers with different skills were defined to perform the tasks. Furthermore, the cycle time proportional to the activity durations was considered. It is observed that in all solved examples, the values of the third objective function (quality objective function) obtained from the third algorithm are better than the values obtained from the first and second algorithms. These results are not unexpected because in the third algorithm, due to the presence of an improvement loop for the third objective function, its value decreases compared to the other two algorithms, resulting in a reduction in the overall objective function and its improvement compared to the other two algorithms. For the cost minimization objective function (first objective function) and the number of workstations minimization objective function (second objective function), the values obtained from the three algorithms are approximately the same, and the difference in the obtained values for the overall objective function is primarily dependent on the value of the quality objective function (third objective function). Additionally, the results of solving the numerical examples show that the third algorithm achieves the best values for the overall objective function (compared to the other two algorithms) on examples with more than 25 activities, indicating that employing a local search for worker allocation in the modified simulated annealing algorithm makes the algorithm stronger and more efficient compared to its classical form.
In this research, the modeling and problem-solving of the U-shaped assembly line balancing problem were investigated considering tool allocation constraints and quality conditions. To this end, a mixed integer nonlinear programming model was presented for the problem, where equipment and workers were simultaneously considered as two objectives in terms of minimizing equipment cost and the level of task quality. In addition to these two objectives, the number of workstations was also minimized. To solve the problem, a metaheuristic algorithm called simulated annealing was employed, as well as two improved versions of it (by introducing innovations in the random allocation of workers to workstations and applying a local search for improving worker allocation). The proposed model was solved using well-known graphs in the literature of assembly line balancing problems (as numerical examples) with the proposed algorithms, and the results obtained from the algorithms were compared and the performance of these algorithms was analyzed and examined.