Flow line balancing problem: A survey

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(14) . Battaïa, Olga and Delorme, Xavier and Dolgui, Alexandre and Frederic, Grimaud and Finel, Brigitte Flow line balancing problem: A survey. (2016) In: 2015 International Conference on Industrial Engineering and Systems Management (IESM), 21 October 2015 - 23 October 2015 (Seville, Spain).. .

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(24) Flow Line Balancing Problem: a survey (presented at the 6th IESM Conference, October 2015, Seville, Spain). Olga Battaïa, Xavier Delorme, Alexandre Dolgui, Grimaud Frédéric. Brigitte Finel. LIMOS EMSE Saint Etienne, France {battaia,delorme,dolgui,grimaud}@emse.fr. LGIPM ENIM / UL Metz, France finel@enim.fr. Abstract— Flow lines are widely used in mechanical industry. They consist to a set of workstations through which parts are manufactured. Designing such a line is a very complex problem due to manufacturing and design constraints and to the large number of possible decisions. Usually, the design of this type of production lines involves the selection of the necessary operations (indivisible units of work) to machine a part, the configuration design, the line scheduling. In this paper we present a survey of flow lines balancing problem, their approach and formulation and some solutions to optimize them studied in the literature. A special attention is paid for the assembly lines balancing problems. Keywords—Line balancing, line design, process planning, resource planning, line scheduling.. I.. INTRODUCTION. A flow line consists of a sequence of workstations through which one or more products move one way in order to be processed. Originally, such a type of manufacturing organization was developed, and used to be employed, in order to enhance the performance and reduce the costs in the context of high-volume or mass production [1]. However, nowadays due to using advanced flexible equipment, it becomes available even for low volume production. Nevertheless, such manufacturing systems are still associated with high investment cost. This makes designing a flow line a long-term decision problem. It is a hard task that requires many crucial decisions affecting the manufacturing time and the cost of the product. Since, in practice, it is impossible to solve all these decision problems globally, by a unique optimization procedure or by a single person, the design process is split into several stages [2]. Each stage is characterized by the length of planning horizon and the data required for decision making process. Usually, they are considered iteratively, each previous stage provides the input data for the consequent one. Schematically, the design approach can be presented as follows [3]: 1) 2) 3) 4) 5). product design or product family constitution, process selection, line balancing, line layout design, production scheduling.. Despite the fact that often these stages are dealt with by different deciders, the common design objective trades off between cost, reliability, imbalance between stations, productivity and functionality [4]. To enhance the final line performance, it is necessary to consider several decision problems simultaneously. In this paper, we present an overview of flow lines balancing problems recently appeared in the literature which try to expand the core optimization problem dealing with assigning tasks to workstations by solving it jointly with another decision problems such as process planning or configuration design. In spite of the fact that previously the most attention was paid for the balancing problems concerning the assembly systems, the approaches and formulations of flow line balancing in machining environment are analysed as well. II.. LINE BALANCING. Under the term line balancing various decision problems have been presented in the literature. One of the first line balancing problems was introduced in an assembly environment by Salveson [5]. This formulation is used to be considered as a core line balancing problem, which deals with assigning the set of indivisible units of work (named tasks or operations) to a sequence of lineally ordered workstations. Each task is characterized by its processing time and the set of its predecessors (other operations that must be imperatively completed before). The given order relations among tasks must be respected while the assignment process, the constraints of this type are known as precedence constraints. The operations assigned to the same station are performed sequentially. The sum of their operation times (the workload of each station) cannot exceed a given value c referred to as cycle time. This problem, referred to as Simple Assembly Line Balancing Problem (SALBP) since 1986 due to (Baybars [6] has been intensively studied in the literature. The objective is to minimize the line idle time by reducing the number of workstations (SALBP-1) or the line cycle time (SALBP-2) while meeting the precedence and cycle time constraints [7], [8]. As a result, many exact and heuristic methods were developed. Reviews of the approaches suggested for solving SALBP can be found, for example in [8], [9], [10], [11]. A solution for the basic line balancing problem indicates which tasks should be completed on which workstations. It.

(25) should be noted that the label “balancing” is not always relevant, because often the used objective criteria do not follow to the equally balanced line configurations (having the workstations with the equal loads).. process selection and line balancing, line layout design and balancing, line balancing and task sequencing.. In parallel, many attempts have been undertaken for introducing more general hypotheses in the formulation of SALBP in order to meet real-world decision problems [12], [13]. As a result, a great number of different formulations for the so-called Generalized Assembly Line Balancing Problem (GALBP) have appeared in the literature. Some of them show a similar problem structure as SALBP whereas others deviate considerably [14], for example, a special GALBP called the Transfer Line Balancing Problem (TLBP) [15] where operations can be combined into blocks, each block of operations is processed by a multi-tool unit called a multispindle head. Each tool of a multi-spindle head executes one operation. All tools of a multi-spindle head are activated simultaneously. The blocks at each workstation are executed in series (Fig. 1).. In the next sections we present the recent approaches suggested for solving these problems in the context of assembly, disassembly or machining environment.. Fig. 1. Transfer Line with blocks of operations. 1) the process planning problem, which aims in selecting one assembly process from the set of possible ones, i.e. the set of tasks to be assigned, their processing times and constraints between them; 2) the balancing problem, which assigns the tasks belonging to the selected assembly process with corresponding to the workstations. Recently, flow line balancing problems have been formulated for an AND/OR precedence graph as well. This graph can express more sophisticated precedence requirements like OR, complex AND/OR and XOR relationships between tasks. Such graphs are usually used for disassembly [17], [18]. Each subassembly of the product to be disassembled is represented by an auxiliary node in the AOG. Each disassembly task gives a basic node. Two types of arcs define the precedence relations between the subassemblies and the disassembly tasks. AND-type arcs dictate the normal precedence relation (in bold). OR-type arcs (remaining arcs) permit the selection of any of the successors (Fig. 2).. Blocks. Spindle head. Tools. .... Loading station. .... Workstation. Unloading station. A taxonomy of line balancing problems and their solution approaches in many industrial environments was recently proposed in [16]. This taxonomy is based on five basic elements. Number of lines to be balanced; Task attributes; Workstations attributes;. III.. PROCESS SELECTION AND LINE BALANCING. Generally, line balancing problems are formulated on the basis of the known process for the part manufacturing, i.e. the task set and their characteristics, such as their processing times and precedence relations between tasks, are supposed to be defined. However, in practice, where may exist a number of alternative process sequences for the same product, each implying different precedence requirements as well as different task sets having different task processing times. Several approaches were elaborated for modelling and solving the two following problems simultaneously:. Fig. 2. An And/Or precedence graph.. Constraints to be respected: they are used to distinguish feasible and unfeasible assignments of the tasks to workstations; Objective criteria: criteria which values can be estimated for each feasible assignment of the tasks to workstations; they are used to distinguish the best (optimal) of better (when it is not possible to choose the best ones) assignments of the tasks to workstations between all feasible ones. In this paper, we focus on such flow lines balancing problems which try to expand the core line balancing problem by solving it jointly with other decision problems derived from “neighbour” stages of the line design. It means that besides a solution indicating which tasks should be completed on which workstations, other decisions must be made. Making simultaneously different decisions allows reaching better final line performance and effectiveness. In this paper, three examples of problem aggregation are discussed:. A hypergraph can be also used to solve these two problems together ([19], [20], [21]) where the alternative assembly subsequences are incorporated in the hypergraph by the means of subgraphs, each of them defines a set of tasks and the precedence constraints on this set. Each subgraph corresponds to one available order of subassembly. Different alternative subgraphs can contain the same tasks, but in this case the.

(26) processing times and/or the order relations with another tasks differ from a subgraph to another one, it is assumed that assembly alternatives do not overlap between each other.. In the second case, where some tasks can be processed by a set of alternative equipment, we can distinguish the following initial conditions:. Another way to model OR precedence constraints is to use If-then rules as proposed by Topaloglu [22].. There exist several types of equipment and task processing time as well as cost (if considered) is function on the set of these types. The facilities of each type are available in unlimited quantity. The selection of a facility to be installed on a workstation does not depend on which facility has been chosen for previous workstations and which one will be installed later in the line. This problem was considered mostly for assembly systems ([33], [46], [47], [51]) and with equipment selection([41], [48], [49], [50]). Recently, this problem has been also formulated for machining lines [28], [31]. Note that the setup costs introduced by [52] for a multimodel assembly line balancing problem are equivalent to equipment costs associated with the facilities required on workstations to process each type of product.. The concept of sequence dependent task time increments has been introduced in [23]. Whenever a task j is performed after another task i has been finished, its standard time tj is incremented by a value sdij. This sequence-dependent increment j measures the prolongation of task j forced by the interference with the status of already having processed task i. Since this type of interaction is supposed existing only for a few pairs of tasks, ordering all given tasks is not necessary, while solving such a problem, only the order of interacting tasks should be defined. IV.. LINE LAYOUT DESIGN AND BALANCING. In the core balancing problem, a workstation is an element of the line to which tasks must be assigned and all workstations are assumed to be equally equipped and manned, but in practice each workstation may have a number of parameters, which determine its configuration and make it different from other workstations. These parameters may define: The number of identical parallel workstations (machines or workers) employed [24], [25], [26], [27], [28], [29], [30], [31], [32]. A piece of equipment [28], [33], [34], [35] or a worker selected from a group [36], [37], [38]. Buffer capacity associated with the corresponding workstation [39], etc. In this paper, we focus only on the problem formulations suggested for modelling and solving two following decision problems simultaneously: 1) the equipment selection problem, which aims in selecting the set of facilities to be installed on each workstation; 2) the balancing problem, which assigns the tasks to be processed by the selected equipment at each workstation. This type of decision problem is more relevant for the flow lines in which the facility investment is considerable and can no more be ignored, such as transfer machining lines or robotic assembly systems. As it has been noticed in [40], two different situations can be distinguished: 1) each task can be processed only by a single type of equipment [40] or 2) there exist tasks that can be completed by different types of equipment, but their execution by different types of equipment has impact on their processing time [33], [41], and cost [34], [43]. The first case was discussed in [40]; this situation can be also implicitly expressed if a simple rule is imposed for selecting a resource for each task (e.g. the one with the minimal processing cost or time, [43], [44], [45].. The set of available equipment or a crew of workers with diverse skill levels is limited and different constraints between equipment exist and have to be taken into account. This problem was considered for transfer machining lines with multi-spindle heads in [53], [54], [36], with partitioning problem in [55], [56], [57], and also in [58], [59], [60], [61], [62], [63], [64], [38]. In these cases, if one of these unique resources is allocated to a workstation, then it becomes unavailable for other workstations. The technological compatibility between tasks is defined by means of exclusion and inclusion constraints which indicate if some tasks can be executed by the same equipment or not. The equipment to be used in the line is designed (created) on the basis of the obtained task assignment. Such a formulation is especially relevant for the transfer machines and lines equipped with the multi-spindle heads where the tools to be fixed in each head and consequently its machining function is designed on the basis of the tasks grouped together by the assignment procedure [3], [65], [66], [15], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76]. Note that exclusion constraints forbid the assignment of certain tasks to the same equipment and on the contrary, inclusion constraints compel to assign the tasks required the same resource to the same workstation [77]. V.. LINE BALANCING AND TASKS SEQUENCING. In the case of paced flow lines, a fixed time value, referred to as cycle time, restricts the work content of all workstations. Generally, the same cycle time applies to all stations. The value of cycle time is calculated on the basis of the required line productivity, therefore, if the given cycle time is not respected, the desired productivity rate will be not attained. That is why the most of line balancing problems involve the cycle time constraint. In the basic problem formulation, the order of tasks completion at a workstation is ignored: it is assumed that all auxiliary times are negligible, constant or already included in task processing times. However in many practical cases, for example in electronic industry, in robotic lines or in machining.

(27) lines, this assumption is unfair. In practice, the order of tasks completion at a workstation can have a considerable impact on the total processing time and the workstation load, since the tool changes, the part rotations, the operator or tool movements, etc. can take even longer time than task processing time. Arcus [78] was one of the first to point this limitation, but publications on this matter have been really scarce until recently. Nevertheless, since 2008 some researchers have begun to fill this lack. These studies on line balancing with auxiliary times can be classified in several branches according to the nature of the auxiliary times considered. A. Standard tool changes The first researches that took auxiliary times into account have considered production systems which use a set of tools for processing tasks. Whenever two successive tasks require two different tools, a constant tool change time occurs. In this case, the value of the auxiliary time is assumed to be independent of the operations between which it occurs. A special case of line balancing in which the sequence of tasks is fixed but workstation are not assumed to be laid out sequentially, was studied in [79]. A multiproduct version of this problem was then considered in [46]. Later a column generation approach for another specific case of assembly line balancing problem with tool changes has been proposed in [51]. B. Various setup between successive tasks Researches have then focused on cases where the auxiliary times are not limited to tool changes: the value of the setup time is defined between each pair of successive tasks which could be processed on the same station. In [80] was studied a special case of flexible assembly line balancing problem with sequence-dependent setup times where the precedence graph is a specific in-tree (a comb graph). A more general case was considered in [81]. Authors proposed a 0-1 Integer Linear Program and some heuristics for a SALBP-1 with sequence-dependent setup times (denoted Generalized Assembly Line Balancing Problem with Setups, i.e. GALBPS). They also presented some lower bounds for this problem (a corrigendum has been published in [82] concerning some of these bounds). Various heuristic rules were also evaluated in [83]. A slight extension of this problem (denoted SetUp Assembly Line Balancing and Scheduling Problem, i.e. SUALBSP) was considered in [84] where authors distinguished the value of setup times between two successive operations on the same part, and between the last operation performed on a part and the first operation performed on the same station on the next part. Indeed these setup times can sometimes differ, for example with operators’ displacements or when setup operations can be performed in parallel with part positioning. A cost oriented version of this problem was also studied in [85]. Beside SALBP-1, this type of setup times has also been considered for various other line balancing problems:. [86] proposed a simulated annealing algorithm for SALBP- 2. A genetic algorithm using a dynamic programming decoder was also presented in [87]. The case of two-sided assembly lines was studied in [88]. [89] considered reconfigurable machining lines using CNC machines. A constraint generation algorithm based on a set partitioning model was proposed for this problem in [25], as well as several heuristics and metaheuristics in [28], [29], [30], [26]. A stochastic version of this problem was studied in [90] for manufacturing lines. Finally, multi-model lines were also considered in [91],[92]. In this case setup times depend on both the sequence of operations assigned to each workstation and the sequence of models processed by the line. A similar problem was studied in [93]. C. Variation of processing time due to learning effect or fatigue A different type of auxiliary times, which depends on the position of each task in the sequence of its workstation, was considered in [94]. Such auxiliary times actually correspond to a learning (or a fatigue) effect. Authors presented two multiobjective metaheuristics for an ALBP with sequencedependent setup times between successive tasks and processing times which depend on the position of tasks in the sequence. D. Variation of processing time related to the part state [23] studied another ALBP (denoted Sequence-Dependent Assembly Line Balancing Problem, i.e. SDALBP) where the processing time of tasks can increase if some other tasks have already been performed. So the processing time of a task actually depends on the subset of already executed tasks. In this case, auxiliary times are related to the state of the part which can, for example, prevent some movements and thus complicate the processing of some tasks. E. General case Finally, [19], [20] introduced the alternative subgraphs ALBP (ASALBP). In this problem, authors enumerate all possible sequences of operations and a total processing time is associated with each of them. By this way, all types of auxiliary times can be considered. However in practical cases such an enumeration can lead to very large computational times. As a consequence, [21] have proposed to use heuristic rules for this problem. F. Comparison of the methods All the problems studied in the literature are resolved using different methods. The principal methods are meta-heuristic, Mixed Integer Programming, Graph Approaches, Branch and bound algorithms, Greedy Randomized Adaptive Search Procedures. Many other methods exist (as for example genetic algorithms, exact heuristic algorithms, 0-1 Integer Linear Program or ant colony optimization techniques [96]).

(28) Table 1 gives a comparison of the principal methods and gives the best methods to be used taking into account the problem size and the level of constraints. TABLE 1. PRINCIPAL METHODS. [9] [10]. [11]. Level of constraints. Best method. Low. Meta-heuristic methods and Mixed integer programming (MIP), [30], [68], [69]. [12]. Small. High. Graph approach [60], [61], [71]and Branch and bound [8], [38], [63]. [13]. Medium Large. Low High Low. Greedy Randomized Adaptive Search Procedure (GRASP) in [31], [69]. [14]. Problem size. High. [15]. VI.. CONCLUSIONS. In this paper, we presented a brief survey of flow lines balancing problems while taking into account the assignment of tasks on workstations working in sequence, and some other decisions problems such as process planning or configuration problems to optimize the line performance. The studied problem is very important for the industry and many researchers are working on this domain. The literature is huge. A classification of assembly line balancing problems is presented in [14], state of art in [10] [13]. Some reviews on line balancing can be found in [13] [96] [97] and a taxonomy of line balancing problems in [16]. Therefore this survey is limited to flow line balancing problem. It should be important in the future to take into account new constraints due to lean manufacturing [98], carbon footprint, sustainable development and reduction of energy consumption.. REFERENCES [1] [2]. [3]. [4]. [5] [6] [7]. [8]. Dolgui, A. and Proth, J. (2010). Supply Chain Engineering: Useful Methods and Techniques. Springer. Dolgui, A., Guschinskaya, O., Guschinsky, N., and Levin, G., (2008). Decision making and support tools for design of machining systems. In: Adam, F., Humphreys, P. (Eds.), Encyclopedia of Decision Making and Decision Support Technologies. Vol. 1. Idea Group Inc., pp. 155–164. Battaïa, O., Dolgui, A., Guschinsky, N., and Levin, G. (2012). 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