Two-Stage orders sequencing system for mixedmodel

IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Two-Stage orders sequencing system for mixedmodel assembly Recent citations - Damian Krenczyk et al To cite this article: M Zemczak et al 2015 IOP Conf. Ser.: Mater. Sci. Eng. 95 012130 View the article online for updates and enhancements. This content was downloaded from IP address 148.251.232.83 on 05/12/2018 at 07:14

Two-Stage orders sequencing system for mixed-model assembly M Zemczak 1, B Skołud 2 and D Krenczyk 2 1 University of Bielsko-Biala, Faculty of Mechanical Engineering and Informatics, Department of Production Engineering, Willowa 2, 43-309 Bielsko-Biala, Poland 2 Silesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing Systems, Konarskiego 18A, 44-100 Gliwice, Poland E-mail: mzemczak@ath.bielsko.pl Abstract. In the paper, the authors focus on the NP-hard problem of orders sequencing, formulated similarly to Car Sequencing Problem (CSP). The object of the research is the assembly line in an automotive industry company, on which few different models of products, each in a certain number of versions, are assembled on the shared resources, set in a line. Such production type is usually determined as a mixed-model production, and arose from the necessity of manufacturing customized products on the basis of very specific orders from single clients. The producers are nowadays obliged to provide each client the possibility to determine a huge amount of the features of the product they are willing to buy, as the competition in the automotive market is large. Due to the previously mentioned nature of the problem (NP-hard), in the given time period only satisfactory solutions are sought, as the optimal solution method has not yet been found. Most of the researchers that implemented inaccurate methods (e.g. evolutionary algorithms) to solving sequencing problems dropped the research after testing phase, as they were not able to obtain reproducible results, and met problems while determining the quality of the received solutions. Therefore a new approach to solving the problem, presented in this paper as a sequencing system is being developed. The sequencing system consists of a set of determined rules, implemented into computer environment. The system itself works in two stages. First of them is connected with the determination of a place in the storage buffer to which certain production orders should be sent. In the second stage of functioning, precise sets of sequences are determined and evaluated for certain parts of the storage buffer under certain criteria. 1. Introduction For many years, studies have been conducted on the issue of the optimization of scheduling and resource allocation [1-3]. Optimization problems, both continuous and discrete groups are classified as NP-hard problems (problems for which finding a solution in polynomial time is not possible), due to their complexity, theoretical and computational. This problem is often encountered in the case of complex production systems, where on limited resources certain technical good must be produced within a given time. Scheduling is supposed to determine the sequence of production, which will utilize the production capacity remaining at the disposal of the company in the most of the advantageous way. Regardless of the specifics of the production system, its structure and organization, Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd 1

before the adoption of new orders review of the current state of the system is required, based on which the decision whether and when a new order can be accepted for implementation is taken [4]. Computational complexity and size of the practical problems clearly eliminates from consideration the exact algorithms (due to the fact that the solution must be given within the prescribed time window), leaving only the use of heuristic algorithms that solve the problems in a short, assumed time and with satisfactory accuracy. However, with assuming appropriate restrictions, a simpler set of rules controlling schedules can be selected to be used. The problem of scheduling jobs on the production lines has been formulated by [5] as MILPA (Mixed Integer Linear Programming), but at the outset the author observed that the complexity of the problem grows exponentially with the number of tasks to rank. For this reason, MILPA algorithms can be used only for small problems. In literature many attempts to solve scheduling problems, e.g. using genetic algorithms [6] can be found. Unfortunately, as any solution, they have their advantages and disadvantages. In most cases, obtaining the best effect requires a time-consuming "tuning" of the algorithm to a class of selected problems. Many authors carried out experiments with the use of algorithms based on heuristic methods [2, 7], wherein it should be noted that the studies were covering the small amount of data (for data with a greater extent, the solution couldn t be found within a reasonable time). Research on heuristic algorithms, providing solutions for problems where it is impossible or inefficient to use exact solutions, are rapidly developing field of science. Suitable arrangement of the tasks leads to many benefits including better utilization of material resources (in this case, devices and tools), ensuring adequate plant production capacity, saturation of the production line, the appropriate management of employee time, as well as his more efficient operation. This translates directly into increased productivity and a reduction in unit costs, on the basis of economies of scale. Furthermore it should be noted that automotive companies are themselves interested in the search for solutions to the problem of scheduling, which can be seen, for example on the base of ROADEF Challenge 2005 competition announced by the French Association for Operations Research and Decision Support (fr. Société française de Recherche Opérationnelle et d'aide à la Décision) and sponsored by the RENAULT group, whose aim was to develop a new universal method for scheduling. 2. Algorithms used for solving scheduling problems Evolution Methods for solving scheduling problems can be generally divided into exact and approximate methods (figure 1). Methods used for scheduling problems solving Exact methods Approximate methods Branch&Bound Controlled revision Dynamic programming Structural algorithms Priority algorithms Insertion technique based algorithms Local search algorithms Simulated annealing Genetic algorithms Tabu search Scatter search Figure 1. Division of methods used for scheduling problems solving. 2

The exact methods they can be divided into e.g. methods based on the principle of branch and bound, the method of controlled revision, methods based on dynamic programming scheme. Due to the aforementioned disadvantages and problems connected with their implementation to more complex tasks - the exact algorithms will not be further discussed. Among the approximate algorithms two major groups can be mentioned: structural algorithms that construct a solution to the problem and local search algorithms. Structural algorithms design is significantly dependent on the specifics of the problem. These algorithms can be divided into priority algorithms and algorithms that use the socalled insertions technique. The first rank the relative priorities of the tasks with the use of the rules of priority. The second group of algorithms, before ranking the tasks, creates a set of test solutions by inserting a task into a test position in current solution (constructed in the previous iteration of the algorithm). Among the selected test solutions, the best solution (in terms of objective function values) is chosen, which at the same becomes the base solution in the next iteration of the algorithm. Local search algorithms start operation from initial solution provided by the structural algorithm and work iteratively to improve the solution, using the techniques of reviewing the solution space. Among the most effective algorithms in this group simulated annealing, genetic algorithms, scatter search algorithms and tabu search algorithms can be specified. Presented methods are also implemented with the use of simulation software in order to visualize the solutions [8]. 3. Scheduling problems description Almost every scheduling problem can be described as a pair (X, F), where X is the set of feasible solutions to the problem (wherein, where X 0 is the set of all solutions), F is the criterion of optimization (objective function). Solutions space is given explicitly only in a few cases, usually it is a set of independent variables, which can take the values of the specified ranges. One of the basic concepts of local search algorithms is the movement. It can be described as an activity involving the transition between the two solutions and presented as a function of v(x): X X, where v(x): x v X, x v x. Solution x v, resulting from movement v is called the neighbouring solution of solution x. For each solution x X, a set of movements V(x) which generates a neighbourhood N(x) (1): N x x : V x (1) of solution x can be defined. The definition of a set of movements and neighbourhood depends on the analysed problem and an algorithm used for its solutions. Another important element is the local optimality of the solution. In the literature, in the context of local search algorithms the term "best solution" found by the algorithm often appears. This concept is the result of a mental shortcut pointing to the solution generating the smallest value of the objective function from all the solutions generated by the algorithm. 4. Structure of the system For the purpose of the research, a structure of the system, corresponding to a real production system has been selected. The system consists of an input buffer, in which orders are stored before being admitted to assembly processes, and an assembly line, on which assembly operations are performed. Due to the fact, that assembly operations are different on each assembly station, their number for the purpose of the research has been limited to 50. The assembly stations on which the biggest differences in labor-consumption have been identified during the research in a company have the biggest impact on the production output. It should be noted, that even after solving major assembly line balancing problems, current assembly systems are still not flexible enough to adapt quickly to the exact version of the product that arrives, i.e the tact time is the same for all the stations in assembly line [3]. It could be observed, especially in car manufacturing companies, that in almost each and every single car the customer may order one of hundreds possible options. If the production plans were stable and not influenced by disturbances, the orders could be grouped and produced in batches. Each batch could have specific takt time, also dynamic assembly line balancing could be performed for each one. This 3

condition, however is rarely met, due to the fact that each time a batch is changed the whole system would have to be emptied and adapted to the requirements of the next production batch. This would, however, decreased the systems efficiency, as usually single assembly line consists of more than a hundred assembly stations. Moreover, batch production usually limits the number of possible products versions. Plant managers usually seek to utilize production resources remaining at their disposal to the maximum extent. The assembly system, chosen for the purpose of presenting the orders sequencing system has been presented on figure 2. Figure 2. General overwiev of a selected assembly system. As mentioned before, the system consists of an input buffer and a single assembly line. The input buffer is organized in four lines, on which the orders, transported via transporting system from the earlier stage of the manufacturing processes, are stored. 5. Orders sequencing software For the purpose of sequencing and because of the fact that almost each car is different, data of each order is kept in a shared database. Data itself is created automatically after the order is taken from the client in the place of sale (usually a new record, containing information about the selected version, engine, options, etc.). The system itself performs sequencing in two stages (figure 3). Line 1 K 1 K 2 K 3 K 4 Line 2 Line 3 Line 4 SE A Assembly line A Database request Input buffer lines Sequencing Assembly line STAGE 1 Division of orders between lines STAGE 2 Creation of a closed set of orders Projecting and evaluation of sequences Figure 2. Main steps performed in orders sequencing system. In the first stage the request for the data is sent, and according to the information obtained from the database orders are assigned to specific sets (K) and then sent to appropriate lines of the input buffer. The idea of the classification is quite simple, according to product labor-consumption matrix. Closed 4

set of orders, with the information about the lines of the buffer they are placed in has been presented in table 1. Table 1. Closed set of orders stored in appropriate lines of the buffer. Buffer line number Orders 1 Z6, Z28, Z27, Z26, Z25, Z24, Z23, Z44, Z43, Z42, Z41, Z40 2 Z1, Z3, Z17, Z16, Z15, Z14, Z13, Z12, Z11, Z32, Z31 3 Z8, Z2, Z30, Z10, Z9, Z4, Z19, Z18, Z35, Z34, Z33 4 Z5, Z39, Z38, Z37, Z36, Z22, Z21, Z20, Z7, Z29, Z45 In the second stage, for orders in a closed set projecting and evaluation of sequences according to selected criterion is conducted. The effect of sequencing and evaluation in a form of best chosen sequence has been presented in table 2. The criteria used for the determination of the best sequence were the number of cycle times exceeded on the assembly line stations (ExC) and the average exceeding of the cycle time (AvEx). Table 2. Best projected sequence according to selected criterion. Best projected sequence Z5,Z39,Z6,Z8,Z2,Z38,Z37,Z36,Z22,Z30,Z1,Z21,Z3,Z17,Z20,Z7, Z29,Z10,Z16,Z45,Z15,Z14,Z28,Z27,Z13,Z26,Z12,Z11,Z25,Z24,Z 23,Z32, Z31,Z9, Z4,Z44,Z43,Z19,Z18,Z42,Z41,Z35,Z40,Z34,Z33 Criterion ExC Criterion AvEx 30 1,57 In the software there is also a possibility to generate schedules, on which assembly stations on which exceeding cycle times occurs may be observed. The example of such schedule has been presented on figure 4. Figure 4. An example of schedule of projected sequence for a closed set of orders. 5

6. Conclusions Application of advanced heuristic methods is not always practical, as there are many problems connected with the determination of quality of obtained solutions. However, the size and complexity of current scheduling problems eliminates the exact methods. One of the ways of solving these problems is connected with the possibility of joining both, exact and heuristic methods in problems solving. In presented paper, such solution has been presented. The first part of the system, basing on the simple rules determines the place in which order should be stored before admitting it to the assembly system. In the second step, basing on heuristic methods, the sequence is projected and evaluated according to selected criteria, the best is chosen and admitted to the assembly. This way, when problem is divided into smaller issues, the quality of solutions may be better. Many experiments are planned in order to prove the value of presented approach to scheduling problems solving. Acknowledgement This paper is a part of extensive work on tools for supporting production planning in mixed-model assembly systems. References [1] Janiak 1991 A Single machine scheduling problem with a common deadline and resource dependent release dates European Journal of Operational Research 53/3 pp 317-325 [2] McMullen P and Frazier G V 2000 A simulated annealing approach to mixed-model sequencing with multiple objectives on adjust in time line IIE Transactions 32/8 pp 679-686 [3] Zemczak M and Krenczyk D 2012 Formulation of a sequencing problem in a mixed-model production system Journal of Machine Engineering 12/3 pp 45-51 [4] Krenczyk D and Zemczak M 2014 Practical example of the integration of planning and simulation systems using the RapidSim software Advanced Materials Research 1036 pp 834-839 [5] Frey G 2000 Assembly line sequencing based on Petri-net T-invariants Control Engineering Practice 8/1 pp 63 69 [6] Srikanth K and Saxena B 2004 Improved genetic algorithm for the permutation flowshop scheduling problem Computers & Operations Research 31/4 pp 593-606 [7] Palshikar G K 2001 Simulated Annealing: A Heuristic Optimization Algorithm Dr. Dobb's Journal 26/9 pp 121-124 [8] Zemczak M 2012 Computer aided simulation of a mixed-model production system Selected Engineering Problems 3 pp 213-218 6