An MIP Approach to the U-line Balancing Problem With Proportional Worker Throughput

One of the major challenges faced by manufacturing companies is to remain competitive in dynamic environments, where fluctuations in customer demand and production rates require systems capable of adapting in a practical and economical way. A U-shaped production cell is considered one of the most flexible designs for adapting the workforce level to varying conditions. However, re-balancing efforts are time consuming and often require a new work allocation and line design. In this paper, a two-stage MIP model to determine the best cell design under varying workforce levels is proposed. The model seeks to maintain proportionality between throughput and the number of workers. Computational experiments considering various line configurations (up to 19 stations) and workloads (up to 79 tasks) are performed. The results show the proposed algorithm provides excellent results for all small and medium size problems addressed in this study, as well as for certain configurations of large problems. This approach can be used to generate lookup tables of line designs to help with quick reallocation of worker assignments on the shop floor and with minimal disruption

Keseimbangan Lintasan Tipe U-line Assembly pada Perakitan Pompa Air

Saat ini, secara umum banyak perusahaan dihadapkan pada masalah meminimalkan beban kerja yang tidak seimbang dan jumlah stasiun kerja dengan batasan proses serta lokasi yang ada. Banyak penelitian yang telah dilakukan untuk menyelesaikan permasalahan di atas. Penelitian ini bertujuan untuk membandingkan keseimbangan lintasan straight line dan tipe U-line menggunakan model mixed integer programming pada suatu perakitan pompa air. Model mixed integer programming diselesaikan dengan menggunakan LINGO. Hasil penelitian menunjukkan tipe U-line memberikan hasil yang lebih baik dibandingkan straight line berdasarkan jumlah work station dan lebih efisien secara signifikan

The Application of Single-Pass Heuristics for U-Lines

U-lines have been adopted in many manufacturing settings as part of JIT implementation. In this paper, we examine the applicability of existing straight-line heuristics for obtaining a balance on a U-line. We modify 13 single-pass heuristics and study the effectiveness of various heuristics under different problem conditions. An extensive computational study is carried out to help identify the best heuristics. In addition, we compare recent U-line procedures with a single-pass heuristic using some literature problems. Based on a single-pass heuristic, we compare the configurations of a straight- and U-line

Balancing of parallel U-shaped assembly lines

Copyright © 2015 Elsevier. This is a PDF file of an unedited manuscript that has been accepted for publication in Computers & Operations Research (doi: 10.1016/j.cor.2015.05.014). As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Please cite this article as: Ibrahim Kucukkoc, David Z. Zhang, Balancing of parallel U-shaped assembly Lines, Computers & Operations Research, http://dx.doi.org/10.1016/j.cor.2015.05.014A new hybrid assembly line design, called Parallel U-shaped Assembly Line system, is introduced and characterised along with numerical examples for the first time. Different from existing studies on U-shaped lines, we combine the advantages of two individual line configurations (namely parallel lines and U-shaped lines) and create an opportunity for assigning tasks to multi-line workstations located in between two adjacent U-shaped lines with the aim of maximising resource utilisation. Utilisation of crossover workstations, in which tasks from opposite areas of a same U-shaped line can be performed, is also one of the main advantages of the U-shaped lines. As in traditional U-shaped line configurations, the newly proposed line configuration also supports the utilisation of crossover workstations. An efficient heuristic algorithm is developed to find well-balanced solutions for the proposed line configurations. Test cases derived from existing studies and modified in accordance with the proposed system in this study are solved using the proposed heuristic algorithm. The comparison of results obtained when the lines are balanced independently and when the lines are balanced together (in parallel to each other) clearly indicates that the parallelisation of U-shaped lines helps decrease the need for workforce significantly.Balikesir UniversityTurkish Council of Higher Educatio

Mixed-integer linear programming approach to U-line balancing with objective of achieving proportional throughput per worker in a dynamic environment

One of the major challenges of manufacturing companies is to remain competitive in a very dynamic environment dictated by fluctuations in production rate and customer demand. These challenges may be attributed to frequent changes in customer expectations, unsteady economic conditions or failure to reach the projected throughput due to inefficiencies in production systems. Survival in such a dynamic environment is contingent on implementing manufacturing systems that are able to adapt to change quickly and economically. The U-Shaped production cell is considered to be one of the most flexible techniques for changing the number of workers in the cell to match cell cycle time to planned cycle time. However, companies currently use a trial-and-error method to develop walk-paths. It is a very iterative and time consuming process that does not always guarantee an optimal solution. Walk-paths need to be performed for all possible number of workers. Fluctuations are adapted to by altering only the number of workers and the worker’s walk-path without changing the number of stations and task allocations. Selecting the best configuration (i.e. optimal number of stations and task allocation) is dependant upon the linearity metric i.e. the measurement of the proportional throughput per worker. Designing the production cell by considering the linearity helps to keep direct labor costs per unit at a minimum for any number of workers employed. This thesis proposes a mixed integer linear model for U-shaped lines that determines the best cell configuration for various number of workers with the objective function of achieving proportional throughput per worker and decreasing the iteration time. The problem originated at Delphi Corporation but has been generalized to be applicable to other Lean systems. The model has been constructed using OPL Studio 3.7

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

Two-sided assembly lines are especially used at the assembly of large-sized products, such as trucks and buses. In this type of a production line, both sides of the line are used in parallel. In practice, it may be necessary to optimize more than one conflicting objectives simultaneously to obtain effective and realistic solutions. This paper presents a mathematical model, a pre-emptive goal programming model for precise goals and a fuzzy goal programming model for imprecise goals for two-sided assembly line balancing. The mathematical model minimizes the number of mated-stations as the primary objective and it minimizes the number of stations as a secondary objective for a given cycle time. The zoning constraints are also considered in this model, and a set of test problems taken from literature is solved. The proposed goal programming models are the first multiple-criteria decision-making approaches for two-sided assembly line balancing problem with multiple objectives. The number of mated-stations, cycle time and the number of tasks assigned per station are considered as goals. An example problem is solved and a computational study is conducted to illustrate the flexibility and the efficiency of the proposed goal programming models. Based on the decision maker's preferences, the proposed models are capable of improving the value of goals

Metaheuristic approach to solving U-shaped assembly line balancing problems using a rule-base coded genetic algorithm

Includes bibliographical references.2015 Summer.The need to achieve line balancing for a U-shaped production line to minimize production time and cost is a problem frequently encountered in industry. This research presents an efficient and quick algorithm to solve the U-shape line-balancing problem. Heuristic rules used to solve a straight line-balancing problem (LBP) were modified and adapted so they could be applied in a U-shape line-balancing problem model. By themselves, the heuristic rules, which were adapted from straight-line systems, can produce good solutions for the U-shape LBP, however, there is nothing that guarantees that this will be the case. One way to achieve improved solutions using heuristic rules can be accomplished by using a number of rules simultaneously to break ties during the task assignment process. In addition to the use of heuristic and simultaneous heuristic rules, basic genetic operations were used to further improve the performance of the assignment process and thus obtain better solutions. Two genetic algorithms are introduced in this research: a direct-coded and an indirect-coded model. The newly introduced algorithms were compared with well-known problems from literature and their performance as compared to other heuristic approaches showed that they perform well. The indirect-coded genetic algorithm uses the adapted heuristic rules from the LBP as genes to find the solutions to the problem. In the direct-coded algorithm, each gene represents an operation in the LBP and the position of the gene in the chromosome represents the order in which an operation, or task, will be assigned to a workstation. The indirect-coded genetic algorithm introduces sixteen heuristic rules adapted from the straight LBP for use in a U-shape LBP. Each heuristic rule was represented inside the chromosome as a gene. The rules were implemented in a way that precedence is preserved and at the same time, facilitate the use of genetic operations. Comparing the algorithm’s results with known results from literature, it obtained better solutions in 26% of the cases; it obtained an equivalent solution in 62% of the cases (not better, not worse); and a worse solution the remaining 12%. The direct-coded genetic algorithm introduces a new way to construct an ordered arrangement of the task assignation without violating any precedence. This method consists of creating a diagram that is isomorphic to the original precedence diagram to facilitate the construction of the chromosome. Also, crossover and mutation operations are conducted in a way that precedence relations are not violated. The direct-coded genetic algorithm was tested with the same set of problems as the indirect-coded algorithm. It obtained better solutions than the known solutions from literature in 22% of the cases; 72% of the problems had an equivalent solution; and 6% of the time it generated a solution less successful than the solution from literature. Something that had not been used in other genetic algorithm studies is a response surface methodology to optimize the levels for the parameters that are involved in the response model. The response surface methodology is used to find the best values for the parameters (% of children, % of mutations, number of genes, number of chromosomes) to produce good solutions for problems of different sizes (large, medium, small). This allows for the best solution to be obtained in a minimum amount of time, thus saving computational effort. Even though both algorithms produce good solutions, the direct-coded genetic algorithm option requires less computational effort. Knowing the capabilities of genetic algorithms, they were then tested in two real industry problems to improve assembly-line functions. This resulted in increased efficiency in both production lines

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.IntroductionNowadays, 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 MethodsIn 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 ResultsIn 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.ConclusionIn 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

A Novel Work-Sharing Protocol for U-Shaped Assembly Lines

Companies worldwide try to employ contemporary manufacturing systems that can cope with changes in external competitive environments and internal process variability. Just In Time (JIT) philosophy helps achieve the required resilience by its policy of having people, machines, and material just-in-time for any given process. U-shaped assembly lines (U-lines) are used to implement JIT principles. Another principle that helps achieve competitive advantage by developing a flexible workforce that responds efficiently to change is that of work-sharing. Operators share work and help each other in a dynamic and floating way, requiring little management effort to distribute workload amongst operators, or balance the assembly line. The aim of this work is to develop an effective work-sharing protocol for U-shaped assembly lines that will provide the combined advantages of U-lines and work-sharing principles. The new protocol is based on two ideas from literature - the Cellular Bucket Brigade (CBB) system, and the Modified Work-Sharing (MWS) system. To keep the focus on developing the protocol, the scope of this work was limited to two worker systems. The methodology used is to model the protocol and U-line system as a discrete event simulation model, and then use an optimization model to maximize throughput and find optimal buffer locations and levels. A physical simulation experiment was conducted in the Toyota Production Systems lab at RIT to validate the model. Once validated, computer simulation experiments were run with industry data, and results obtained were compared with existing protocols from literature. It was found that the new protocol performed at least as well as the CBB protocol, improving the output by an average of 1%, for the scenarios tested. Increase in processing speed variability as well as larger variation among workers were found to negatively impact the performance of the protocol. The results were analyzed further to understand why these factors are significant, and why there are anomalies and patterns, or lack thereof. Finally, limitations of the protocol, and opportunities for future research in the field are presented. Major limitations of the protocol are that it is difficult to comprehend, and the assumption of an assembly line divided into equal tasks is not practical in the industry

Bulanık aksiyomatik tasarım ve hedef programlama ile bir ürün tasarımı : içecek üretim tesisinde bir uygulama

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Anahtar kelimeler: Ürün tasarımı problemi, hedef programlama, bulanık aksiyomatik tasarım tekniği Bu tez çalışmasında içecek sektöründe faaliyet gösteren bir firmanın ürün tasarım problemi ele alınarak çözülmüştür. Firma başlangıçta bir parti olarak üreteceği ve sonrasında seri üretimine devam edip etmeyeceği belirsiz olan bir içeceğin şişesinin tasarım problemi ile karşı karşıya kalmıştır. Firma ilgili ürün için üretim hattında kalıp ve reçete yatırımı yapmak durumunda kalırsa, birim ürüne ait sabit maliyetler artacağı için proje kârlı bulunmayacaktır. Bu sebeple firma, mevcut üretim hattı spesifikasyonlarını değiştirmeden müşterisinin talebine cevap vermek istemektedir. Bunu yapabilmek için de üretimini yapacağı ürüne ait şişenin tasarım problemini mevcut bir şişe tasarımı üzerinden yola çıkarak çözmeye karar vermiştir. Yeni şişe tasarım problemi, mevcut hat spesifikasyonlarında değişikliğe neden olmaması, üretim hızını belirli bir seviyede tutması ve aynı zamanda müşteri beğenisine de hitap etmesi olmak üzere üç hedefe sahiptir. Bu hedeflerden müşteri beğenisi, insanın doğal karar verme süreçlerini daha iyi ifade edebilmesi bakımından bulanık verilerle ifade edilmiştir. Çalışmada müşteri beğenisine ait bulanık veriler bulanık aksiyomatik tasarım (BAT) tekniği ile ele alınmış ve elde edilen değerler, söz konusu üç hedefi de dikkate alan bir karma tamsayılı doğrusal olmayan hedef programlama modelinde kullanılmıştır. Bu çalışmayı yapmadan önce, yeni şişe tasarım projeleri deneme yanılma yöntemi ile yapılmaktaydı. Kabaca hesaplanan şişe parametreleri terdarikçiye verilerek çizim yaptırılmakta, yaptırılan çizim onaylanırsa deneme kalıbı satın alınmaktaydı. Fabrikaya gelen deneme kalıbında preformlar şişirilmekte ve bunlara dolum hattında su doldurularak test edilmekteydi. Bu test sonucunda tedarikçinin tasarımına onay verilmekte veya düzeltmeler talep edilmekteydi. Söz konusu aşamalar onay alana kadar devam etmekteydi. Bu tezde önerilen çözüm yaklaşımı sayesinde, problem analitik olarak ele alınmış, deneme yanılma yöntemi terk edildiği için de zamandan, iş gücünden, enerji, kalıp ve preform maliyetlerinden tasarruf sağlanmıştır. Ürün tasarımı problemi için aksiyomatik tasarım ve hedef programlama yaklaşımlarının ayrı ayrı kullanıldığı çalışmalara literatürde rastlamak mümkün olsa da bu çalışmada birlikte kullanılan BAT ve doğrusal olmayan hedef programlama yöntemlerinin literatürde daha önce hiç birlikte kullanıldığı bir çalışmaya rastlanmamıştır. Bu açıdan çalışma, ürün tasarımı probleminin ele alınışı ve çözümüyle farklı bir bakış açısı sunmakta ve literatüre katkı sağlamaktadırKeywords: Product design problem, goal programming, fuzzy axiomatic design technique In this thesis, a product design problem of a company operating in the beverage sector was handled and solved. The firm was faced with a beverage bottle design problem, which is unclear whether it would continue mass production after the first batch of production. If the company has to make mold and recipe investments on the production line for the product concerned, the project will not be profitable as the fixed costs for the unit product will increase. Therefore, the company wants to respond to the customer's demand without changing the existing production line specifications. In order to do this, it decided to design the bottle of the product to be produced based on an existing bottle design. The new bottle design problem has three goals: not changing the current line specifications, keeping the production speed at a certain level, and also considering customer liking. Customer liking was expressed by fuzzy data to better express the natural decision-making processes of human. In this study, fuzzy data belonging to customer liking was defuzzificated by the Fuzzy Axiomatic Design (FAD) technique and the obtained values were used in a mixed integer non-linear Goal Programming model which also took into consideration these three objectives. Before doing this study, new bottle design projects had been carried out by trial and error method. Roughly determined bottle parameters had been given to the supplier. If the drawing was approved, the trial mold had been purchased. The preforms had been blowing by the test mold and they had been tested in the line filling with water. As a result of this test, the supplier's design had been approved or corrections had been requested. These stages continued until the approval had been received. Under favour of proposed solution approach in this thesis, the problem has been dealt with analytically, and since the trial and error method was abandoned, time, labor, energy, mold and preform costs were saved. Although it is possible to find the studies which uses the Axiomatic Design and Goal Programming approaches separately in the literature, there is no study which uses FAD and non-linear Goal Programming approaches together in the literature. In this respect, this thesis presents a different perspective with the proposed solution approach of the product design problem and contributes to the literature