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5 Case Study and Discussions
5.1 Case study
To verify the above model and algorithm, a reconfigurable product line and its production process are taken for example, which can adapt to the part family of cylinder parts. The 3D drawing of cylinder head is shown in Fig. 6. Moreover, the main processes of parts are as follows. (1) Cylinder head top and some holes processing; (2) Cylinder head bottom and some holes processing; (3) Cylinder head slant-hole processing; (4) Cylinder head end and some holes processing; (5) Special precision hole semi-finished processing, bottom semi-finished processing (top position); (6) Spare parts processing; (7) Special hole finish processing; (8) Special hole processing (bottom position). Fig. 6. 3D drawing of cylinder head In accordance with the following rules to arrange processes: (1) Rough process first, fine process later; (2) Face process first, hole process later; (3) Base first. The OP graph is obtained from the production process, which is shown in Fig. 7. OP1 to OP8 in Fig. 7 correspond to the above eight processes, meanwhile the figure also represents the order and constraint relations between these processes.
Fig. 7. Operation precedence graph
During production, the different factors such as production cost, reconfiguration cost, cycle time and line balance are all considered in the developed model and algorithm. The reconfiguration cost for different configurations of RMT is shown in Table 1. For example, RMT has three configurations, each of which needs different reconfiguration cost. 1M
Table 1. Reconfigurable cost of different
configurations of RMTs ¥ RMT Configuration Unit cost
M1 M11 200
M12 300
M13 150
M2 M21 500
M22 600
M23 700
M3 M31 750
M32 700
M33 1 000
Table 4. Machining precision Configuration of RMT Operation
OP1 OP2 OP3 OP4 OP5 OP6 OP7 OP8
Mi1 High High High High High High High Low
Mi2 High High High High Low High High High
Mi3 Low Low Low High Low Low Low Low
The specific OP for different configuration has different production time and cost. Table 2 shows the production cost for OPs and their corresponding configurations. Table 3 shows the production time. Table 4 shows the different precision using different configurations of machine tools.
5.2 Results discussion
The optimization process is shown in Fig. 8(a), and the optimization process for cost objective and nonmonetary objective are shown in Fig. 8(b) and Fig. 8(c), respectively. The weight and are both 0.5. The population size is 100, mutation rate is 0.05 and the volume is 5. The weighted sum approach is a straightforward implementation for multiple objectives, and the optimization process is computationally efficient, which is very fast, and ended within 20 s. It is shown that the product process plan and configuration of RMT are concurrently optimized. The optimization process for only cost objective is shown in Fig. 9 and for only nonmonetary objective is shown in Fig. 10. Because the contradiction between different objectives of optimization, it is difficult to achieve optimal at the same time. The configuration schemes for the stations and the distribution plan for operations which are from the optimal chromosome are shown in the following Fig. 11. Fig. 8. Optimization process Fig. 9. Optimization process for cost single-objective Fig 1w2w
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