# High-Mix Low-Volume Flow Shop Manufacturing System Scheduling

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3 Scheduling algorithm assigns machines on each of the stages to the production orders that left to be processed on these stages according to the selected criterion. Step 1, Time = 0 All production orders left to be processed on each of the stages. The production schedule (assignment of the machines to the production orders) in Time = 0 is depicted in igure 2. Step n, Time = N ig. 2 Production schedule in Time = 0 Production schedule is recalculated each time when new production order enters to the production system or when any of the production orders is completely processed at any of the stages. Production order number 3 is completely processed at stages number 1, 2, 3 and 4 and left to be processed at stages 5 and 6. Production order number 2 is completely processed at stages number 1, 2 and 3 and left to be processed at stages 4, 5 and 6. All other production orders still have to be processed at stages 1,2,3,4,5 and 6. Recalculated production schedule in Time = N is depicted in igure ALGORITHM PROPOSALS The scheduling problem may be described in general as follows: K - number of production stages, s = 1 K - number of product families, M s - number of machines at stage s - production order of product family f - number of products of production order f that left to be processed on stage s - job - production orders divided into production batches, i = 1 O f / B f - batch size of production order of product family f - processing time of production order of product family f on stage s - number of machines at stage s assigned to the jobs of product family f Since the priorities of the families are equal an assumption M >, s have been made to ensure that at least one job s of each family can be produced at each stage at a time. Considering processing times, batch sizes and order sizes of the production orders, three different algorithms have been proposed. 1. Processing times algorithm This algorithm balances the assignment of the machines according to the processing times of production orders. T A = round M f, f, O > 0 s T Since the processing times are not integer values, proposed algorithm consider round value of the equation result. This fact can caused unequality between sum of the machines assigned to the production orders and total number of machines at stage s. or the purpose of equalization between sum of the machines assigned to the production orders and total number of machines, following sub-algorithms are used. T If A < M then" A = A + 1", s f, max A = (2) (1) ig. 3 Production schedule in Time = N If A > M then" A A 1" s =, f, A = max (3) Number of machines assigned to the specific production order is increased for the production stream, where T / A is maximal or decreased, where A is minimal. The process of 147

4 equalization assignment ends when sum of the machines assigned to the production orders is equal to the total number of machines. 2. Batch size algorithm This algorithm balances the assignment of the machines according to the processing times and batch sizes of production orders. Bf T A = round M s f, f, O > 0 B f T B T f If A < M then" A = A + 1", s f, = max (5) A (4) ig. 4 Graphical representation of the simulation model in Witness Block diagram of the algorithms implementation is depicted in igure 5. If A > M then" A A 1" s =, f, A = max (6) 3. Production order size algorithm This algorithm balances the assignment of the machines according to the processing times, batch sizes and number of products from a specific product family that left to be processed on the stages. B T O f A = round M f, f, O > 0 s B T O f B T O f If A < M then" A = A + 1", f, = max (8) s A If A > M then" A = A 1", f, A = max (9) s 5. IMPLEMENTATION or the purpose of the scheduling algorithms verification, the proposed algorithms have been implemented to the simulation model of HMLV flow shop manufacturing system created in Witness 3.0 simulation software. Simulation model considers the random character of processing and setup times by ± 10 % deviations, which make the simulation results even more credible. Production schedules are calculated using the functions, automatically modified according to the current algorithm chosen by user. Graphical representation of the simulation model in Witness simulation software is depicted in igure 4 (example with 6 production stages). (7) ig. 5 Scheduling algorithm implementation 6. CASE STUDY In the example case study we have considered 10 production stages and 10 product families. Processing times of jobs from product families A-J at production stages 1-10 are shown in table 2, number of machines at each stage in table 3 and production orders are summarized in table 4. All input data were obtained from real manufacturing system. Table 2. Processing times O\S A B C D E G

5 H I J Sum of the machines assigned to the production orders is 28. Number of machines at stage 1 is 29. This unequality will be solved using equation (2) considering T f1 / A f1 values shown in Table 6. Product family Table 3. Number of machines S M Table 4. Production orders Time of arrival Order size Product family Time of arrival Order size A B B H C G D J E D A E J G I H C I A B Table 6. T / A T 11 /A 11 T 21 /A 21 T 31 /A 31 T 41 /A 41 T 51 /A 51 T 61 /A 61 2,6 3,3 3,1 3 3,1 3,1 Number of machines assigned to the product family B is increased by 1. inal assignment of the machines at stage 1 to the production orders (families) in TIME = 0: Table 7. inal machine assignments (Stage 1) A 11 A 21 A 31 A 41 A 51 A inal assignment of the machines at all stages to the production orders (families) in TIME = 0: Table 8. inal machine assignments O\S A In the following example we have used Processing times algorithm and input data as shown in Tables 1,2 and 3. Assignment of the machines at stage 1 to the production orders (families) in TIME = 0: Using equation (1) for product family A: T 11 A = round M 11 1 T f 1 A 11 = round 10,5 85,1.29 A = 4 11 Analogically for all of the product families where. Table 5. Machine assignments (Stage 1) A 11 A 21 A 31 A 41 A 51 A B C D E G H I J Simulation experiments have been run using five different production scheduling approaches (1-5): 1 - Processing times algorithm 2 - Batch size algorithm 3 - Production order size algorithm 4 - Basic schedule Basic schedule 2 Basic schedules assign free machines to the first available job in the buffer. Job sequencing in buffers is random, when Basic schedules are used. 149

6 our different sets of fifty simulation experiments have been run. Average values of the total processing times (makespan) for 5 different scheduling approaches in four different experiment sets are summarized in igure 6. where the proposed scheduling algorithms were compared with basic solutions, has been presented. ig. 6 Total processing time (makespan) ACKNOWLEDGMENTS This work was supported by the Scientific Grant Agency of the Ministry of Education of the Slovak Republic Grant No. 1/1241/12. REERENCES Bley, H.; ranke, C.; Ostermann, A., Methods and Tools for the Building of Huge Simulation Models, Proceedings of the 2nd CIRP International Seminar on Intelligent Computation in Manufacturing Engineering (ICME 2000),, rom the results in igure 6 it is obvious that average values of the production makespan obtained using production schedules calculated by the proposed algorithms were better than values obtained using basic schedules in all cases. All the results obtained using proposed algorithms are very similar but production schedule calculated by Production order size algorithm ensured the best value of the production makespan in all of the experiments. Processing times of the production orders and batch sizes were identical in all experiments. or that reason all the saving of production makespan was caused only by reduction of setup requirements. Comparison of the setup requirements in four experiments sets is shown in igure 7. Guan, Z., Wang, Ch., Huang, j., Wan, L., Shao, X., Optimization of manufacturing systems using genetic search and multi-resolution simulation, 8th IEEE International Conference on Control and Automation, pp , Mahoney, R.M.: High-Mix Low-Volume manufacturing. Hewlett-Packard Company, Neoh, S.C., Morad, N., Lim, Ch. P., Abdul-Aziz, Z.: Optimization of Product Mix Planning in High-Mix-Low- Volume Industries Using Genetic Algorithms, WSEAS Transactions on Systems, Issue 7, Volume 3, pp , Shen, W., Wang, L., Hao, Q.: Agent-Based Distributed Manufacturing Process Planning and Scheduling: A State of the Art Survey, IEEE Transactions on Systems, Man and Cybernetics, Vol. 36, No.4, Svancara, J., Kralova, Z.: Case study on simulation analysis of a multiple product manufacturing system. Proceedings of the 5 th IAC International Conference on Management and Control of Production on and Logistics, MCPL 2010, Coimbra, Portugal. Zulch, G., Johnson, U., ischer, J.: Hierarchical simulation of complex production systems by coupling of models, Int. J. Production Economics 77, ig. 7 Setup requirements 7. CONCLUSION The paper deals with the production scheduling optimization in High-Mix Low-Volume flow shop manufacturing systems. Three new heuristic production scheduling algorithms have been proposed and implemented in the simulation model of the HMLV manufacturing system created in Witness simulation software. All three algorithms balance the machines assignment to the production orders (families) according to the selected criterion. An example case study, 150

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